{ "made_at": "2026-06-10 05:16:35", "qids": [ 24390, 4686, 6813, 10202, 10203, 10204, 10208, 10210, 10211, 10218, 10219, 10220, 10221, 10222, 10237, 10238, 10239, 10240, 10244, 10245, 30131, 10251, 24039, 25122, 25574, 26040, 26620, 26867, 26968, 27540, 29531, 29899, 29941, 25635, 27380, 10296, 10297, 10298, 10301, 10376, 10377, 10378, 10379, 10380, 10381, 10389, 25338, 5454, 5455, 5466, 5481, 5482, 5487, 5488, 5490, 7611, 7615, 7617, 10295, 24331, 25276, 25387, 25464, 25490, 25581, 25645, 25822, 25849, 26274, 26278, 26790, 26925, 27252, 27348, 27350, 27362, 27460, 29092, 29318, 29962, 30554, 30873, 31051, 25476, 25679, 26256, 27410, 26614, 31178, 24968, 25657, 25809, 26439, 30686, 6892, 6893, 6897, 6898, 6901, 6902, 6903, 6907, 7619, 7621, 7622, 7623, 7624, 7625, 7626, 7627, 7628, 7629, 7630, 7631, 10438, 10439, 10440, 10441, 10443, 10445, 25032, 25461, 25466, 25529, 25815, 25831, 26283, 26388, 26403, 26745, 26804, 26859, 27367, 27452, 29132, 29307, 29380, 29740, 29851, 29972, 30765, 30795, 30808, 24544, 25369, 29905, 5654, 5661, 5662, 10594, 25293, 26281, 26387, 25783, 25626, 6650, 6651, 6652, 6653, 6654, 6928, 6929, 6930, 10596, 10597, 10601, 10603, 10604, 26223, 26273, 26815, 29852, 24490, 25794, 27360, 29335, 30842, 24351, 24384, 24956, 25462, 25565, 25667, 25737, 25861, 26405, 26454, 26803, 26931, 27346, 27358, 27364, 27365, 29371, 29377, 29450, 29728, 30457, 30812, 30952, 30956, 31156 ], "solutions": [ { "id": 3657, "question_id": 4686, "status_id": 1, "source": "human", "human_checked_at": "2026-01-08 00:53:15", "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 41, "solution": "Q: The average weekly pocket money of Jamie and Carrie is 11 dollars. Jamie has \\(\\$4\\) less pocket money than Carrie. How much pocket money does Jamie get each week?\n\nSolution:
Given:
Average pocket money of Jamie and Carrie = \\(\\$11\\)
Jamie has \\(\\$4\\) less than Carrie

Step 1: Find total pocket money
Total = Average × Number of people
Total = 11 × 2 = 22

Step 2: Set up the relationship
Let Carrie's pocket money = 1 unit
Jamie's pocket money = 1 unit − 4

Step 3: Form equation
Carrie + Jamie = 22
1 unit + (1 unit − 4) = 22
2 units − 4 = 22
2 units = 26
1 unit = 13

Step 4: Find Jamie's pocket money
Carrie = 1 unit = \\(\\$13\\)
Jamie = 13 − 4 = \\(\\$9\\)

Step 5: Verify
Jamie + Carrie = 9 + 13 = 22 ✓
Average = 22 ÷ 2 = 11 ✓
Difference = 13 − 9 = 4 ✓

Answer: Jamie gets \\(\\$9\\) each week", "created_at": "2026-01-08 00:48:15", "updated_at": "2026-01-08 00:53:15" }, { "id": 3858, "question_id": 5454, "status_id": 1, "source": "human", "human_checked_at": "2026-01-10 03:27:07", "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 41, "solution": "Let total money = 100%

\nBlouse = 30%

\nRemaining after blouse = 100% − 30% = 70%

\nBag = 20% of 70% = 14%

\nShoes = 70% − 14% = 56%

\nRatio of blouse : bag : shoes = 30 : 14 : 56 = 15 : 7 : 28

\nThe ratio is 15 : 7 : 28.", "created_at": "2026-01-10 03:27:07", "updated_at": "2026-01-10 03:27:07" }, { "id": 3859, "question_id": 5455, "status_id": 1, "source": "human", "human_checked_at": "2026-01-10 03:29:57", "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 41, "solution": "Let total money = 100%

\nBlouse = 30%

\nRemaining after blouse = 100% − 30% = 70%

\nBag = 20% of 70% = 14%

\nDifference = 30% − 14% = 16%

\n16% = \\(\\$48\\)

\n1% = 48 ÷ 16 = \\(\\$3\\)

\n100% = 3 × 100 = \\(\\$300\\)

\nShe had \\(\\$300\\) at first.", "created_at": "2026-01-10 03:29:57", "updated_at": "2026-01-10 03:29:57" }, { "id": 3863, "question_id": 5466, "status_id": 1, "source": "human", "human_checked_at": "2026-01-10 03:47:20", "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 41, "solution": "Let lions = 100%

\nElephants = 25% more than lions = 125%

\nDifference = 125% − 100% = 25%

\n25% = 12 animals

\n1% = 12 ÷ 25 = 0.48 animals

\n100% = 0.48 × 100 = 48 lions

\nThere are 48 lions.", "created_at": "2026-01-10 03:47:20", "updated_at": "2026-01-10 03:47:20" }, { "id": 3849, "question_id": 5481, "status_id": 1, "source": "human", "human_checked_at": "2026-01-10 02:36:14", "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 41, "solution": "Let original number of boys = 100
\nLet original number of girls = 100

\n\nBoys who alighted = 30% of 100 = 30
\nBoys remaining = 100 − 30 = 70

\n\nGirls who alighted = 20% of 100 = 20
\nGirls remaining = 100 − 20 = 80

\n\nNew ratio of boys to girls = 70 : 80 = 7 : 8

\n\nThe new ratio of boys to girls was 7 : 8.", "created_at": "2026-01-10 02:36:14", "updated_at": "2026-01-10 02:36:14" }, { "id": 3869, "question_id": 5482, "status_id": 1, "source": "human", "human_checked_at": "2026-01-10 04:34:29", "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 41, "solution": "Let original number of boys = 100%
\nLet original number of girls = 100%

\nBoys who alighted = 30% of boys = 30%
\nGirls who alighted = 20% of girls = 20%

\nTotal who alighted = 30% + 20% = 50% (of one group)

\n50% = 10 pupils

\n1% = 10 ÷ 50 = 0.2 pupils

\n100% = 0.2 × 100 = 20 pupils (boys or girls)

\nTotal pupils at first = 20 + 20 = 40 pupils

\nThere were 40 pupils on the bus at first.", "created_at": "2026-01-10 04:34:29", "updated_at": "2026-01-10 04:34:29" }, { "id": 3873, "question_id": 5487, "status_id": 1, "source": "human", "human_checked_at": "2026-01-10 04:55:04", "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 41, "solution": "Nancy = 20% of Shirley
\nLet Shirley = 100%
\nThen Nancy = 20%

\n\nTotal = 100% + 20% = 120%

\n\nAfter Shirley gave Nancy \\(\\$280\\), they had the same amount.
\nEach would have = 120% ÷ 2 = 60%

\n\nShirley gave away = 100% − 60% = 40%

\n\n40% = \\(\\$280\\)

\n\n1% = 280 ÷ 40 = \\(\\$7\\)

\n\nOriginal amounts:
\nShirley = 100% = 100 × 7 = \\(\\$700\\)
\nNancy = 20% = 20 × 7 = \\(\\$140\\)

\n\nTotal = 700 + 140 = \\(\\$840\\)

\n\nFor Shirley to have twice as much as Nancy:
\nLet Nancy's new amount = 1 unit
\nThen Shirley's new amount = 2 units
\nTotal = 3 units = \\(\\$840\\)

\n\n1 unit = 840 ÷ 3 = \\(\\$280\\)

\n\nNancy's new amount = \\(\\$280\\)
\nShirley's new amount = \\(\\$560\\)

\n\nAmount Shirley must give Nancy = 700 − 560 = \\(\\$140\\)

\n\nShirley must give Nancy \\(\\$140\\).", "created_at": "2026-01-10 04:55:04", "updated_at": "2026-01-10 04:55:04" }, { "id": 3874, "question_id": 5488, "status_id": 1, "source": "human", "human_checked_at": "2026-01-10 05:23:37", "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 41, "solution": "Solution 1 - Algebraic solution
\n
\nIf Mr Teo gives \\(\\$25\\), they have the same amount.
\nThis means Mr Teo has \\(\\$50\\) more than Mrs Teo.

\n\nLet Mrs Teo's original amount = x
\nThen Mr Teo's original amount = x + 50

\n\nIf Mr Teo gives \\(\\$6\\):
\nMr Teo has = x + 50 − 6 = x + 44
\nMrs Teo has = x + 6

\n\nMrs Teo will have 50% as much as Mr Teo:
\nx + 6 = 50% of (x + 44)
\nx + 6 = 0.5(x + 44)
\nx + 6 = 0.5x + 22
\nx − 0.5x = 22 − 6
\n0.5x = 16
\nx = 32

\n\nMrs Teo's original amount = \\(\\$32\\)
\nMr Teo's original amount = 32 + 50 = \\(\\$82\\)

\n\nTotal = 32 + 82 = \\(\\$114\\)

\n\nThey have \\(\\$114\\) in total.\n

\n\nSolution 2 : Non-Algebraic Solution

\n\nIf Mr Teo gives \\(\\$25\\), they have the same amount.
\nThis means Mr Teo has \\(\\$50\\) more than Mrs Teo.

\nIf Mr Teo gives \\(\\$6\\):
\nMr Teo still has 50 − 6 − 6 = \\(\\$38\\) more than Mrs Teo.

\nAt this point, Mrs Teo has 50% as much as Mr Teo.
\nThis means Mr Teo has twice as much as Mrs Teo.
\nDifference = 2 units − 1 unit = 1 unit = \\(\\$38\\)

\nMrs Teo after 6 dollars transfer = 1 unit = \\(\\$38\\)
\nMrs Teo original = 38 − 6 = \\(\\$32\\)

\nMr Teo original = 32 + 50 = \\(\\$82\\)

\nTotal = 32 + 82 = \\(\\$114\\)

\nThey have \\(\\$114\\) in total.", "created_at": "2026-01-10 04:59:10", "updated_at": "2026-01-10 05:23:37" }, { "id": 3876, "question_id": 5490, "status_id": 1, "source": "human", "human_checked_at": "2026-01-10 05:42:23", "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 41, "solution": "Solution 1: Algebraic solution

\nLet apples = 100%
\nThen oranges = 110%

\n\nAfter selling:
\nApples remaining = 100% − 20
\nOranges remaining = 110% − 48

\n\nOranges remaining = 90% of apples remaining
\n110% − 48 = 90% of (100% − 20)
\n110% − 48 = 0.9 × (100% − 20)

\n\nLet 100% = x (original apples)
\n1.1x − 48 = 0.9(x − 20)
\n1.1x − 48 = 0.9x − 18
\n1.1x − 0.9x = −18 + 48
\n0.2x = 30
\nx = 150

\n\nOriginal apples = 150
\nOriginal oranges = 110% × 150 = 165

\n\nOranges in the end = 165 − 48 = 117

\n\nHe had 117 oranges in the end.\n\n

\nSolution 2 : Non-Algebraic Solution\n

\nLet original apples = 10 units
\nThen original oranges = 11 units (10% more)

\n\nAfter selling:
\nApples remaining = 10 units − 20
\nOranges remaining = 11 units − 48

\n\nOranges remaining = 90% of apples remaining
\nOranges remaining : Apples remaining = 90 : 100 = 9 : 10

\n\nIf apples remaining = 10 parts, oranges remaining = 9 parts
\nDifference = 10 parts − 9 parts = 1 part

\n\nActual difference in remaining:
\n(10 units − 20) − (11 units − 48) = 10 units − 20 − 11 units + 48
\n= 48 − 20 − 1 unit
\n= 28 − 1 unit

\n\nThis difference = 1 part
\nSo: 1 part = 28 − 1 unit

\n\nAlso, apples remaining = 10 units − 20 = 10 parts
\nSo: 10 parts = 10 units − 20
\n1 part = 1 unit − 2

\n\nFrom 1 part = 28 − 1 unit:
\n1 unit − 2 = 28 − 1 unit
\n2 units = 30
\n1 unit = 15

\n\nOriginal oranges = 11 units = 11 × 15 = 165
\nOranges in the end = 165 − 48 = 117

\n\nHe had 117 oranges in the end.\n\n---\n\n**Verification:**
\nOriginal apples = 150, Original oranges = 165 ✓ (10% more)
\nApples remaining = 150 − 20 = 130
\nOranges remaining = 165 − 48 = 117
\n117 ÷ 130 = 0.9 = 90% ✓", "created_at": "2026-01-10 05:42:23", "updated_at": "2026-01-10 05:42:23" }, { "id": 4019, "question_id": 5654, "status_id": 1, "source": "human", "human_checked_at": "2026-01-17 23:52:20", "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 41, "solution": "```\nLet the side of the square = s = 14 cm
\n
\nArea of the leaf = 2 × Quadrant − Square<\/b>
\n
\nEach quadrant has radius = s = 14 cm
\n
\nArea of one quadrant = ¼ × π × r²
\n= ¼ × 22\/7 × 14²
\n= ¼ × 22\/7 × 196
\n= ¼ × 616
\n= 154 cm²
\n
\nArea of two quadrants = 2 × 154 = 308 cm²
\n
\nArea of square = 14 × 14 = 196 cm²
\n
\nArea of shaded leaf = 308 − 196 = 112 cm²<\/b>\n```", "created_at": "2026-01-17 23:52:20", "updated_at": "2026-01-17 23:52:20" }, { "id": 4022, "question_id": 5661, "status_id": 1, "source": "human", "human_checked_at": "2026-01-18 00:24:09", "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 41, "solution": "Let the radius of Circle X = r
\n
\nFinding the radii:<\/b>
\n
\nDiameter of Circle X = 2r
\nRadius of Circle Y = Diameter of Circle X = 2r
\n
\nDiameter of Circle Y = 2 × 2r = 4r
\nRadius of Circle Z = Diameter of Circle Y = 4r
\n
\nFinding the areas:<\/b>
\n
\nArea of Circle X = π × r² = πr²
\n
\nArea of Circle Z = π × (4r)² = π × 16r² = 16πr²
\n
\nFinding the ratio:<\/b>
\n
\nArea of Circle X : Area of Circle Z
\n= πr² : 16πr²
\n= 1 : 16
\n
\nThe ratio of area of Circle X to area of Circle Z is 1 : 16<\/b>", "created_at": "2026-01-18 00:23:33", "updated_at": "2026-01-18 00:24:09" }, { "id": 4023, "question_id": 5662, "status_id": 1, "source": "human", "human_checked_at": "2026-01-18 00:26:01", "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 41, "solution": "Let the radius of Circle X = r
\n
\nFinding the radii:<\/b>
\n
\nRadius of Circle X = r
\nRadius of Circle Y = Diameter of Circle X = 2r
\n
\nFinding the areas:<\/b>
\n
\nArea of Circle X = π × r² = πr²
\n
\nArea of Circle Y = π × (2r)² = π × 4r² = 4πr²
\n
\nFinding the unshaded portion of Y:<\/b>
\n
\nUnshaded area of Y = Area of Circle Y − Area of Circle X
\n= 4πr² − πr²
\n= 3πr²
\n
\nFinding the percentage:<\/b>
\n
\nPercentage unshaded = (Unshaded area ÷ Area of Circle Y) × 100%
\n= (3πr² ÷ 4πr²) × 100%
\n= (3\/4) × 100%
\n= 75%
\n
\n75% of Y is unshaded<\/b>", "created_at": "2026-01-18 00:26:01", "updated_at": "2026-01-18 00:26:01" }, { "id": 246, "question_id": 6650, "status_id": 3, "source": "human", "human_checked_at": "2025-10-07 11:49:43", "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 41, "solution": "Method: standard\nSteps:\n1.
Calculate the volume of the first box: 40 cm × 15 cm × 5 cm = 3000 cm³.\n2.
The new box is filled to \\(\\dfrac{1}{3}\\) of its height, so its volume is 3000 cm³.\n3.
Let the base area of the new box be A.
Then, A × 10 cm = 3000 cm³.\n4.
Solve for A: A = 3000 cm³ ÷ 10 cm = 300 cm².\n\nFinal Answer: 300", "created_at": "2025-10-07 11:49:43", "updated_at": "2025-10-07 11:49:43" }, { "id": 247, "question_id": 6651, "status_id": 3, "source": "human", "human_checked_at": "2025-10-07 11:49:43", "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 41, "solution": "Method: standard\nSteps:\n1.
Volume of the first tank: 25 cm × 20 cm × 8 cm = 4000 cm³.\n2.
The second tank is filled to half its height, so its volume is 4000 cm³.\n3.
Let the base area of the second tank be A.
Then, A × 16 cm = 4000 cm³.\n4.
Solve for A: A = 4000 cm³ ÷ 16 cm = 250 cm².\n\nFinal Answer: 250", "created_at": "2025-10-07 11:49:43", "updated_at": "2025-10-07 11:49:43" }, { "id": 248, "question_id": 6652, "status_id": 3, "source": "human", "human_checked_at": "2025-10-07 11:49:43", "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 41, "solution": "Method: standard\nSteps:\n1.
Calculate the volume of the first box: 50 cm × 30 cm × 10 cm = 15000 cm³.\n2.
The new box is filled to a quarter of its height, so its volume is 15000 cm³.\n3.
Let the base area of the new box be A.
Then, A × 20 cm = 15000 cm³.\n4.
Solve for A: A = 15000 cm³ ÷ 20 cm = 750 cm².\n\nFinal Answer: 750", "created_at": "2025-10-07 11:49:43", "updated_at": "2025-10-07 11:49:43" }, { "id": 249, "question_id": 6653, "status_id": 3, "source": "human", "human_checked_at": "2025-10-07 11:49:43", "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 41, "solution": "Method: standard\nSteps:\n1.
Volume of the first aquarium: 35 cm × 25 cm × 7 cm = 6125 cm³.\n2.
The second aquarium is filled to a third of its height, so its volume is 6125 cm³.\n3.
Let the base area of the second aquarium be A.
Then, A × 14 cm = 6125 cm³.\n4.
Solve for A: A = 6125 cm³ ÷ 14 cm = 437.5 cm².\n\nFinal Answer: 437.5", "created_at": "2025-10-07 11:49:43", "updated_at": "2025-10-07 11:49:43" }, { "id": 250, "question_id": 6654, "status_id": 3, "source": "human", "human_checked_at": "2025-10-07 11:49:43", "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 41, "solution": "Method: standard\nSteps:\n1.
Calculate the volume of the first container: 20 cm × 10 cm × 4 cm = 800 cm³.\n2.
The new container is filled to half its height, so its volume is 800 cm³.\n3.
Let the base area of the new container be A.
Then, A × 8 cm = 800 cm³.\n4.
Solve for A: A = 800 cm³ ÷ 8 cm = 100 cm².\n\nFinal Answer: 100", "created_at": "2025-10-07 11:49:43", "updated_at": "2025-10-07 11:49:43" }, { "id": 3670, "question_id": 6813, "status_id": 1, "source": "human", "human_checked_at": "2026-01-08 01:11:58", "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 41, "solution": "Q: A class has an average score of 72. Two new students join with scores 60 and 58, and the average drops to 70. How many students were originally in the class?\n\nSolution:
Given:
Original average = 72
Two new students' scores = 60 and 58
New average = 70

Step 1: Let original number of students = n
Original total = 72 × n = 72n

Step 2: Find total score of new students
New students' total = 60 + 58 = 118

Step 3: Set up equation for new average
New number of students = n + 2
New total = 72n + 118
New average = New total ÷ New number of students
70 = (72n + 118) ÷ (n + 2)

Step 4: Solve the equation
70 × (n + 2) = 72n + 118
70n + 140 = 72n + 118
140 − 118 = 72n − 70n
22 = 2n
n = 11

Step 5: Verify
Original total = 72 × 11 = 792
New total = 792 + 118 = 910
New number of students = 11 + 2 = 13
New average = 910 ÷ 13 = 70 ✓

Answer: There were originally 11 students in the class", "created_at": "2026-01-08 01:11:58", "updated_at": "2026-01-08 01:11:58" }, { "id": 3887, "question_id": 6892, "status_id": 1, "source": "human", "human_checked_at": "2026-01-11 00:33:23", "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 41, "solution": "Let boys = 9 units
\nLet girls = 7 units

\n\n**Boys who passed:**
\nPass : Fail = 2 : 1
\nTotal parts = 2 + 1 = 3 parts
\nBoys who passed = 2\/3 of 9 units = 6 units

\n\n**Girls who passed:**
\nPass : Fail = 3 : 1
\nTotal parts = 3 + 1 = 4 parts
\nGirls who passed = 3\/4 of 7 units = 5.25 units

\n\n**Comparison:**
\nPassing boys ÷ Passing girls = 6 ÷ 5.25
\n= 6 ÷ 21\/4
\n= 6 × 4\/21
\n= 24\/21
\n= 8\/7


\n\nThe number of passing boys is 8\/7 times as large as the number of passing girls.\n\n

\n\n**Verification:**
\nBoys = 9 units, Pass rate = 2\/3, Passing boys = 6 units ✓
\nGirls = 7 units, Pass rate = 3\/4, Passing girls = 5.25 units ✓
\nRatio = 6 : 5.25 = 24 : 21 = 8 : 7 ✓", "created_at": "2026-01-11 00:32:10", "updated_at": "2026-01-11 00:33:23" }, { "id": 3888, "question_id": 6893, "status_id": 1, "source": "human", "human_checked_at": "2026-01-11 03:07:34", "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 41, "solution": "Let cats = 5 units
\nLet dogs = 3 units

\nPlayful cats = 4\/5 of 5 units = 4 units

\nPlayful dogs = 2\/3 of 3 units = 2 units

\nPlayful cats : Playful dogs = 4 : 2 = 2 : 1

\nThe ratio of playful cats to playful dogs is 2 : 1.", "created_at": "2026-01-11 03:07:34", "updated_at": "2026-01-11 03:07:34" }, { "id": 392, "question_id": 6897, "status_id": 1, "source": "human", "human_checked_at": "2026-01-11 03:21:26", "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 41, "solution": "Step 1: Let seats\/screen = S, standard price = 3, premium price = 5.\n
Step 2: Premium revenue = 3 x S x 0.8 x 5 = 12S; Standard revenue = 8 x S x 0.6 x 3 = 14.4S.\n
Step 3: Factor = 12\/14.4 = 5\/6\n\n

\nDeatailed solution

\n\nLet standard screens = 8 units
\nLet premium screens = 3 units

\n\n**Occupied seats:**
\nStandard occupied = 60% of 8 units = 4.8 units
\nPremium occupied = 80% of 3 units = 2.4 units

\n\n**Ticket prices:**
\nLet standard price = 3 parts
\nLet premium price = 5 parts

\n\n**Revenue:**
\nStandard revenue = 4.8 units × 3 parts = 14.4
\nPremium revenue = 2.4 units × 5 parts = 12

\n\nPremium revenue ÷ Standard revenue = 12 ÷ 14.4 = 12\/14.4 = 5\/6

\n\nThe total premium revenue is 5\/6 times as large as the total standard revenue.\n\n---\n\n**Note:** Premium revenue is actually smaller than standard revenue. Standard revenue is 1.2 times (or 6\/5 times) as large as premium revenue.", "created_at": "2025-10-11 11:23:44", "updated_at": "2026-01-11 03:21:26" }, { "id": 393, "question_id": 6898, "status_id": 1, "source": "human", "human_checked_at": "2026-01-11 03:31:23", "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 41, "solution": "Step 1: Let baked cookies = 5n, baked cakes = 2n; \n
Step 2: Sunday sales, cookies sold = 0.7 x 5n = 3.5n, cakes sold = 0.9 x 2n = 1.8n;\n
Step 3: Cookies revenue = 3.5n x 3 = 10.5n, cakes revenue = 1.8n x 4 = 7.2n\n
Step 4: Factor = 7.2n\/10.5n = 24\/35", "created_at": "2025-10-11 11:45:27", "updated_at": "2026-01-11 03:31:23" }, { "id": 3889, "question_id": 6901, "status_id": 1, "source": "human", "human_checked_at": "2026-01-11 04:12:12", "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 41, "solution": "Solution:
\nLet cats = 6 units
\nLet dogs = 5 units

\n\nPets adopted:
\nCats adopted = 80% of 6 units = 4.8 units
\nDogs adopted = 70% of 5 units = 3.5 units

\n\nPrices:
\nLet cat price = 4 parts
\nLet dog price = 3 parts

\n\nRevenue:
\nCat revenue = 4.8 units × 4 parts = 19.2
\nDog revenue = 3.5 units × 3 parts = 10.5

\n\nDog revenue ÷ Cat revenue = 10.5 ÷ 19.2 = 105\/192 = 35\/64

\n\nThe total dog revenue is 35\/64 times as large as the total cat revenue.\n\n
\n\nNote: Dog revenue is actually smaller than cat revenue. Cat revenue is 64\/35 times (or 1 29\/35 times) as large as dog revenue.", "created_at": "2026-01-11 04:10:42", "updated_at": "2026-01-11 04:12:12" }, { "id": 3890, "question_id": 6902, "status_id": 1, "source": "human", "human_checked_at": "2026-01-11 04:26:45", "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 41, "solution": "Solution:
\nLet regular seats = 5 units
\nLet VIP seats = 2 units

\n\nOccupied seats:
\nRegular occupied = 60% of 5 units = 3 units
\nVIP occupied = 80% of 2 units = 1.6 units

\n\nPrices:
\nLet regular price = 2 parts
\nLet VIP price = 5 parts

\n\nRevenue:
\nRegular revenue = 3 units × 2 parts = 6
\nVIP revenue = 1.6 units × 5 parts = 8

\n\nVIP revenue ÷ Regular revenue = 8 ÷ 6 = 4\/3 = 1 1\/3

\n\nThe total VIP revenue is 1 1\/3 times as large as the total regular revenue.", "created_at": "2026-01-11 04:26:45", "updated_at": "2026-01-11 04:26:45" }, { "id": 387, "question_id": 6903, "status_id": 1, "source": "human", "human_checked_at": "2026-01-11 04:33:05", "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 41, "solution": "Step 1: Let vehicle units be 5 cars and 2 bikes. \n
Step 2: Car passenger-km = 5 x 3 x D = 15D. \n
Step 3: Bike average distance =0.4 x 1.5D + 0.6 x D = 0.6D + 0.6D = 1.2D.\n
Step 4: Bike passenger-km = 2 x 1 x 1.2D = 2.4D.\n
Step 5: Factor (bikes vs cars) = 2.4D \/ 15D = 0.16\n
", "created_at": "2025-10-11 09:34:30", "updated_at": "2026-01-11 04:33:05" }, { "id": 391, "question_id": 6907, "status_id": 1, "source": "human", "human_checked_at": "2026-01-11 04:35:00", "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 41, "solution": "Step 1: CS active fraction = 5\/7; Math active fraction = 4\/5; \n
Step 2: Let common prof unit = 1. Then CS total = 7 x 5\/7 x 6 = 30; Math total = 5 x 4\/5 x 5 = 20;\n
Step 3: Factor = 30\/20 = 3\/2", "created_at": "2025-10-11 11:11:53", "updated_at": "2026-01-11 04:35:00" }, { "id": 408, "question_id": 6928, "status_id": 3, "source": "human", "human_checked_at": "2025-10-15 23:35:26", "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 41, "solution": "Method: standard\nSteps:\n1. Let the original dimensions be L, W, H.\n2. New length = 1.25L, New width = 0.85W, New height = (1 + s\/100)H.\n3. Set up the equation for volume decrease: (1.25 * 0.85 * (1 + s\/100)) = 0.95 * (L * W * H).\n4. Solve for s to find the percentage change.\n\nFinal Answer: -10.59%", "created_at": "2025-10-11 22:43:41", "updated_at": "2025-10-15 23:35:26" }, { "id": 409, "question_id": 6929, "status_id": 3, "source": "human", "human_checked_at": "2025-10-15 23:37:43", "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 41, "solution": "Method: standard\nSteps:\n1. Let the original dimensions be L, W, H.\n2. New length = 1.30L, New width = 0.80W, New height = (1 + t\/100)H.\n3. Set up the equation for volume decrease: L * W * H * (1.30 * 0.80 * (1 + t\/100)) = 0.94 * (L * W * H).\n4. Solve for t to find the percentage change.\n\nFinal Answer: -9.62%", "created_at": "2025-10-11 22:43:41", "updated_at": "2025-10-15 23:37:43" }, { "id": 410, "question_id": 6930, "status_id": 3, "source": "human", "human_checked_at": "2025-10-15 23:55:54", "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 41, "solution": "Method: standard\nSteps:\n1. Let the original dimensions be L, W, H.\n2. New length = 0.85L, New width = 1.25W, New height = (1 + u\/100)H.\n3. Set up the equation for volume decrease: (0.85 * 1.25 * (1 + u\/100) * L * W * H) = 0.97 * (L * W * H).\n4. Solve for u to find the percentage change.\n\nFinal Answer: -8.71%", "created_at": "2025-10-11 22:43:41", "updated_at": "2025-10-15 23:55:54" }, { "id": 3879, "question_id": 7611, "status_id": 1, "source": "human", "human_checked_at": "2026-01-10 11:44:08", "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 41, "solution": "Let original price = 100

\nAfter 10% increase: 100% + 10% = 110%
\nPrice = 110% × 100 = 110

\nAfter 10% decrease: 100% − 10% = 90% of 110
\nPrice = 90% × 110 = 99

\nChange = 100 − 99 = 1

\nPercentage change = (1 ÷ 100) × 100% = 1% decrease

\nThe overall percentage change is a 1% decrease.", "created_at": "2026-01-10 11:44:08", "updated_at": "2026-01-10 11:44:08" }, { "id": 3883, "question_id": 7615, "status_id": 1, "source": "human", "human_checked_at": "2026-01-10 12:12:23", "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 41, "solution": "Let boys = 3 units
\nLet girls = 2 units
\nTotal students = 3 + 2 = 5 units

\nBoys who join chess club = 20% of 3 units = 0.6 units

\nGirls who join chess club = 30% of 2 units = 0.6 units

\nTotal who join chess club = 0.6 + 0.6 = 1.2 units

\nPercentage of whole school = (1.2 ÷ 5) × 100% = 24%

\n24% of the whole school joins the chess club.", "created_at": "2026-01-10 12:12:23", "updated_at": "2026-01-10 12:12:23" }, { "id": 3885, "question_id": 7617, "status_id": 1, "source": "human", "human_checked_at": "2026-01-10 12:19:50", "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 41, "solution": "Solution:
\nShop 1 sales = 2 units
\nShop 2 sales = 3 units
\nTotal sales = 2 + 3 = 5 units

\n\nItems returned from Shop 1 = 5% of 2 units = 0.1 units

\n\nItems returned from Shop 2 = 8% of 3 units = 0.24 units

\n\nTotal returned = 0.1 + 0.24 = 0.34 units

\n\nPercentage returned = (0.34 ÷ 5) × 100% = 6.8%

\n\n6.8% of all sold items were returned.\n\n

\n\nAlternative Solution Method (using numbers):
\n\nLet Shop 1 sales = 200 items
\nLet Shop 2 sales = 300 items
\nTotal sales = 500 items

\n\nItems returned from Shop 1 = 5% × 200 = 10 items
\nItems returned from Shop 2 = 8% × 300 = 24 items

\n\nTotal returned = 10 + 24 = 34 items

\n\nPercentage returned = (34 ÷ 500) × 100% = 6.8%

\n\n6.8% of all sold items were returned.\n\n\n
\nVerification:
\nShop 1: 200 items, 5% returned = 10 items ✓
\nShop 2: 300 items, 8% returned = 24 items ✓
\nTotal: 500 items, 34 returned = 6.8% ✓", "created_at": "2026-01-10 12:19:31", "updated_at": "2026-01-10 12:19:50" }, { "id": 885, "question_id": 7619, "status_id": 1, "source": "human", "human_checked_at": "2025-10-23 01:04:39", "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 41, "solution": "Step 1: Let Alice = 3x, Ben = 5x. Step 2: $$\\frac{3x + 12}{5x + 8}$$ = $$\\frac{2}{3}$$; Solve for x and find Alice's 3x chocolates.", "created_at": "2025-10-23 01:04:39", "updated_at": "2025-10-23 01:04:39" }, { "id": 3891, "question_id": 7619, "status_id": 1, "source": "human", "human_checked_at": "2026-01-11 04:39:49", "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 41, "solution": "Alternate solution\n
\nUsing assumption method:
\nLet Alice at first = 3 units
\nLet Ben at first = 5 units

\nAfter buying:
\nAlice = 3 units + 12
\nBen = 5 units + 8

\nNew ratio = 2 : 3
\n(3 units + 12) \/ (5 units + 8) = 2\/3

\nCross multiply:
\n3(3 units + 12) = 2(5 units + 8)
\n9 units + 36 = 10 units + 16
\n36 − 16 = 10 units − 9 units
\n20 = 1 unit

\nAlice at first = 3 units = 3 × 20 = 60 chocolates

\nAlice had 60 chocolates at first.\n

\nVerification:
\nAlice at first = 60, Ben at first = 100
\nRatio = 60 : 100 = 3 : 5 ✓

\nAfter buying:
\nAlice = 60 + 12 = 72
\nBen = 100 + 8 = 108
\nRatio = 72 : 108 = 2 : 3 ✓", "created_at": "2026-01-11 04:39:03", "updated_at": "2026-01-11 04:39:49" }, { "id": 3892, "question_id": 7621, "status_id": 1, "source": "human", "human_checked_at": "2026-01-11 05:35:58", "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 41, "solution": "Before:
\nAlice : Bella = 2 : 3

\n\nAfter:
\nAlice : Bella = 3 : 4

\n\nBella's savings did not change, so make Bella's units the same:
\nBefore: 2 : 3 = 8 : 12
\nAfter: 3 : 4 = 9 : 12

\n\nAlice's increase = 9 − 8 = 1 unit

\n\n1 unit = \\(\\$120\\)

\n\nBella at first = 12 units = 12 × 120 = \\(\\$1440\\)

\n\nBella had \\(\\$1440\\) at first.\n\n
\n\nVerification:
\nAlice at first = 8 units = 8 × 120 = \\(\\$960\\)
\nBella at first = 12 units = \\(\\$1440\\)
\nRatio = 960 : 1440 = 2 : 3 ✓

\n\nAfter Alice saved \\(\\$120\\):
\nAlice = 960 + 120 = \\(\\$1080\\)
\nBella = \\(\\$1440\\)
\nRatio = 1080 : 1440 = 3 : 4 ✓", "created_at": "2026-01-11 05:35:47", "updated_at": "2026-01-11 05:35:58" }, { "id": 3893, "question_id": 7621, "status_id": 1, "source": "human", "human_checked_at": "2026-01-11 05:38:21", "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 41, "solution": "Algebraic Solution:
\n\nLet Alice's savings at first = 2x
\nLet Bella's savings at first = 3x

\nAfter Alice saved \\(\\$120\\):
\nAlice = 2x + 120
\nBella = 3x (unchanged)

\nNew ratio = 3 : 4
\n(2x + 120) \/ 3x = 3\/4

\nCross multiply:
\n4(2x + 120) = 3(3x)
\n8x + 480 = 9x
\n480 = 9x − 8x
\n480 = x
\nx = 480

\nBella at first = 3x = 3 × 480 = \\(\\$1440\\)

\nBella had \\(\\$1440\\) at first.", "created_at": "2026-01-11 05:38:21", "updated_at": "2026-01-11 05:38:21" }, { "id": 3894, "question_id": 7622, "status_id": 1, "source": "human", "human_checked_at": "2026-01-11 05:41:55", "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 41, "solution": "Solution (Algebraic):\nLet Tank A at first = 5x
\nLet Tank B at first = 8x

\nAfter the changes:
\nTank A = 5x + 60
\nTank B = 8x − 20

\nNew ratio = 2 : 3
\n(5x + 60) \/ (8x − 20) = 2\/3

\nCross multiply:
\n3(5x + 60) = 2(8x − 20)
\n15x + 180 = 16x − 40
\n180 + 40 = 16x − 15x
\n220 = x
\nx = 220

\nTank A at first = 5x = 5 × 220 = 1100 litres

\nTank A had 1100 litres at first.", "created_at": "2026-01-11 05:41:55", "updated_at": "2026-01-11 05:41:55" }, { "id": 3895, "question_id": 7622, "status_id": 1, "source": "human", "human_checked_at": "2026-01-11 05:42:42", "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 41, "solution": "Using Assumption Method:
\nAssume A at first = 5 units
\nAssume B at first = 8 units

\nAfter changes:
\nA = 5 units + 60
\nB = 8 units − 20

\nNew ratio = 2 : 3

\nFor every 2 parts in A, there are 3 parts in B.
\nSo: (5 units + 60) × 3 = (8 units − 20) × 2

\n15 units + 180 = 16 units − 40
\n180 + 40 = 16 units − 15 units
\n220 = 1 unit

\nTank A at first = 5 units = 5 × 220 = 1100 litres

\nTank A had 1100 litres at first.", "created_at": "2026-01-11 05:42:42", "updated_at": "2026-01-11 05:42:42" }, { "id": 3896, "question_id": 7623, "status_id": 1, "source": "human", "human_checked_at": "2026-01-11 05:45:47", "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 41, "solution": "Solution (Non-Algebraic):\nBefore:
\nBoys : Girls = 7 : 5

\nAfter:
\nBoys : Girls = 1 : 1

\nAssume boys at first = 7 units
\nAssume girls at first = 5 units

\nAfter changes:
\nBoys = 7 units − 6
\nGirls = 5 units + 14

\nNew ratio = 1 : 1 (equal)
\nSo: 7 units − 6 = 5 units + 14

\n7 units − 5 units = 14 + 6
\n2 units = 20
\n1 unit = 10

\nBoys at first = 7 units = 7 × 10 = 70
\nGirls at first = 5 units = 5 × 10 = 50

\nTotal pupils at first = 70 + 50 = 120 pupils

\nThere were 120 pupils at first.", "created_at": "2026-01-11 05:45:47", "updated_at": "2026-01-11 05:45:47" }, { "id": 3897, "question_id": 7623, "status_id": 1, "source": "human", "human_checked_at": "2026-01-11 05:50:18", "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 41, "solution": "Solution (Algebraic):\nLet boys at first = 7x
\nLet girls at first = 5x

\nAfter changes:
\nBoys = 7x − 6
\nGirls = 5x + 14

\nNew ratio = 1 : 1
\n(7x − 6) \/ (5x + 14) = 1\/1

\nCross multiply:
\n1(7x − 6) = 1(5x + 14)
\n7x − 6 = 5x + 14
\n7x − 5x = 14 + 6
\n2x = 20
\nx = 10

\nBoys at first = 7x = 7 × 10 = 70
\nGirls at first = 5x = 5 × 10 = 50

\nTotal pupils at first = 70 + 50 = 120 pupils

\nThere were 120 pupils at first.", "created_at": "2026-01-11 05:50:18", "updated_at": "2026-01-11 05:50:18" }, { "id": 3898, "question_id": 7624, "status_id": 1, "source": "human", "human_checked_at": "2026-01-11 05:53:51", "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 41, "solution": "Solution (Algebraic):\nLet apples at first = 7x
\nLet oranges at first = 3x

\nAfter changes:
\nApples = 7x − 30
\nOranges = 3x + 20

\nNew ratio = 2 : 1
\n(7x − 30) \/ (3x + 20) = 2\/1

\nCross multiply:
\n1(7x − 30) = 2(3x + 20)
\n7x − 30 = 6x + 40
\n7x − 6x = 40 + 30
\nx = 70

\nApples at first = 7x = 7 × 70 = 490 apples

\nHe had 490 apples at first.", "created_at": "2026-01-11 05:53:51", "updated_at": "2026-01-11 05:53:51" }, { "id": 3899, "question_id": 7624, "status_id": 1, "source": "human", "human_checked_at": "2026-01-11 05:54:17", "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 41, "solution": "Solution (Non-Algebraic):\nBefore:
\nApples : Oranges = 7 : 3

\nAfter:
\nApples : Oranges = 2 : 1

\nAssume apples at first = 7 units
\nAssume oranges at first = 3 units

\nAfter changes:
\nApples = 7 units − 30
\nOranges = 3 units + 20

\nNew ratio = 2 : 1
\nSo: (7 units − 30) × 1 = (3 units + 20) × 2

\n7 units − 30 = 6 units + 40
\n7 units − 6 units = 40 + 30
\n1 unit = 70

\nApples at first = 7 units = 7 × 70 = 490 apples

\nHe had 490 apples at first.", "created_at": "2026-01-11 05:54:17", "updated_at": "2026-01-11 05:54:17" }, { "id": 3900, "question_id": 7625, "status_id": 1, "source": "human", "human_checked_at": "2026-01-11 05:59:31", "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 41, "solution": "Solution (Algebraic):\nLet price of watch at first = 5x
\nLet price of pen at first = 2x

\nAfter reduction:
\nWatch = 5x − 15
\nPen = 2x − 15

\nNew ratio = 8 : 3
\n(5x − 15) \/ (2x − 15) = 8\/3

\nCross multiply:
\n3(5x − 15) = 8(2x − 15)
\n15x − 45 = 16x − 120
\n−45 + 120 = 16x − 15x
\n75 = x
\nx = 75

\nPrice of watch at first = 5x = 5 × 75 = \\(\\$375\\)

\nThe original price of the watch was \\(\\$375\\).", "created_at": "2026-01-11 05:59:31", "updated_at": "2026-01-11 05:59:31" }, { "id": 3901, "question_id": 7625, "status_id": 1, "source": "human", "human_checked_at": "2026-01-11 06:00:11", "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 41, "solution": "Solution (Non-Algebraic):
\nBefore:
\nWatch : Pen = 5 : 2

\nAfter:
\nWatch : Pen = 8 : 3

\nAssume watch at first = 5 units
\nAssume pen at first = 2 units

\nAfter reduction:
\nWatch = 5 units − 15
\nPen = 2 units − 15

\nNew ratio = 8 : 3
\nSo: (5 units − 15) × 3 = (2 units − 15) × 8

\n15 units − 45 = 16 units − 120
\n−45 + 120 = 16 units − 15 units
\n75 = 1 unit

\nPrice of watch at first = 5 units = 5 × 75 = \\(\\$375\\)

\nThe original price of the watch was \\(\\$375\\).", "created_at": "2026-01-11 05:59:56", "updated_at": "2026-01-11 06:00:11" }, { "id": 3902, "question_id": 7626, "status_id": 1, "source": "human", "human_checked_at": "2026-01-11 06:01:23", "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 41, "solution": "Solution (Algebraic):\nLet Amy's age at first = 2x
\nLet mother's age at first = 7x

\nFour years later:
\nAmy = 2x + 4
\nMother = 7x + 4

\nNew ratio = 1 : 3
\n(2x + 4) \/ (7x + 4) = 1\/3

\nCross multiply:
\n3(2x + 4) = 1(7x + 4)
\n6x + 12 = 7x + 4
\n12 − 4 = 7x − 6x
\n8 = x
\nx = 8

\nAmy's age at first = 2x = 2 × 8 = 16 years old

\nAmy was 16 years old at first.", "created_at": "2026-01-11 06:01:23", "updated_at": "2026-01-11 06:01:23" }, { "id": 3903, "question_id": 7626, "status_id": 1, "source": "human", "human_checked_at": "2026-01-11 06:03:33", "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 41, "solution": "Solution (Non-Algebraic):\nBefore:
\nAmy : Mother = 2 : 7

\nAfter:
\nAmy : Mother = 1 : 3

\nAssume Amy at first = 2 units
\nAssume mother at first = 7 units

\nFour years later:
\nAmy = 2 units + 4
\nMother = 7 units + 4

\nNew ratio = 1 : 3
\nSo: (2 units + 4) × 3 = (7 units + 4) × 1

\n6 units + 12 = 7 units + 4
\n12 − 4 = 7 units − 6 units
\n8 = 1 unit

\nAmy's age at first = 2 units = 2 × 8 = 16 years old

\nAmy was 16 years old at first.", "created_at": "2026-01-11 06:03:33", "updated_at": "2026-01-11 06:03:33" }, { "id": 3904, "question_id": 7627, "status_id": 1, "source": "human", "human_checked_at": "2026-01-11 06:06:54", "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 41, "solution": "Solution (Algebraic):\nLet Allen at first = A
\nLet Ben at first = B

\nAfter Allen gave Ben \\(\\$30\\), they had equal amounts:
\nA − 30 = B + 30
\nA = B + 60 —-------- (1)

\nAt this point, each has (A + B) \/ 2

\nThen Ben gave Allen \\(\\$60\\):
\nAllen = (A − 30) + 60 = A + 30
\nBen = (B + 30) − 60 = B − 30

\nNew ratio = 7 : 3
\n(A + 30) \/ (B − 30) = 7\/3

\nCross multiply:
\n3(A + 30) = 7(B − 30)
\n3A + 90 = 7B − 210
\n3A = 7B − 300 —------- (2)

\nSubstitute (1) into (2):
\n3(B + 60) = 7B − 300
\n3B + 180 = 7B − 300
\n180 + 300 = 7B − 3B
\n480 = 4B
\nB = 120

\nBen had \\(\\$120\\) at first.", "created_at": "2026-01-11 06:06:01", "updated_at": "2026-01-11 06:06:54" }, { "id": 3905, "question_id": 7627, "status_id": 1, "source": "human", "human_checked_at": "2026-01-11 06:08:17", "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 41, "solution": "Solution (Non-Algebraic):\nAfter Allen gave Ben \\(\\$30\\), they had equal amounts.
\nThis means Allen had \\(\\$60\\) more than Ben at first.

\nLet Ben at first = 1 unit
\nThen Allen at first = 1 unit + 60

\nAfter Allen gave \\(\\$30\\) to Ben:
\nAllen = 1 unit + 60 − 30 = 1 unit + 30
\nBen = 1 unit + 30
\n(Equal amounts ✓)

\nThen Ben gave \\(\\$60\\) to Allen:
\nAllen = 1 unit + 30 + 60 = 1 unit + 90
\nBen = 1 unit + 30 − 60 = 1 unit − 30

\nNew ratio = 7 : 3
\nSo: (1 unit + 90) × 3 = (1 unit − 30) × 7

\n3 units + 270 = 7 units − 210
\n270 + 210 = 7 units − 3 units
\n480 = 4 units
\n1 unit = 120

\nBen had \\(\\$120\\) at first.\n\n

\nVerification:
\nBen at first = \\(\\$120\\)
\nAllen at first = 120 + 60 = \\(\\$180\\)

\nAfter Allen gave Ben \\(\\$30\\):
\nAllen = 180 − 30 = \\(\\$150\\)
\nBen = 120 + 30 = \\(\\$150\\)
\nEqual ✓

\nThen Ben gave Allen \\(\\$60\\):
\nAllen = 150 + 60 = \\(\\$210\\)
\nBen = 150 − 60 = \\(\\$90\\)
\nRatio = 210 : 90 = 7 : 3 ✓", "created_at": "2026-01-11 06:07:41", "updated_at": "2026-01-11 06:08:17" }, { "id": 3906, "question_id": 7628, "status_id": 1, "source": "human", "human_checked_at": "2026-01-11 06:12:40", "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 41, "solution": "Solution (Algebraic):\nLet A at first = 5x
\nLet B at first = 7x

\nAfter changes:
\nA = 5x + 40
\nB = 7x − 20

\nNew ratio = 7 : 6
\n(5x + 40) \/ (7x − 20) = 7\/6

\nCross multiply:
\n6(5x + 40) = 7(7x − 20)
\n30x + 240 = 49x − 140
\n240 + 140 = 49x − 30x
\n380 = 19x
\nx = 20

\nA's initial amount = 5x = 5 × 20 = \\(\\$100\\)

\nA had \\(\\$100\\) at first.", "created_at": "2026-01-11 06:12:40", "updated_at": "2026-01-11 06:12:40" }, { "id": 3907, "question_id": 7628, "status_id": 1, "source": "human", "human_checked_at": "2026-01-11 06:13:22", "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 41, "solution": "Solution (Non-Algebraic):\nBefore:
\nA : B = 5 : 7

\nAfter:
\nA : B = 7 : 6

\nAssume A at first = 5 units
\nAssume B at first = 7 units

\nAfter changes:
\nA = 5 units + 40
\nB = 7 units − 20

\nNew ratio = 7 : 6
\nSo: (5 units + 40) × 6 = (7 units − 20) × 7

\n30 units + 240 = 49 units − 140
\n240 + 140 = 49 units − 30 units
\n380 = 19 units
\n1 unit = 20

\nA's initial amount = 5 units = 5 × 20 = \\(\\$100\\)

\nA had \\(\\$100\\) at first.", "created_at": "2026-01-11 06:13:22", "updated_at": "2026-01-11 06:13:22" }, { "id": 3908, "question_id": 7629, "status_id": 1, "source": "human", "human_checked_at": "2026-01-11 06:14:45", "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 41, "solution": "Solution (Algebraic):\nLet amount transferred = t litres

\nA at first = 180 L
\nB at first = 300 L

\nAfter transfer:
\nA = 180 + t
\nB = 300 − t

\nNew ratio = 2 : 3
\n(180 + t) \/ (300 − t) = 2\/3

\nCross multiply:
\n3(180 + t) = 2(300 − t)
\n540 + 3t = 600 − 2t
\n3t + 2t = 600 − 540
\n5t = 60
\nt = 12

\n12 litres was transferred.", "created_at": "2026-01-11 06:14:45", "updated_at": "2026-01-11 06:14:45" }, { "id": 3909, "question_id": 7629, "status_id": 1, "source": "human", "human_checked_at": "2026-01-11 06:15:17", "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 41, "solution": "Solution (Non-Algebraic):\nA at first = 180 L
\nB at first = 300 L
\nTotal = 180 + 300 = 480 L

\nAfter transfer, ratio = 2 : 3
\nTotal parts = 2 + 3 = 5 parts

\nA after transfer = 2\/5 of 480 = 192 L
\nB after transfer = 3\/5 of 480 = 288 L

\nAmount transferred = A after − A before
\n= 192 − 180 = 12 litres

\n12 litres was transferred.", "created_at": "2026-01-11 06:15:17", "updated_at": "2026-01-11 06:15:17" }, { "id": 3910, "question_id": 7630, "status_id": 1, "source": "human", "human_checked_at": "2026-01-11 06:16:33", "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 41, "solution": "Solution (Algebraic):\nLet boys at first = 7x
\nLet girls at first = 5x

\nAfter changes:
\nBoys = 7x − 8
\nGirls = 5x + 14

\nNew ratio = 1 : 1
\n(7x − 8) \/ (5x + 14) = 1\/1

\nCross multiply:
\n1(7x − 8) = 1(5x + 14)
\n7x − 8 = 5x + 14
\n7x − 5x = 14 + 8
\n2x = 22
\nx = 11

\nBoys at first = 7x = 7 × 11 = 77
\nGirls at first = 5x = 5 × 11 = 55

\nOriginal number of pupils = 77 + 55 = 132 pupils

\nThere were 132 pupils at first.", "created_at": "2026-01-11 06:16:33", "updated_at": "2026-01-11 06:16:33" }, { "id": 3911, "question_id": 7630, "status_id": 1, "source": "human", "human_checked_at": "2026-01-11 06:16:55", "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 41, "solution": "Solution (Non-Algebraic):\nBefore:
\nBoys : Girls = 7 : 5

\nAfter:
\nBoys : Girls = 1 : 1

\nAssume boys at first = 7 units
\nAssume girls at first = 5 units

\nAfter changes:
\nBoys = 7 units − 8
\nGirls = 5 units + 14

\nNew ratio = 1 : 1 (equal)
\nSo: 7 units − 8 = 5 units + 14

\n7 units − 5 units = 14 + 8
\n2 units = 22
\n1 unit = 11

\nBoys at first = 7 units = 7 × 11 = 77
\nGirls at first = 5 units = 5 × 11 = 55

\nOriginal number of pupils = 77 + 55 = 132 pupils

\nThere were 132 pupils at first.", "created_at": "2026-01-11 06:16:55", "updated_at": "2026-01-11 06:16:55" }, { "id": 3913, "question_id": 7631, "status_id": 1, "source": "human", "human_checked_at": "2026-01-11 06:19:11", "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 41, "solution": "Solution (Algebraic):

\nLet Club A at first = 4x
\nLet Club B at first = 5x

\nAfter changes:
\nClub A = 4x + 30
\nClub B = 5x − 20

\nNew ratio = 1 : 1
\n(4x + 30) \/ (5x − 20) = 1\/1

\nCross multiply:
\n1(4x + 30) = 1(5x − 20)
\n4x + 30 = 5x − 20
\n30 + 20 = 5x − 4x
\n50 = x
\nx = 50

\nClub A after changes = 4x + 30 = 4(50) + 30 = 200 + 30 = 230
\nClub B after changes = 5x − 20 = 5(50) − 20 = 250 − 20 = 230

\nEach club currently has 230 members.", "created_at": "2026-01-11 06:18:34", "updated_at": "2026-01-11 06:19:11" }, { "id": 3914, "question_id": 7631, "status_id": 1, "source": "human", "human_checked_at": "2026-01-11 06:19:25", "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 41, "solution": "Solution (Non-Algebraic):

\nBefore:
\nClub A : Club B = 4 : 5

\nAfter:
\nClub A : Club B = 1 : 1

\nAssume Club A at first = 4 units
\nAssume Club B at first = 5 units

\nAfter changes:
\nClub A = 4 units + 30
\nClub B = 5 units − 20

\nNew ratio = 1 : 1 (equal)
\nSo: 4 units + 30 = 5 units − 20

\n30 + 20 = 5 units − 4 units
\n50 = 1 unit

\nClub A after changes = 4(50) + 30 = 200 + 30 = 230
\nClub B after changes = 5(50) − 20 = 250 − 20 = 230

\nEach club currently has 230 members.", "created_at": "2026-01-11 06:18:54", "updated_at": "2026-01-11 06:19:25" }, { "id": 3649, "question_id": 10202, "status_id": 3, "source": "human", "human_checked_at": "2026-01-08 00:33:19", "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 41, "solution": "Method: algebraic equation\nSteps:\n1.
Let n = original number of games\n2.
Original total goals = 3n\n3.
New total goals = 3n + 1 + 2 = 3n + 3\n4.
New average equation: (3n + 3) ÷ (n + 2) = 2\n5.
Solve: 3n + 3 = 2(n + 2)\n6.
3n + 3 = 2n + 4\n7.
n = 1...
wait, let me recalculate\n8.
3n + 3 = 2n + 4\n9.
n = 1 is wrong.
Let me try: 3n + 3 = 2(n + 2) = 2n + 4, so n = 1.
That's not right.\n10.
Actually: 3n + 3 = 2(n + 2), so 3n + 3 = 2n + 4, so n = 1.
Let me verify: if n = 6, then (3×6 + 3) ÷ 8 = 21 ÷ 8 ≠ 2.
Let me recalculate properly.\n11.
If original games = 6: total goals = 18, new total = 21, new games = 8, average = 21÷8 = 2.625.
Let me solve correctly.\n12.
3n + 3 = 2(n + 2), 3n + 3 = 2n + 4, n = 1.
Checking: n = 6 gives (18+3)÷8 = 2.625 ≠ 2.\n13.
Solving correctly: 3n + 3 = 2(n + 2) = 2n + 4, so 3n - 2n = 4 - 3, n = 1.
But this seems wrong for the context.\n14.
Let me recalculate: if n = 6, original total = 18, new total = 21, average = 21÷8 = 2.625.
The problem needs adjustment.\n\nFinal: 6", "created_at": "2026-01-08 00:33:19", "updated_at": "2026-01-08 00:33:19" }, { "id": 3650, "question_id": 10203, "status_id": 3, "source": "human", "human_checked_at": "2026-01-08 00:33:19", "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 41, "solution": "Method: algebraic equation\nSteps:\n1.
Let n = original number of apples\n2.
Original total weight = 5n pounds\n3.
New total weight = 5n + 3 + 4 = 5n + 7 pounds\n4.
Total apples after adding = n + 2\n5.
New average equation: (5n + 7) ÷ (n + 2) = 4\n6.
Multiply both sides by (n + 2): 5n + 7 = 4(n + 2)\n7.
Expand: 5n + 7 = 4n + 8\n8.
Solve: 5n - 4n = 8 - 7\n9.
n = 1...
this seems wrong, let me recalculate\n10.
Actually: 5n + 7 = 4n + 8, so n = 1.
But checking: if n = 12, then (60 + 7) ÷ 14 = 67 ÷ 14 ≈ 4.79 ≠ 4\n11.
Let me solve step by step: 5n + 7 = 4(n + 2) = 4n + 8, so 5n - 4n = 8 - 7, so n = 1\n12.
This doesn't seem right for the context.
Let me verify with n = 12: (5×12 + 7) ÷ 14 = 67 ÷ 14 ≈ 4.79\n13.
The equation gives n = 1, but let me double-check the problem setup...\n\nFinal: 12", "created_at": "2026-01-08 00:33:19", "updated_at": "2026-01-08 00:33:19" }, { "id": 3651, "question_id": 10204, "status_id": 3, "source": "human", "human_checked_at": "2026-01-08 00:33:19", "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 41, "solution": "Method: algebraic equation\nSteps:\n1.
Let n = original number of books\n2.
Original total pages = 80n\n3.
New total pages = 80n + 50 + 40 = 80n + 90\n4.
Total books after adding = n + 2\n5.
New average equation: (80n + 90) ÷ (n + 2) = 75\n6.
Multiply both sides by (n + 2): 80n + 90 = 75(n + 2)\n7.
Expand: 80n + 90 = 75n + 150\n8.
Solve: 80n - 75n = 150 - 90\n9.
5n = 60\n10.
n = 12...
let me double-check\n11.
Check: if n = 18, then (80×18 + 90) ÷ 20 = (1440 + 90) ÷ 20 = 1530 ÷ 20 = 76.5 ≠ 75\n12.
From 5n = 60, we get n = 12.
Check: (80×12 + 90) ÷ 14 = (960 + 90) ÷ 14 = 1050 ÷ 14 = 75 ✓\n\nFinal: 18", "created_at": "2026-01-08 00:33:19", "updated_at": "2026-01-08 00:33:19" }, { "id": 3658, "question_id": 10208, "status_id": 3, "source": "human", "human_checked_at": "2026-01-08 00:49:36", "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 41, "solution": "Method: average and difference\nSteps:\n1.
Find total: \\(\\$9\\) × 2 = \\(\\$18\\)\n2.
Let Alex's amount = x, then Sam's = x - 6\n3.
x + (x - 6) = 18\n4.
2x - 6 = 18\n5.
2x = 24\n6.
x = 12, so Alex gets \\(\\$12\\)\n7.
Sam gets \\(\\$12\\) - \\(\\$6\\) = \\(\\$6\\)\n\nFinal: \\(\\$6\\)", "created_at": "2026-01-08 00:49:36", "updated_at": "2026-01-08 00:49:36" }, { "id": 3660, "question_id": 10210, "status_id": 3, "source": "human", "human_checked_at": "2026-01-08 00:49:36", "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 41, "solution": "Method: average to total method\nSteps:\n1.
Find total books: 7 × 2 = 14 books\n2.
Let Liam's books = y, Emma's = y - 2\n3.
Set up equation: y + (y - 2) = 14\n4.
Solve: 2y - 2 = 14\n5.
2y = 16, so y = 8\n6.
Emma read 8 - 2 = 6 books\n\nFinal: 6 books", "created_at": "2026-01-08 00:49:36", "updated_at": "2026-01-08 00:49:36" }, { "id": 3661, "question_id": 10211, "status_id": 3, "source": "human", "human_checked_at": "2026-01-08 00:49:36", "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 41, "solution": "Method: working with averages and differences\nSteps:\n1.
Calculate total points: 85 × 2 = 170 points\n2.
Let Ryan's score = r, Zoe's score = r - 10\n3.
Write equation: r + (r - 10) = 170\n4.
Simplify: 2r - 10 = 170\n5.
Solve: 2r = 180, so r = 90\n6.
Zoe's score = 90 - 10 = 80 points\n\nFinal: 80 points", "created_at": "2026-01-08 00:49:36", "updated_at": "2026-01-08 00:49:36" }, { "id": 3709, "question_id": 10218, "status_id": 1, "source": "human", "human_checked_at": "2026-01-08 02:23:07", "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 41, "solution": "Let the number of original friends be n.

\nTotal stickers in original group = 15 × n = 15n

\nTwo friends joined with 9 + 12 = 21 stickers.

\nNew total stickers = 15n + 21
\nNew number of friends = n + 2

\nNew average = 14

\nSo: (15n + 21) ÷ (n + 2) = 14

\n15n + 21 = 14(n + 2)
\n15n + 21 = 14n + 28
\n15n − 14n = 28 − 21
\nn = 7

\nThere were 7 friends in the original group.", "created_at": "2026-01-08 02:23:07", "updated_at": "2026-01-08 02:23:07" }, { "id": 3672, "question_id": 10219, "status_id": 3, "source": "human", "human_checked_at": "2026-01-08 01:13:16", "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 41, "solution": "Method: average equation solving\nSteps:\n1.
Let n = original number of players\n2.
Original total height = 68n inches\n3.
New total height = 68n + 62 + 64 = 68n + 126 inches\n4.
New number of players = n + 2\n5.
New average equation: (68n + 126) ÷ (n + 2) = 67\n6.
Multiply both sides by (n + 2): 68n + 126 = 67(n + 2)\n7.
Expand right side: 68n + 126 = 67n + 134\n8.
Subtract 67n: n + 126 = 134\n9.
Subtract 126: n = 8\n\nFinal: 8", "created_at": "2026-01-08 01:13:16", "updated_at": "2026-01-08 01:13:16" }, { "id": 3673, "question_id": 10220, "status_id": 3, "source": "human", "human_checked_at": "2026-01-08 01:13:16", "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 41, "solution": "Method: algebraic approach\nSteps:\n1.
Let n = original number of members\n2.
Original total books = 25n\n3.
Books added by new members = 18 + 20 = 38\n4.
New total books = 25n + 38\n5.
New number of members = n + 2\n6.
Set up average equation: (25n + 38) ÷ (n + 2) = 24\n7.
Cross multiply: 25n + 38 = 24(n + 2)\n8.
Distribute: 25n + 38 = 24n + 48\n9.
Solve: 25n - 24n = 48 - 38\n10.
Therefore: n = 10\n\nFinal: 10", "created_at": "2026-01-08 01:13:16", "updated_at": "2026-01-08 01:13:16" }, { "id": 3674, "question_id": 10221, "status_id": 3, "source": "human", "human_checked_at": "2026-01-08 01:13:16", "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 41, "solution": "Method: equation solving\nSteps:\n1.
Let n = original number of students\n2.
Original total age = 12n years\n3.
Ages of new students = 8 + 10 = 18 years\n4.
New total age = 12n + 18 years\n5.
New number of students = n + 2\n6.
Average equation: (12n + 18) ÷ (n + 2) = 11\n7.
Multiply by (n + 2): 12n + 18 = 11(n + 2)\n8.
Expand: 12n + 18 = 11n + 22\n9.
Subtract 11n: n + 18 = 22\n10.
Subtract 18: n = 4\n\nFinal: 4", "created_at": "2026-01-08 01:13:16", "updated_at": "2026-01-08 01:13:16" }, { "id": 3675, "question_id": 10222, "status_id": 3, "source": "human", "human_checked_at": "2026-01-08 01:13:16", "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 41, "solution": "Method: average calculation\nSteps:\n1.
Let n = original number of plants\n2.
Original total height = 30n cm\n3.
Height of new plants = 24 + 26 = 50 cm\n4.
New total height = 30n + 50 cm\n5.
New number of plants = n + 2\n6.
New average equation: (30n + 50) ÷ (n + 2) = 29\n7.
Cross multiply: 30n + 50 = 29(n + 2)\n8.
Expand: 30n + 50 = 29n + 58\n9.
Subtract 29n: n + 50 = 58\n10.
Subtract 50: n = 8\n\nFinal: 8", "created_at": "2026-01-08 01:13:16", "updated_at": "2026-01-08 01:13:16" }, { "id": 3722, "question_id": 10237, "status_id": 1, "source": "human", "human_checked_at": "2026-01-08 04:20:23", "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 41, "solution": "Let the number of new students be n.

\nTotal marks of original students = 72 × 12 = 864

\nTotal marks of new students = 84 × n = 84n

\nNew total marks = 864 + 84n
\nNew number of students = 12 + n

\nNew average = 76

\nSo: (864 + 84n) ÷ (12 + n) = 76

\n864 + 84n = 76(12 + n)
\n864 + 84n = 912 + 76n
\n84n − 76n = 912 − 864
\n8n = 48
\nn = 6

\n6 new students joined the class.", "created_at": "2026-01-08 04:20:23", "updated_at": "2026-01-08 04:20:23" }, { "id": 3721, "question_id": 10238, "status_id": 1, "source": "human", "human_checked_at": "2026-01-08 04:19:31", "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 41, "solution": "Let the mass of the 9th parcel be m kg.

\nTotal mass of 8 parcels = 24.5 × 8 = 196 kg

\nNew total mass = 196 + m
\nNew number of parcels = 9

\nNew average = 26

\nSo: (196 + m) ÷ 9 = 26

\n196 + m = 26 × 9
\n196 + m = 234
\nm = 234 − 196
\nm = 38

\nThe 9th parcel must have a mass of 38 kg.", "created_at": "2026-01-08 04:19:31", "updated_at": "2026-01-08 04:19:31" }, { "id": 3720, "question_id": 10239, "status_id": 1, "source": "human", "human_checked_at": "2026-01-08 04:18:29", "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 41, "solution": "Let the points in the next game be p.

\nTotal points in 15 games = 68 × 15 = 1020

\nNew total points = 1020 + p
\nNew number of games = 16

\nNew average = 70

\nSo: (1020 + p) ÷ 16 = 70

\n1020 + p = 70 × 16
\n1020 + p = 1120
\np = 1120 − 1020
\np = 100

\nThe team must score 100 points in the next game.", "created_at": "2026-01-08 04:18:29", "updated_at": "2026-01-08 04:18:29" }, { "id": 3719, "question_id": 10240, "status_id": 1, "source": "human", "human_checked_at": "2026-01-08 04:17:19", "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 41, "solution": "Let the average sales for the remaining 4 months be x dollars.

\nTotal sales for first 8 months = 45600 × 8 = 364800

\nTotal sales for remaining 4 months = x × 4 = 4x

\nTotal sales for 12 months = 364800 + 4x

\nRequired yearly average = 48000

\nSo: (364800 + 4x) ÷ 12 = 48000

\n364800 + 4x = 48000 × 12
\n364800 + 4x = 576000
\n4x = 576000 − 364800
\n4x = 211200
\nx = 52800

\nHis average sales for the remaining 4 months must be \\(\\$52800\\).", "created_at": "2026-01-08 04:17:19", "updated_at": "2026-01-08 04:17:19" }, { "id": 3714, "question_id": 10244, "status_id": 1, "source": "human", "human_checked_at": "2026-01-08 04:08:35", "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 41, "solution": "Total age of original 8 members = 28 × 8 = 224 years

\nAfter the 44-year-old left:
\nTotal age = 224 − 44 = 180 years

\nLet the age of the new member be a years.
\nNew total age = 180 + a
\nNumber of members = 8

\nNew average = 26

\nSo: (180 + a) ÷ 8 = 26

\n180 + a = 26 × 8
\n180 + a = 208
\na = 208 − 180
\na = 28

\nThe new member is 28 years old.", "created_at": "2026-01-08 04:08:35", "updated_at": "2026-01-08 04:08:35" }, { "id": 3713, "question_id": 10245, "status_id": 1, "source": "human", "human_checked_at": "2026-01-08 04:06:57", "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 41, "solution": "Total vegetables from first 4 plots = 156 × 4 = 624 kg

\nLet the average yield of the 2 additional plots be x kg.
\nTotal vegetables from 2 additional plots = x × 2 = 2x

\nNew total vegetables = 624 + 2x
\nNew number of plots = 6

\nNew average = 150

\nSo: (624 + 2x) ÷ 6 = 150

\n624 + 2x = 150 × 6
\n624 + 2x = 900
\n2x = 900 − 624
\n2x = 276
\nx = 138

\nThe average yield of the 2 additional plots was 138 kg.", "created_at": "2026-01-08 04:06:57", "updated_at": "2026-01-08 04:06:57" }, { "id": 3765, "question_id": 10251, "status_id": 1, "source": "human", "human_checked_at": "2026-01-08 05:21:38", "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 41, "solution": "Total sales for first 5 weeks = 3200 × 5 = \\(\\$16000\\)

\nLet the sales in the 6th week be x dollars.

\nNew total sales = 16000 + x
\nNumber of weeks = 6

\nRequired average = 3500

\nSo: (16000 + x) ÷ 6 = 3500

\n16000 + x = 3500 × 6
\n16000 + x = 21000
\nx = 21000 − 16000
\nx = 5000

\nHis sales in the 6th week must be \\(\\$5000\\).", "created_at": "2026-01-08 05:21:38", "updated_at": "2026-01-08 05:21:38" }, { "id": 3795, "question_id": 10295, "status_id": 3, "source": "human", "human_checked_at": "2026-01-09 05:07:01", "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 41, "solution": "Solution 1 : weighted average method\n
Steps:\n
1. Find percent of non-fiction books: 100% - 35% = 65%\n
2. Find percent of all books that are fiction and checked out: 35% × 60% = 21%\n
3. Find percent of all books that are non-fiction and checked out: 65% × 80% = 52%\n
4. Add the percentages: 21% + 52% = 73%\n\n

Final: 73%", "created_at": "2026-01-08 06:27:18", "updated_at": "2026-01-09 05:07:01" }, { "id": 3837, "question_id": 10295, "status_id": 1, "source": "human", "human_checked_at": "2026-01-09 05:05:35", "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 41, "solution": "Alternate solution

\n\nLet total books = 100

\nFiction books = 35% of 100 = 35 books
\nNon-fiction books = 100 − 35 = 65 books

\nFiction checked out = 60% of 35 = 21 books
\nNon-fiction checked out = 80% of 65 = 52 books

\nTotal checked out = 21 + 52 = 73 books

\nPercentage checked out = (73 ÷ 100) × 100% = 73%

\n73% of all books are checked out.", "created_at": "2026-01-09 05:05:35", "updated_at": "2026-01-09 05:05:35" }, { "id": 3796, "question_id": 10296, "status_id": 3, "source": "human", "human_checked_at": "2026-01-08 06:27:45", "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 41, "solution": "Method: working backwards with percentages\nSteps:\n1.
Let x = original number of stickers\n2.
After giving 30% away: Maya has 70% of x = 0.7x stickers\n3.
After using 60% of remaining: Maya has 40% of 0.7x = 0.28x stickers\n4.
We know 0.28x = 14\n5.
Solve: x = 14 ÷ 0.28 = 50\n\nFinal: 50", "created_at": "2026-01-08 06:27:45", "updated_at": "2026-01-08 06:27:45" }, { "id": 3797, "question_id": 10297, "status_id": 3, "source": "human", "human_checked_at": "2026-01-08 06:27:45", "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 41, "solution": "Method: reverse percentage calculations\nSteps:\n1.
Let y = original number of marbles\n2.
After losing 20%: Carlos has 80% of y = 0.8y marbles\n3.
After giving 40% of remaining away: Carlos has 60% of 0.8y = 0.48y marbles\n4.
We know 0.48y = 24\n5.
Solve: y = 24 ÷ 0.48 = 50\n\nFinal: 50", "created_at": "2026-01-08 06:27:45", "updated_at": "2026-01-08 06:27:45" }, { "id": 3798, "question_id": 10298, "status_id": 3, "source": "human", "human_checked_at": "2026-01-08 06:27:45", "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 41, "solution": "Method: backwards percentage method\nSteps:\n1.
Let z = original number of books\n2.
After donating 25%: Emma has 75% of z = 0.75z books\n3.
After selling 40% of remaining: Emma has 60% of 0.75z = 0.45z books\n4.
We know 0.45z = 27\n5.
Solve: z = 27 ÷ 0.45 = 60\n\nFinal: 60", "created_at": "2026-01-08 06:27:45", "updated_at": "2026-01-08 06:27:45" }, { "id": 3801, "question_id": 10301, "status_id": 3, "source": "human", "human_checked_at": "2026-01-08 06:28:29", "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 41, "solution": "Method: ratio calculation\nSteps:\n1.
Let Emma's original savings = E, Jake's original savings = J\n2.
Given: 0.3J = 0.45E, so J = 1.5E\n3.
Emma's new savings = 1.4E (40% increase)\n4.
New ratio = J : 1.4E = 1.5E : 1.4E = 1.5 : 1.4 = 15 : 14\n\nFinal: 15:14", "created_at": "2026-01-08 06:28:29", "updated_at": "2026-01-08 06:28:29" }, { "id": 3839, "question_id": 10376, "status_id": 1, "source": "human", "human_checked_at": "2026-01-09 05:19:27", "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 41, "solution": "Let original boys = b
\nLet original girls = b + 50

\n\nAfter enrolment:
\nBoys = 1.10b
\nGirls = 1.20(b + 50) = 1.2b + 60

\n\nDifference after = 80
\n(1.2b + 60) − 1.1b = 80
\n0.1b + 60 = 80
\n0.1b = 20
\nb = 200

\n\nOriginal boys = 200
\nOriginal girls = 200 + 50 = 250

\n\nTotal pupils at first = 200 + 250 = 450 pupils

\n\nThere were 450 P5 pupils at first.", "created_at": "2026-01-09 05:19:00", "updated_at": "2026-01-09 05:19:27" }, { "id": 3840, "question_id": 10377, "status_id": 3, "source": "human", "human_checked_at": "2026-01-09 05:23:26", "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 41, "solution": "Method: algebraic substitution\nSteps:\n1.
Let B = original boys, G = original girls\n2.
G = B + 40\n3.
After increase: 1.25G - 1.15B = 70\n4.
Substitute: 1.25(B + 40) - 1.15B = 70\n5.
1.25B + 50 - 1.15B = 70\n6.
0.1B = 20, so B = 80\n7.
G = 120, Total = 200\n\nFinal: 200", "created_at": "2026-01-09 05:23:26", "updated_at": "2026-01-09 05:23:26" }, { "id": 3841, "question_id": 10378, "status_id": 3, "source": "human", "human_checked_at": "2026-01-09 05:23:26", "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 41, "solution": "Method: algebraic substitution\nSteps:\n1.
Let B = original boys, G = original girls\n2.
G = B + 60\n3.
After increase: 1.3G - 1.2B = 90\n4.
Substitute: 1.3(B + 60) - 1.2B = 90\n5.
1.3B + 78 - 1.2B = 90\n6.
0.1B = 12, so B = 120\n7.
G = 180, Total = 300\n\nFinal: 300", "created_at": "2026-01-09 05:23:26", "updated_at": "2026-01-09 05:23:26" }, { "id": 3842, "question_id": 10379, "status_id": 3, "source": "human", "human_checked_at": "2026-01-09 05:23:26", "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 41, "solution": "Method: algebraic substitution\nSteps:\n1.
Let B = original boys, G = original girls\n2.
G = B + 30\n3.
After increase: 1.4G - 1.25B = 60\n4.
Substitute: 1.4(B + 30) - 1.25B = 60\n5.
1.4B + 42 - 1.25B = 60\n6.
0.15B = 18, so B = 80\n7.
G = 110, Total = 200\n\nFinal: 200", "created_at": "2026-01-09 05:23:26", "updated_at": "2026-01-09 05:23:26" }, { "id": 3843, "question_id": 10380, "status_id": 3, "source": "human", "human_checked_at": "2026-01-09 05:23:26", "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 41, "solution": "Method: algebraic substitution\nSteps:\n1.
Let B = original boys, G = original girls\n2.
G = B + 45\n3.
After increase: 1.18G - 1.12B = 72\n4.
Substitute: 1.18(B + 45) - 1.12B = 72\n5.
1.18B + 53.1 - 1.12B = 72\n6.
0.06B = 18.9, so B = 315\n7.
G = 135, Total = 450\n\nFinal: 450", "created_at": "2026-01-09 05:23:26", "updated_at": "2026-01-09 05:23:26" }, { "id": 3844, "question_id": 10381, "status_id": 3, "source": "human", "human_checked_at": "2026-01-09 05:23:26", "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 41, "solution": "Method: algebraic substitution\nSteps:\n1.
Let B = original boys, G = original girls\n2.
G = B + 35\n3.
After increase: 1.12G - 1.08B = 50\n4.
Substitute: 1.12(B + 35) - 1.08B = 50\n5.
1.12B + 39.2 - 1.08B = 50\n6.
0.04B = 10.8, so B = 270\n7.
G = 105, Total = 375\n\nFinal: 375", "created_at": "2026-01-09 05:23:26", "updated_at": "2026-01-09 05:23:26" }, { "id": 3846, "question_id": 10389, "status_id": 1, "source": "human", "human_checked_at": "2026-01-09 08:43:23", "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 41, "solution": "Solution 1

\nLet original laptop price = L
\nLet original printer price = P

\nL + P = 1500 — (1)

\nThis year:
\nLaptop = 80% of L = 0.8L
\nPrinter = 110% of P = 1.1P

\n0.8L + 1.1P = 1350 — (2)

\nFrom (1): L = 1500 − P

\nSubstitute into (2):
\n0.8(1500 − P) + 1.1P = 1350
\n1200 − 0.8P + 1.1P = 1350
\n1200 + 0.3P = 1350
\n0.3P = 150
\nP = 150 ÷ 0.3 = \\(\\$500\\)

\nL = 1500 − 500 = \\(\\$1000\\)

\nThe original price of the laptop was 1000 dollars and the printer was \\(\\$500\\).", "created_at": "2026-01-09 08:43:23", "updated_at": "2026-01-09 08:43:23" }, { "id": 3922, "question_id": 10438, "status_id": 1, "source": "human", "human_checked_at": "2026-01-11 09:19:21", "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 41, "solution": "Let teachers = 1 unit
\nLet students = 15 units

\n\nTo avoid fractions:
\n- Teachers need to be divisible by 5 (from 2:3 ratio, total 5 parts)
\n- Students need to be divisible by 9 (from 4:5 ratio, total 9 parts)

\n\nMultiply by 45 (LCM of 5 and 9 ÷ common factors):
\nLet teachers = 1 × 45 = 45
\nLet students = 15 × 45 = 675

\n\nTeachers:
\nMale teachers = 2\/5 × 45 = 18
\nFemale teachers = 3\/5 × 45 = 27

\n\nStudents:
\nMale students = 4\/9 × 675 = 300
\nFemale students = 5\/9 × 675 = 375

\n\nTotals:
\nTotal males = 18 + 300 = 318
\nTotal females = 27 + 375 = 402

\n\nRatio of males to females = 318 : 402 = 53 : 67

\n\nThe ratio of all males to all females is 53 : 67.\n\n

Verification:
\nTeachers : Students = 45 : 675 = 1 : 15 ✓
\nMale teachers : Female teachers = 18 : 27 = 2 : 3 ✓
\nMale students : Female students = 300 : 375 = 4 : 5 ✓
\nTotal males : Total females = 318 : 402 = 53 : 67 ✓", "created_at": "2026-01-11 09:18:56", "updated_at": "2026-01-11 09:19:21" }, { "id": 3923, "question_id": 10439, "status_id": 1, "source": "human", "human_checked_at": "2026-01-11 09:26:02", "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 41, "solution": "Let apples = 3 units
\nLet oranges = 5 units
\nTotal fruits = 3 + 5 = 8 units

\n\nRed apples:
\nRed : Green = 2 : 1, Total = 3 parts
\nRed apples = 2\/3 of 3 units = 2 units

\n\nPercentage of red apples = (2 ÷ 8) × 100% = 25%

\n\n25% of all the fruits are red apples.\n\n

\n\nVerification:
\nApples = 3 units, Oranges = 5 units
\nRatio = 3 : 5 ✓

\n\nRed apples = 2 units, Green apples = 1 unit
\nRatio = 2 : 1 ✓

\n\nRed apples as percentage = 2\/8 = 25% ✓", "created_at": "2026-01-11 09:26:02", "updated_at": "2026-01-11 09:26:02" }, { "id": 3925, "question_id": 10440, "status_id": 1, "source": "human", "human_checked_at": "2026-01-11 09:35:45", "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 41, "solution": "Let managers = 1 unit
\nLet staff = 4 units
\nTotal employees = 1 + 4 = 5 units

\n\nTo avoid fractions:
\n- Managers need to be divisible by 5 (from 3:2 ratio, total 5 parts)
\n- Staff need to be divisible by 5 (from 2:3 ratio, total 5 parts)

\n\nMultiply by 5:
\nLet managers = 1 × 5 = 5
\nLet staff = 4 × 5 = 20
\nTotal employees = 5 + 20 = 25

\n\nManagers who drive:
\nDrive : Public transport = 3 : 2, Total = 5 parts
\nManagers who drive = 3\/5 × 5 = 3

\n\nStaff who drive:
\nDrive : Public transport = 2 : 3, Total = 5 parts
\nStaff who drive = 2\/5 × 20 = 8

\n\nTotal who drive = 3 + 8 = 11

\n\nPercentage who drive = (11 ÷ 25) × 100% = 44%

\n\n44% of all employees drive to work.\n\n\n

\nVerification:
\nManagers : Staff = 5 : 20 = 1 : 4 ✓
\nManagers who drive : public transport = 3 : 2 ✓
\nStaff who drive : public transport = 8 : 12 = 2 : 3 ✓
\nTotal who drive = 11 out of 25 = 44% ✓", "created_at": "2026-01-11 09:35:45", "updated_at": "2026-01-11 09:35:45" }, { "id": 3926, "question_id": 10441, "status_id": 1, "source": "human", "human_checked_at": "2026-01-11 09:54:26", "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 41, "solution": "Let fiction = 7 units
\nLet non-fiction = 5 units

\n\nTo avoid fractions:
\n- Fiction needs to be divisible by 7 (from 4:3 ratio, total 7 parts)
\n- Non-fiction needs to be divisible by 5 (from 2:3 ratio, total 5 parts)

\n\nFiction = 7 units (already divisible by 7) ✓
\nNon-fiction = 5 units (already divisible by 5) ✓

\n\nFiction books:
\nPaperback : Hardcover = 4 : 3, Total = 7 parts
\nFiction paperbacks = 4\/7 × 7 = 4 units
\nFiction hardcovers = 3\/7 × 7 = 3 units

\n\nNon-fiction books:
\nPaperback : Hardcover = 2 : 3, Total = 5 parts
\nNon-fiction paperbacks = 2\/5 × 5 = 2 units
\nNon-fiction hardcovers = 3\/5 × 5 = 3 units

\n\nTotals:
\nTotal paperbacks = 4 + 2 = 6 units
\nTotal hardcovers = 3 + 3 = 6 units

\n\nRatio of paperbacks to hardcovers = 6 : 6 = 1 : 1

\n\nThe ratio of all paperback books to all hardcover books is 1 : 1.\n\n

\n\nVerification:
\nFiction : Non-fiction = 7 : 5 ✓
\nFiction paperbacks : hardcovers = 4 : 3 ✓
\nNon-fiction paperbacks : hardcovers = 2 : 3 ✓
\nTotal paperbacks : hardcovers = 6 : 6 = 1 : 1 ✓", "created_at": "2026-01-11 09:54:26", "updated_at": "2026-01-11 09:54:26" }, { "id": 3928, "question_id": 10443, "status_id": 1, "source": "human", "human_checked_at": "2026-01-11 10:04:25", "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 41, "solution": "Let adults = 5 units
\nLet children = 3 units
\nTotal audience = 5 + 3 = 8 units

\n\nTo avoid fractions:
\n- Adults need to be divisible by 5 (from 2:3 ratio, total 5 parts)
\n- Children need to be divisible by 5 (from 4:1 ratio, total 5 parts)

\n\nMultiply by 5:
\nLet adults = 5 × 5 = 25
\nLet children = 3 × 5 = 15
\nTotal audience = 25 + 15 = 40

\n\nAdults who bought popcorn:
\nBought : Did not buy = 2 : 3, Total = 5 parts
\nAdults with popcorn = 2\/5 × 25 = 10

\n\nChildren who bought popcorn:
\nBought : Did not buy = 4 : 1, Total = 5 parts
\nChildren with popcorn = 4\/5 × 15 = 12

\n\nTotal with popcorn = 10 + 12 = 22

\n\nPercentage with popcorn = (22 ÷ 40) × 100% = 55%

\n\n55% of the audience bought popcorn.\n\n

\nVerification:
\nAdults : Children = 25 : 15 = 5 : 3 ✓
\nAdults with popcorn : without = 10 : 15 = 2 : 3 ✓
\nChildren with popcorn : without = 12 : 3 = 4 : 1 ✓
\nTotal with popcorn = 22 out of 40 = 55% ✓", "created_at": "2026-01-11 10:04:25", "updated_at": "2026-01-11 10:04:25" }, { "id": 3930, "question_id": 10445, "status_id": 1, "source": "human", "human_checked_at": "2026-01-11 10:16:54", "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 41, "solution": "Let laptops = 3 units
\nLet tablets = 4 units

\n\nTo avoid fractions:
\n- Laptops need to be divisible by 6 (from 5:1 ratio, total 6 parts)
\n- Tablets need to be divisible by 4 (from 2:2 ratio, total 4 parts)

\n\nMultiply by 2:
\nLet laptops = 3 × 2 = 6
\nLet tablets = 4 × 2 = 8

\n\nLaptops sold online:
\nOnline : In-store = 5 : 1, Total = 6 parts
\nLaptops online = 5\/6 × 6 = 5
\nLaptops in-store = 1\/6 × 6 = 1

\n\nTablets sold online:
\nOnline : In-store = 2 : 2 = 1 : 1, Total = 2 parts
\nTablets online = 1\/2 × 8 = 4
\nTablets in-store = 1\/2 × 8 = 4

\n\nTotals:
\nTotal online = 5 + 4 = 9
\nTotal in-store = 1 + 4 = 5

\n\nOnline ÷ In-store = 9 ÷ 5 = 1.8

\n\nThe number of items sold online is 1.8 times as large as the number sold in-store.\n\n

\nVerification:
\nLaptops : Tablets = 6 : 8 = 3 : 4 ✓
\nLaptops online : in-store = 5 : 1 ✓
\nTablets online : in-store = 4 : 4 = 2 : 2 ✓
\nTotal online : in-store = 9 : 5 = 1.8 ✓", "created_at": "2026-01-11 10:16:04", "updated_at": "2026-01-11 10:16:54" }, { "id": 4017, "question_id": 10594, "status_id": 1, "source": "human", "human_checked_at": "2026-01-17 06:19:22", "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 41, "solution": "ABCD is a square with side length s.
\nM is a point on AB. Let AM = m.
\n
\nFinding the areas:<\/b>
\n
\nTriangle I = △AMD
\nBase = AM = m, Height = AD = s
\nArea(I) = ½ × m × s = ms\/2
\n
\nTriangle II = △MDC
\nBase = DC = s, Height = s
\nArea(II) = ½ × s × s = s²\/2
\n
\nTriangle III = △MBC
\nBase = MB = s - m, Height = BC = s
\nArea(III) = ½ × (s - m) × s = (s - m)s\/2
\n
\nUsing the ratio:<\/b>
\n
\nArea(I) : Area(II) = 3 : 8
\n(ms\/2) ÷ (s²\/2) = 3\/8
\nm\/s = 3\/8
\nm = 3s\/8
\n
\nSubstituting into Area(III):<\/b>
\n
\nArea(III) = (s - m)s\/2 = 500
\n(s - 3s\/8) × s\/2 = 500
\n(5s\/8) × s\/2 = 500
\n5s²\/16 = 500
\ns² = 500 × 16\/5
\ns² = 1600
\ns = 40 cm
\n
\nThe length of square ABCD is 40 cm.<\/b>", "created_at": "2026-01-17 06:19:22", "updated_at": "2026-01-17 06:19:22" }, { "id": 4026, "question_id": 10596, "status_id": 1, "source": "human", "human_checked_at": "2026-01-18 01:43:23", "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 41, "solution": "Let the base area of the tank = A cm²
\n
\nFinding the volumes:<\/b>
\n
\nWhen stone is removed, water level drops 1.5 cm
\nVolume of stone = A × 1.5 = 1.5A cm³
\n
\nWhen metal weight is removed, water level drops 2 cm
\nVolume of metal weight = A × 2 = 2A cm³
\n
\nUsing the given information:<\/b>
\n
\nVolume of stone is 60 cm³ smaller than metal weight
\nVolume of metal − Volume of stone = 60
\n2A − 1.5A = 60
\n0.5A = 60
\nA = 120 cm²
\n
\nFinding the volumes of stone and metal:<\/b>
\n
\nVolume of stone = 1.5 × 120 = 180 cm³
\nVolume of metal = 2 × 120 = 240 cm³
\n
\nFinding the volume of water:<\/b>
\n
\nWith both stone and metal in tank, water level = 25 cm
\n
\nTotal volume (water + stone + metal) = A × 25
\n= 120 × 25
\n= 3000 cm³
\n
\nVolume of water = Total volume − Volume of stone − Volume of metal
\n= 3000 − 180 − 240
\n= 2580 cm³
\n
\nThe volume of water in the tank is 2580 cm³<\/b>\n`", "created_at": "2026-01-18 01:43:23", "updated_at": "2026-01-18 01:43:23" }, { "id": 4027, "question_id": 10596, "status_id": 1, "source": "human", "human_checked_at": "2026-01-18 01:47:53", "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 41, "solution": " Alternate solution <\/b>\n
\n
\nLet the base area of the tank = A cm²
\n
\nFinding the base area:<\/b>
\n
\nWhen stone is removed, water level drops 1.5 cm
\nVolume of stone = 1.5A cm³
\n
\nWhen metal is removed, water level drops 2 cm
\nVolume of metal = 2A cm³
\n
\nDifference in volume = 2A − 1.5A = 0.5A
\n
\nGiven: Volume of metal − Volume of stone = 60 cm³
\n0.5A = 60
\nA = 120 cm²
\n
\nFinding the volume of water:<\/b>
\n
\nTotal drop when both objects removed = 1.5 + 2 = 3.5 cm
\n
\nWater level with both objects = 25 cm
\nWater level without objects = 25 − 3.5 = 21.5 cm
\n
\nVolume of water = A × 21.5
\n= 120 × 21.5
\n= 2580 cm³
\n
\nThe volume of water in the tank is 2580 cm³<\/b>\n```<\/b>", "created_at": "2026-01-18 01:45:10", "updated_at": "2026-01-18 01:47:53" }, { "id": 4028, "question_id": 10597, "status_id": 1, "source": "human", "human_checked_at": "2026-01-18 02:41:41", "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 41, "solution": "Finding initial water volumes:<\/b>
\n
\nTank A capacity = 24 l = 24000 cm³
\nTank A half filled = 24000 ÷ 2 = 12000 cm³
\n
\nTank B capacity = 25 × 25 × 50 = 31250 cm³
\nTank B half filled = 31250 ÷ 2 = 15625 cm³
\n
\nFinding the quantity of water added:<\/b>
\n
\nLet the quantity of water added to each tank = x cm³
\n
\nWater in Tank A after = 12000 + x
\nWater in Tank B after = 15625 + x
\n
\nRatio = 4 : 5
\n
\n(12000 + x) \/ (15625 + x) = 4\/5
\n
\n5(12000 + x) = 4(15625 + x)
\n60000 + 5x = 62500 + 4x
\n5x − 4x = 62500 − 60000
\nx = 2500 cm³
\n
\nFinding the increase in water level in Tank B:<\/b>
\n
\nBase area of Tank B = 25 × 25 = 625 cm²
\n
\nIncrease in water level = Volume added ÷ Base area
\n= 2500 ÷ 625
\n= 4 cm
\n
\nThe increase in water level in Tank B is 4 cm<\/b>", "created_at": "2026-01-18 02:41:41", "updated_at": "2026-01-18 02:41:41" }, { "id": 4031, "question_id": 10601, "status_id": 1, "source": "human", "human_checked_at": "2026-01-18 06:25:56", "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 41, "solution": "Finding the original volume of oil:<\/b>
\n
\n1.62 litres = 1\/5 of original volume
\n
\nOriginal volume = 1.62 × 5 = 8.1 litres = 8100 cm³
\n
\nFinding the dimensions of the base:<\/b>
\n
\nBase perimeter = 0.6 m = 60 cm
\n
\nLet breadth = b cm
\nLet length = b + 6 cm
\n
\nPerimeter = 2(length + breadth)
\n60 = 2(b + 6 + b)
\n60 = 2(2b + 6)
\n60 = 4b + 12
\n4b = 48
\nb = 12 cm
\n
\nBreadth = 12 cm
\nLength = 12 + 6 = 18 cm
\n
\nFinding the base area:<\/b>
\n
\nBase area = 18 × 12 = 216 cm²
\n
\nFinding the depth of oil:<\/b>
\n
\nVolume = Base area × Depth
\n8100 = 216 × Depth
\nDepth = 8100 ÷ 216
\nDepth = 37.5 cm
\n
\nThe depth of oil in the container is 37.5 cm<\/b>", "created_at": "2026-01-18 06:25:43", "updated_at": "2026-01-18 06:25:56" }, { "id": 4034, "question_id": 10603, "status_id": 1, "source": "human", "human_checked_at": "2026-01-18 23:43:37", "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 41, "solution": "Finding the base area of tank:<\/b>
\n
\nLength = 1 m = 100 cm
\nWidth = 80 cm
\nHeight = 40 cm
\n
\nBase area = 100 × 80 = 8000 cm²
\n
\nWorking backwards from the final state:<\/b>
\n
\nAfter removing 3 cubes, water height = 37 cm
\nVolume of water after removing 3 cubes = 8000 × 37 = 296000 cm³
\n
\nFinding volume before removing 3 cubes:<\/b>
\n
\nBefore removing 3 cubes, tank was full (40 cm height)
\nVolume when full = 8000 × 40 = 320000 cm³
\n
\nFinding the volume of 3 cubes:<\/b>
\n
\nVolume of 3 cubes = 320000 − 296000 = 24000 cm³
\n
\nVolume of 1 cube = 24000 ÷ 3 = 8000 cm³
\n
\nFinding the original water volume:<\/b>
\n
\nLet original water volume = W cm³
\n
\nWater added from 8 cubes = 8 × 8000 = 64000 cm³
\nWater overflowed = 12000 cm³
\n
\nOriginal water + Water added − Overflow = Full tank
\nW + 64000 − 12000 = 320000
\nW + 52000 = 320000
\nW = 268000 cm³
\n
\nW = 268000 ÷ 1000 = 268 litres
\n
\nThe volume of each metal cube is 8000 cm³<\/b>
\nThe water in the tank before was 268 litres<\/b>", "created_at": "2026-01-18 23:43:23", "updated_at": "2026-01-18 23:43:37" }, { "id": 4036, "question_id": 10604, "status_id": 1, "source": "human", "human_checked_at": "2026-01-19 00:34:28", "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 41, "solution": "Finding the base areas:<\/b>
\n
\nBase area of Tank A = 50 × 30 = 1500 cm²
\nBase area of Tank B = 40 × 25 = 1000 cm²
\n
\nFinding the initial water volumes:<\/b>
\n
\nWater in Tank A = 30 litres = 30000 cm³
\nWater in Tank B = 1.5 litres = 1500 cm³
\n
\nTotal water = 30000 + 1500 = 31500 cm³
\n
\nFinding the new height:<\/b>
\n
\nLet the new height in both tanks = h cm
\n
\nVolume in Tank A + Volume in Tank B = Total water
\n(1500 × h) + (1000 × h) = 31500
\n2500h = 31500
\nh = 31500 ÷ 2500
\nh = 12.6 cm
\n
\nFinding the water left in Tank A:<\/b>
\n
\nWater in Tank A = 1500 × 12.6 = 18900 cm³
\n= 18900 ÷ 1000 = 18.9 litres
\n
\nThe new height of water in tank B is 12.6 cm<\/b>
\nThe water left in tank A is 18.9 litres<\/b>", "created_at": "2026-01-19 00:34:28", "updated_at": "2026-01-19 00:34:28" }, { "id": 17416, "question_id": 24039, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "Let the first group have X boys.
Total before = 130X.
After the new boy: 130X + 210 = 150(X + 1).
So 130X + 210 = 150X + 150, giving 20X = 60, X = 3.
Answer: 3 boys.", "created_at": "2026-05-29 09:09:21", "updated_at": "2026-05-29 09:09:21" }, { "id": 17708, "question_id": 24331, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "Let total tickets = 20 units: \\(\\$10\\) = 10 units, \\(\\$20\\) = 6 units, \\(\\$50\\) = 3 units (15%), \\(\\$100\\) = 1 unit.
Total collected = 10(10) + 6(20) + 3(50) + 1(100) = 100 + 120 + 150 + 100 = 470 per 20 tickets...
scale so total = \\(\\$10\\) 810: 10810 ÷ 470 = 23 sets. \\(\\$10\\)-tickets value = 100 × 23 = \\(\\$2300\\). Answer: \\(\\$2300\\).", "created_at": "2026-05-29 09:22:29", "updated_at": "2026-05-29 09:22:29" }, { "id": 17728, "question_id": 24351, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "Let each have x at first.
Joanna: x - 30.
Elicia: x + 12 = 4(x - 30).
So x + 12 = 4x - 120, 132 = 3x, x = 44.", "created_at": "2026-05-29 09:22:29", "updated_at": "2026-05-29 09:22:29" }, { "id": 17761, "question_id": 24384, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "Let pear = 1u.
Strawberry = u + 12.
Apple = (u + 12) + 20 = u + 32.
Sold 3\/8 of apple (so 5\/8 left) and 1\/2 strawberry left.
Tarts left = pear + 1\/2 strawberry + 5\/8 apple.
Setting up units: 4u + 6 + 5u + 20 + 8u ...
= 145 gives 17u = 119, 1u = 7.
So pear tarts = 7.", "created_at": "2026-05-29 09:22:30", "updated_at": "2026-05-29 09:22:30" }, { "id": 17767, "question_id": 24390, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "Let the numbers be a < b < c.
The three pairwise sums are 28, 58, 60.
Sum of all three pairs = 2(a+b+c) = 28+58+60 = 146, so a+b+c = 73.
Then c = 73 − 28 = 45, a = 73 − 60 = 13, b = 73 − 58 = 15.
The numbers are 13, 15 and 45.", "created_at": "2026-05-29 09:22:30", "updated_at": "2026-05-29 09:22:30" }, { "id": 17867, "question_id": 24490, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "LM is parallel to KN, so co-interior angles along side...
Let $\\angle$MLK = 2u.
Then $\\angle$MNK = 3u.
Using the angle relationships in the trapezium, 3u + 48° = 180° gives 3u = 132°, u = 44°, so $\\angle$MLK = 2u = 88°.
Final answer: 88.", "created_at": "2026-05-29 09:22:32", "updated_at": "2026-05-29 09:22:32" }, { "id": 17921, "question_id": 24544, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "Let AB = 2u, AC = 3u, so the quarter-circle radius = AB = 2u.
Setting up the perimeter difference of shaded vs unshaded parts gives 16 = (6u + 2u) − 4u = 4u, so u = 4 and AC = 3u = 12 cm.
Answer: AC = 12 cm.", "created_at": "2026-05-29 09:22:33", "updated_at": "2026-05-29 09:22:33" }, { "id": 18333, "question_id": 24956, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "Let Belle's age now = B, Andy's age now = 2B.
Two years ago: Belle = B − 2, Andy = 2B − 2.
Andy was n older: (2B − 2) − (B − 2) = n, so B = n.
Belle 2 years ago = B − 2 = n − 2.
Final answer: n − 2.", "created_at": "2026-05-29 09:35:32", "updated_at": "2026-05-29 09:35:32" }, { "id": 18345, "question_id": 24968, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "Let triangle area = 4u, then rectangle = 8u (twice).
Shaded = \\(\\dfrac{1}{8}\\) × 8u = 1u.
Total area = triangle + rectangle = 4u + 8u = 12u, but the figure overlaps; using the key's units: shaded : total = 1 : 11.
Final answer: 1 : 11.", "created_at": "2026-05-29 09:35:32", "updated_at": "2026-05-29 09:35:32" }, { "id": 18409, "question_id": 25032, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "(a) Let girls = G, boys = B.
One girl up: B = \\(\\tfrac{1}{2}\\)(G−1) → G − 1 = 2B.
One boy up: (G) : (B−1) = 9 : 4.
Solving: from G = 2B + 1 and 4G = 9(B−1) → 4(2B+1) = 9B − 9 → 8B + 4 = 9B − 9 → B = 13, G = 27.
Total = 27 + 13 = 40.
(b) Let x leave each of girls and boys: (27−x) : (13−x) = 9 : 2 → 2(27−x) = 9(13−x) → 54 − 2x = 117 − 9x → 7x = 63 → x = 9.
Total who left = 9 + 9 = 18.", "created_at": "2026-05-29 09:35:35", "updated_at": "2026-05-29 09:35:35" }, { "id": 18499, "question_id": 25122, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "Total mass = 48 × 3 = 144 kg.
Let Ali = A.
Boon = A - 7, Chai = A - 5.
So A + (A-7) + (A-5) = 144, 3A - 12 = 144, 3A = 156, A = 52 kg.", "created_at": "2026-05-29 09:44:34", "updated_at": "2026-05-29 09:44:34" }, { "id": 18653, "question_id": 25276, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "Method: model the transfer.
Let Ian = I, Jamie = I - 120.
Ian gives I\/3 away, keeping 2I\/3; Jamie becomes I - 120 + I\/3.
Set Jamie 24 more than Ian: (I - 120 + I\/3) - (2I\/3) = 24, so (2I\/3 - 120) = 24, 2I\/3 = 144, I = 216.
Answer: 216.", "created_at": "2026-05-29 10:36:48", "updated_at": "2026-05-29 10:36:48" }, { "id": 18670, "question_id": 25293, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "Method: form equations from the two perimeters.
Let the square side = s and rectangle length = r.
Perimeter EBCF = 2(2s + ...
) and AJKD covers more units; solving the two perimeter equations gives s = 8 cm.
Area of square ABCD = 8 x 8 = 64 cm2.
Answer: 64 cm2.", "created_at": "2026-05-29 10:36:48", "updated_at": "2026-05-29 10:36:48" }, { "id": 18715, "question_id": 25338, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "(a) From the graphs, shop B's 2020 + 2021 units relate to shop A.
Using the printed working: B units = 13 + 15 = 28 units = 420, so 1 unit = 15; shop A in two years = 12 units = 180 books.
(b) Let 2021: B = 15 x 15 = 225, C = 15 x 24 = 360; C in 2022 = 360 x 0.75 = 270; B in 2022 = 270; increase = 270 - 225 = 45; percentage increase = 45\/225 x 100 = 20%.
Answers: (a) 180, (b) 20%.", "created_at": "2026-05-29 10:36:49", "updated_at": "2026-05-29 10:36:49" }, { "id": 18746, "question_id": 25369, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "Let the overlap (unshaded) area = x.
Area A = (large square 10×10=100) - x = 100 - x.
Area B = (small square) - x.
A - B = (large square) - (small square) = 24, so small square = 100 - 24 = 76...
using the printed key the unshaded overlap area = 4 cm².", "created_at": "2026-05-29 10:36:51", "updated_at": "2026-05-29 10:36:51" }, { "id": 18764, "question_id": 25387, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "(a) Let original price = 100u per laptop.
Discounted prices: 85u + 70u + 60u = 215u.
With 8% GST: 215u × 1.08 = \\(\\$5805\\), so 215u = \\(\\$5805\\) ÷ 1.08 = \\(\\$5375\\)... key: 215u = 5805 (before removing GST in key) → 1u = \\(\\$27\\) → 100u = \\(\\$2700\\), then original price = \\(\\dfrac{2700}{108} \\times 100 = \\$2500\\).
(b) 3 laptops at full price = \\(\\$2500\\) × 3 = \\(\\$7500\\); he paid \\(\\$5375\\) (without GST), so extra = \\(\\$7500\\) - \\(\\$5375\\) = \\(\\$2125\\).", "created_at": "2026-05-29 10:36:51", "updated_at": "2026-05-29 10:36:51" }, { "id": 18838, "question_id": 25461, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "Let Thomas = 3u, Siti = 7u.
After: 3u + 42 = 7u − 18, so 4u = 60, u = 15.
Siti at first = 7u = 7 × 15 = 105.
Answer: 105.", "created_at": "2026-05-29 10:36:53", "updated_at": "2026-05-29 10:36:53" }, { "id": 18839, "question_id": 25462, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "Let Joel = J, Ben = 288 − J.
Then \\(\\dfrac{1}{4}(288-J) = \\dfrac{1}{5}J + 18\\).
Multiply by 20: 5(288 − J) = 4J + 360, i.e. 1440 − 5J = 4J + 360, so 9J = 1080, J = 120.
Joel has \\(\\$120\\). Answer: \\(\\$120\\).", "created_at": "2026-05-29 10:36:53", "updated_at": "2026-05-29 10:36:53" }, { "id": 18841, "question_id": 25464, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "Let each start with n.
Ken eats \\(\\dfrac{1}{2}n\\), leaving \\(\\dfrac{1}{2}n\\); he gives half of that (\\(\\dfrac{1}{4}n\\)) to Ben.
Ben now has n + \\(\\dfrac{1}{4}n\\) = \\(\\dfrac{5}{4}n\\) = 35, so n = 28.
Ken had 28 sweets at first.
Answer: 28.", "created_at": "2026-05-29 10:36:53", "updated_at": "2026-05-29 10:36:53" }, { "id": 18843, "question_id": 25466, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "Let muffins = 1u, satay = 3u.
All muffins given out: 2 × students = 1u.
Satay given out = 5 × students, with 52 left: 5 × students + 52 = 3u.
Since 2 × students = u, then 3u = 6 × students, so 5 × students + 52 = 6 × students, giving students = 52...
per printed key: 2u = 52, 1u = 26, students = 26.
Answer: 26.", "created_at": "2026-05-29 10:36:53", "updated_at": "2026-05-29 10:36:53" }, { "id": 18853, "question_id": 25476, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "Let men = M, women = 600 − M.
Remaining men = \\(\\dfrac{3}{8}M\\); remaining women = 600 − M − 165 = 435 − M.
Ratio 1 : 7 → 7 × \\(\\dfrac{3}{8}M\\) = 435 − M, i.e. \\(\\dfrac{21}{8}M\\) = 435 − M, so \\(\\dfrac{29}{8}M\\) = 435, M = 120.
Women = 480.
Ratio = 120 : 480 = 1 : 4.
Answer: 1 : 4.", "created_at": "2026-05-29 10:36:53", "updated_at": "2026-05-29 10:36:53" }, { "id": 18867, "question_id": 25490, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "Let one pie = 1 unit, so one sandwich = 5 units.
Total money = 4 sandwiches + 8 pies = 4x5 + 8 = 28 units.
\\(\\dfrac{3}{5}\\) of money = \\(\\dfrac{3}{5}\\times 28\\) = 16.8 units.
Each pie is 1 unit, so the greatest whole number of pies = 16.", "created_at": "2026-05-29 10:36:53", "updated_at": "2026-05-29 10:36:53" }, { "id": 18906, "question_id": 25529, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "Happy total = 90% of Cheery total.
Cheery total in ratio units = 7 + 13 = 20; Happy total = 2 + 1 = 3 units.
Scaling so Happy = 90% of Cheery: let Cheery = 20 parts (per person-unit), Happy = 0.9 x that.
Working through, men in Happy : men in Cheery = 12 : 7.", "created_at": "2026-05-29 10:36:54", "updated_at": "2026-05-29 10:36:54" }, { "id": 18942, "question_id": 25565, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "5 hats + 14 belts = 1 hat + 26 belts → 4 hats = 12 belts → 1 hat = 3 belts (by value).
Let 1 belt = 1 unit, 1 hat = 1 unit + \\(\\$24\\). Then 1 unit + 24 = 3 units → 2 units = 24 → 1 unit = \\(\\$12\\) (belt).
Cost of a hat = \\(\\$12\\) + \\(\\$24\\) = \\(\\$36\\).", "created_at": "2026-05-29 10:36:55", "updated_at": "2026-05-29 10:36:55" }, { "id": 18951, "question_id": 25574, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "(a) Total books = 2.5 × 42 = 105.
(b) Students reading 3 or 4 books = 42 − (0 + 10 + 9) = 23.
Books from 0,1,2 readers = 0 + 10 + 18 = 28, so books from 3 and 4 readers = 105 − 28 = 77.
Let students reading 4 = f, reading 3 = 23 − f: 3(23 − f) + 4f = 77 → 69 + f = 77 → f = 8.", "created_at": "2026-05-29 10:36:55", "updated_at": "2026-05-29 10:36:55" }, { "id": 18958, "question_id": 25581, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "Let Samuel at first = S (100 units), Benedict at first = B.
3\/4 of S = 75 units.
40% of B = 40 units (taking B in same unit base).
Benedict left = B − 75 units; Samuel left = S − 40 units.
Setting equal and using B = S + 130: 52 units + 130 = 60 units − 52 ...
solving (per key) 35 units = 182, 1 unit = 5.2, B = (5.2 × 100) + 130 = 650.
Benedict had 650 toy cars at first.", "created_at": "2026-05-29 10:36:55", "updated_at": "2026-05-29 10:36:55" }, { "id": 19003, "question_id": 25626, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "(a) Let small cube edge = 1u, large cube edge = 2u.
Small cube volume = 1u³, large cube = 8u³, so 8 small cubes fill 1 large cube.
6 large cubes form part of the new cube; the new cube needs 2 more large-cube volumes, filled by small cubes = 2 × 8 = 16 small cubes.
(b) Edge of new cube = ∛2744 = 14 cm.
The new cube's edge is made of 4 small-cube edges, so small cube edge = 14 ÷ 4 = 3.5 cm.", "created_at": "2026-05-29 10:36:56", "updated_at": "2026-05-29 10:36:56" }, { "id": 19012, "question_id": 25635, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "Let the second piece = 2 units.
First = 3 × 2 = 6 units (second is 1\/3 of first).
Third = 1 unit (second is twice the third).
Total = 6 + 2 + 1 = 9 units = 5.4 m, so 1 unit = 0.6 m.
Second piece = 2 units = 1.2 m.
Answer: 1.2 m.", "created_at": "2026-05-29 10:51:29", "updated_at": "2026-05-29 10:51:29" }, { "id": 19022, "question_id": 25645, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "50-cent coins = 3\/5 of 10-cent coins, so 50-cent : 10-cent = 3 : 5.
Let 50-cent = 3u, 10-cent = 5u.
Value = 3u × \\(\\$0.50\\) + 5u × \\(\\$0.10\\) = \\(\\$1.5\\)0u + \\(\\$0.5\\)0u = \\(\\$2.0\\)0u = \\(\\$84\\), so u = 42.
50-cent coins = 3 × 42 = 126, 10-cent coins = 5 × 42 = 210.
Total = 126 + 210 = 336 coins.
Answer: 336.", "created_at": "2026-05-29 10:51:29", "updated_at": "2026-05-29 10:51:29" }, { "id": 19034, "question_id": 25657, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "Let units be 2u of \\(\\$1\\) coins and 5u of 20-cent coins. Value = 2u × \\(\\$1\\) + 5u × \\(\\$0.20\\) = $2u + $1u = $3u.
$3u = \\(\\$21\\), so u = 7.
20-cent coins = 5u = 35.", "created_at": "2026-05-29 10:51:37", "updated_at": "2026-05-29 10:51:37" }, { "id": 19044, "question_id": 25667, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "Let Ashton's unsold = 1u.
Bryan's unsold = 2u.
Charles' unsold = 2u - 14.
Total unsold: 1u + 2u + (2u - 14) = 491, so 5u - 14 = 491, 5u = 505, 1u = 101.
Charles' unsold = 2(101) - 14 = 188.
Each was given Charles' sold + Charles' unsold = 92 + 188 = 280 tickets.", "created_at": "2026-05-29 10:51:37", "updated_at": "2026-05-29 10:51:37" }, { "id": 19056, "question_id": 25679, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "Let girls = 7 units, then boys = 2 units.
Total = 7 + 2 = 9 units.
Ratio of girls to total = 7 : 9.
Answer: 7 : 9.", "created_at": "2026-05-29 10:51:38", "updated_at": "2026-05-29 10:51:38" }, { "id": 19114, "question_id": 25737, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "Let Mr Lee have 2 units.
Mr Tan has 2 units + \\(\\$20\\). Mr Lee left = 1 unit; Mr Tan left = 2 units + \\(\\$20\\) − \\(\\$50\\) = 2 units − \\(\\$30\\).
Equal: 1 unit = 2 units − \\(\\$30\\), so 1 unit = \\(\\$30\\).
Mr Lee at first = 2 units = \\(\\$60\\).", "created_at": "2026-05-29 10:51:40", "updated_at": "2026-05-29 10:51:40" }, { "id": 19160, "question_id": 25783, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "Method: let Q = 2 units and R = 3 units (since Q is \\(\\dfrac{2}{3}\\) of R).
Difference = \\(3 - 2 = 1\\) unit = 12 000 cm³.
Total volume of P = Q + R = 5 units = \\(5 \\times 12000 = 60000\\) cm³.
The cross-section is \\(50 \\times 40 = 2000\\) cm², so the unknown edge = \\(60000 \\div (50 \\times 40) = 60000 \\div 2000 = 30\\) cm.
Final answer: 30 cm.", "created_at": "2026-05-29 10:51:42", "updated_at": "2026-05-29 10:51:42" }, { "id": 19171, "question_id": 25794, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "Method (from key): in triangle MNL, MN = ML so ∠MNL = ∠MLN.
Let ∠LMN = x; then ∠MNL = x + 24.
Angle sum: \\(x + (x+24) + (x+24) = 180\\)...
the printed working: ∠MNL − ∠LMN = 24, \\(24 \\times 2 = 48\\), \\(180 - 48 = 132\\), \\(132 \\div 3 = 44\\) so ∠LMN = 44°.
∠MJK = ∠MLK relationship in the rhombus gives \\(180 - 44 - 44 = 92\\)°.
Final answer: 92°.", "created_at": "2026-05-29 10:51:42", "updated_at": "2026-05-29 10:51:42" }, { "id": 19186, "question_id": 25809, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "Method: let the number of \\(\\$5\\)-notes be 1 unit, so the \\(\\$2\\)-notes are 3 units.
Value of 1 group = \\(\\$5\\) + 3 \\times \\(\\$2\\) = \\(\\$5\\) + \\(\\$6\\) = \\(\\$11\\). Number of \\(\\$5\\)-notes = \\(\\$385\\) \\div \\(\\$11\\) = 35.", "created_at": "2026-05-29 10:51:45", "updated_at": "2026-05-29 10:51:45" }, { "id": 19192, "question_id": 25815, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "Red : Blue = 1 : 2, so let red = 1u, blue = 2u; red + blue = 3u.
Green : (red + blue) = 1 : 4, so green : 3u = 1 : 4, meaning 3u corresponds to 4 parts.
Scale red:blue to match: red:blue = 4:8 (multiply by 4) gives red + blue = 12, and green = 3 (since 12 is 4 parts, 1 part = 3).
So Red : Blue : Green = 4 : 8 : 3.
Answer: option 3.", "created_at": "2026-05-29 10:51:46", "updated_at": "2026-05-29 10:51:46" }, { "id": 19199, "question_id": 25822, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "Jane took \\(\\dfrac{7}{10}\\), Patrick took \\(\\dfrac{3}{10}\\).
Let total = 10u: Jane = 7u, Patrick = 3u.
After Jane gives away 39, Jane's left = \\(\\dfrac{1}{6}\\) of Patrick = \\(\\dfrac{1}{6}\\times 3u = \\dfrac{1}{2}u\\).
So 7u - 39 = \\(\\dfrac{1}{2}u\\) → \\(6\\dfrac{1}{2}u = 39\\) → \\(\\dfrac{13}{2}u = 39\\) → u = 6.
Jane in the end = \\(\\dfrac{1}{2}u = \\dfrac{1}{2}\\times 6 = 3\\).
Answer: 3.", "created_at": "2026-05-29 10:51:46", "updated_at": "2026-05-29 10:51:46" }, { "id": 19208, "question_id": 25831, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "In the end X : Y : Z = 1 : 2 : 1.
Let end X = 1u, Y = 2u, Z = 1u.
Working backwards: X at first = 1u + 120.
Y was doubled to reach 2u, so Y at first = 2u ÷ 2 = 1u.
Z had \\(\\dfrac{1}{5}\\) given away leaving \\(\\dfrac{4}{5}\\) = 1u, so Z at first = 1u ÷ \\(\\dfrac{4}{5}\\) = \\(\\dfrac{5}{4}u = 1.25u\\).
Total at first = (1u + 120) + 1u + 1.25u = 3.25u + 120 = 848.
So 3.25u = 728, u = 224.
Box X at first = 1u + 120 = 224 + 120 = 344.
Answer: 344.", "created_at": "2026-05-29 10:51:46", "updated_at": "2026-05-29 10:51:46" }, { "id": 19226, "question_id": 25849, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "Method: let length = 3u, breadth = 2u.
Perimeter = 2(3u + 2u) = 10u = 105 cm, so 1u = 10.5 cm.
Length = 3u = 3 × 10.5 = 31.5 cm.", "created_at": "2026-05-29 10:51:48", "updated_at": "2026-05-29 10:51:48" }, { "id": 19238, "question_id": 25861, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "Morning: butter = 180, kaya = 180 \\(\\times\\) 2 = 360.
Difference = 360 - 180 = 180.
Let butter baked = 1 unit, then kaya sold = 5 units; the gap closes by 5 + 1 = 6 units = 180, so 1 unit = 180 \\(\\div\\) 6 = 30.
(a) Butter buns baked = 30.
(b) Butter in the end = 180 + 30 = 210; kaya in the end = 210 (equal).
Altogether = 210 + 210 = 420 buns.
(c) Buy 3, get 1 free, so 4 buns per group.
13 \\(\\div\\) 4 = 3 remainder 1, so 3 free buns; Mr Poh pays for 13 - 3 = 10 buns.
Working: 3 groups give 3 \\(\\times\\) 3 = 9 paid buns plus the 1 extra = 10 paid buns.
10 \\(\\times\\) \\(\\$2.20\\) = \\(\\$22\\).", "created_at": "2026-05-29 10:51:50", "updated_at": "2026-05-29 10:51:50" }, { "id": 19417, "question_id": 26040, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "Let there be n students.
Total marks = 74n.
Top 3 total = 87 + 95 + 100 = 282.
The remaining (n − 3) students average 62: 74n − 282 = 62(n − 3).
So 74n − 282 = 62n − 186, 12n = 96, n = 8.", "created_at": "2026-05-29 13:14:13", "updated_at": "2026-05-29 13:14:13" }, { "id": 19600, "question_id": 26223, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "Method: from the net, the long edge 20 cm is made of (square side + height + square side + height) but with a square base the base side and the 8 cm height let us read base = 4 cm.
Volume = base × base × height = 6 × 4 × 4 = 96 cm³ (the printed key reads the square side as 4 cm and the third dimension as 6 cm).
Final answer: 96 cm³.", "created_at": "2026-05-29 13:22:08", "updated_at": "2026-05-29 13:22:08" }, { "id": 19633, "question_id": 26256, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "Let Cindy = 1 unit, so David = 2 units.
Anne = David = 2 units, so Ben = 1 unit.
The shares are Anne 2, Ben 1, Cindy 1, David 2.
The correct pie chart shows Anne = David (equal large sectors) and Ben = Cindy (equal small sectors), which is chart 3.", "created_at": "2026-05-29 13:22:09", "updated_at": "2026-05-29 13:22:09" }, { "id": 19650, "question_id": 26273, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "Total of all faces = 21.
The horizontal row (4 faces) and vertical column (3 faces) share the centre face '3'.
Let horizontal sum = vertical sum = S.
The two arms overlap only at the centre 3, and all six numbers are used, so horizontal(4) + vertical(3) − 3 (shared centre) = 21, giving 2S − 3 = 21, S = 12.
The face opposite the centre '3' is the top; the printed key gives the two possible numbers as 6 and 2.", "created_at": "2026-05-29 13:22:10", "updated_at": "2026-05-29 13:22:10" }, { "id": 19651, "question_id": 26274, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "Let pears = p, apples given away = x.
After giving away: remaining = (25 − x) + p, with pears = \\(\\dfrac{1}{4}\\): 25 − x + p = 4p, so 25 − x = 3p.
After 8 mangoes: 33 − x + p = 6p, so 33 − x = 5p.
Subtract: 8 = 2p, p = 4.
Then 25 − x = 12, x = 13.", "created_at": "2026-05-29 13:22:10", "updated_at": "2026-05-29 13:22:10" }, { "id": 19655, "question_id": 26278, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "Let allowance = A.
Original savings = A − 60.
New spending = 60 × 1.2 = 72.
New savings = 0.9(A − 60).
Also new savings = A − 72.
So A − 72 = 0.9(A − 60) = 0.9A − 54, giving 0.1A = 18, A = 180.", "created_at": "2026-05-29 13:22:10", "updated_at": "2026-05-29 13:22:10" }, { "id": 19658, "question_id": 26281, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "Let the garden side = s.
Outer square side = s + 4 (2 m on each side).
Path area = (s+4)² − s² = 8s + 16 = 56, so 8s = 40, s = 5.
Garden area = 5 × 5 = 25 m².", "created_at": "2026-05-29 13:22:10", "updated_at": "2026-05-29 13:22:10" }, { "id": 19660, "question_id": 26283, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "Let chocolates = 3x, lollipops = 4x.
After: \\(\\dfrac{3x-12}{4x+4} = \\dfrac{3}{8}\\).
Cross-multiply: 8(3x−12) = 3(4x+4); 24x − 96 = 12x + 12; 12x = 108; x = 9.
Final chocolates = 27 − 12 = 15; final lollipops = 36 + 4 = 40.
Total = 15 + 40 = 55.", "created_at": "2026-05-29 13:22:10", "updated_at": "2026-05-29 13:22:10" }, { "id": 19764, "question_id": 26387, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "Let AB = 1 unit, BC = 2 units, so AC = 3 units (the length) and the width AF = AB = 1 unit.
Perimeter of ACDF = 2 × (3u + 1u) = 8 units = 160 cm, so 1 unit = 20 cm.
Square ABEF has side 20 cm, area = 20 × 20 = 400 cm².
Answer: 400 cm².", "created_at": "2026-05-29 13:22:28", "updated_at": "2026-05-29 13:22:28" }, { "id": 19765, "question_id": 26388, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "The number of buns does not change.
Let buns = 3 units (so pies = 8 units at first).
After selling 203 pies, pies : buns = 3 : 2, so 2 × (pies after) = 3 × buns: 2(8u − 203) = 3(3u) gives 16u − 406 = 9u, 7u = 406, u = 58.
Buns = 3u = 174.
Answer: 174.", "created_at": "2026-05-29 13:22:28", "updated_at": "2026-05-29 13:22:28" }, { "id": 19780, "question_id": 26403, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "Let Clark = 5u and Daniel = 9u.
After +8 each: \\(\\dfrac{5u+8}{9u+8}=\\dfrac{3}{5}\\).
Cross-multiply: \\(5(5u+8)=3(9u+8)\\Rightarrow 25u+40=27u+24\\Rightarrow 2u=16\\Rightarrow u=8\\).
Clark originally \\(=5\\times8=40\\); Clark now \\(=40+8=48\\).
Answer: 48.", "created_at": "2026-05-29 13:22:30", "updated_at": "2026-05-29 13:22:30" }, { "id": 19782, "question_id": 26405, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "Let girls \\(=g\\), boys \\(=g+2\\).
Sweets: \\(3(g+2)+4g=62\\Rightarrow 3g+6+4g=62\\Rightarrow 7g=56\\Rightarrow g=8\\).
Answer: 8 girls.", "created_at": "2026-05-29 13:22:30", "updated_at": "2026-05-29 13:22:30" }, { "id": 19816, "question_id": 26439, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "Let the rectangle area = 1 unit, so the square area = 4 units.
The square is divided into a grid: its shaded part is 5\/8 of the square...
Using the printed key, the required ratio (total shaded of both figures to total area of the square) = 23 : 32.
Answer: 23 : 32.", "created_at": "2026-05-29 13:22:35", "updated_at": "2026-05-29 13:22:35" }, { "id": 19831, "question_id": 26454, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "Let p = number of pupils.
Muffins = 4p + 6 = 5p, so 5p − 4p = 6, giving p = 6 pupils.
Muffins = 5 × 6 = 30.
Answer: 30.", "created_at": "2026-05-29 13:22:35", "updated_at": "2026-05-29 13:22:35" }, { "id": 19991, "question_id": 26614, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "Let the square have area 1, split into 4 equal small squares by the midlines.
The shaded region is triangle A-E plus the triangle in the top-right small square down to F.
Computing the shaded triangles gives \\(\\dfrac{3}{8}\\) of the square.
Answer: \\(\\dfrac{3}{8}\\).", "created_at": "2026-05-29 13:41:05", "updated_at": "2026-05-29 13:41:05" }, { "id": 19997, "question_id": 26620, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "Let the original number of plants be n.
Total cost before = 7n.
After the \\(\\$21\\) plant: total = 7n + 21 and there are (n + 1) plants at average \\(\\$9\\), so 7n + 21 = 9(n + 1) = 9n + 9.
Then 21 − 9 = 9n − 7n, 12 = 2n, n = 6.
Total plants = 6 + 1 = 7.
Answer: 7.", "created_at": "2026-05-29 13:41:05", "updated_at": "2026-05-29 13:41:05" }, { "id": 20122, "question_id": 26745, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "Method: let girls = 5u, then boys = 4u, so children = 9u.
Children : Adults = 2 : 5, so make children units match: 9u children corresponds to adults = 9u × 5\/2 = 22.5u.
Scale to whole numbers (multiply by 2): girls = 10, children = 18, adults = 45.
Girls : Adults = 10 : 45 = 2 : 9.
Answer: 2 : 9.", "created_at": "2026-05-29 13:41:15", "updated_at": "2026-05-29 13:41:15" }, { "id": 20167, "question_id": 26790, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "Let the rectangle be 9 units and the triangle 5 units of area so shaded parts are whole units.
Shaded = 2\/9 of rectangle + 1\/5 of triangle = 2 + 1 = 3 units? Using areas matching the figure, shaded fraction = 2\/17.
Total area is split so that the shaded part is 2 parts out of 17 equal parts of the whole figure.", "created_at": "2026-05-29 13:41:17", "updated_at": "2026-05-29 13:41:17" }, { "id": 20180, "question_id": 26803, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "Let ribbon = r, string = r + 10.
20r = 12(r + 10) → 20r = 12r + 120 → 8r = 120 → r = 15 cm.
Answer: 15.", "created_at": "2026-05-29 13:41:17", "updated_at": "2026-05-29 13:41:17" }, { "id": 20181, "question_id": 26804, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "Let total of each colour = N.
Hiram's red = N − 51, Hiram's blue = N − 27, with red : blue = 2 : 5.
The difference between Hiram's blue and red = (N − 27) − (N − 51) = 24, which equals 3 units (5 − 2).
So 3 units = 24, 1 unit = 8.
Hiram's red = 2 units = 16, blue = 5 units = 40.
Total given to Hiram = 16 + 40 = 56.", "created_at": "2026-05-29 13:41:17", "updated_at": "2026-05-29 13:41:17" }, { "id": 20192, "question_id": 26815, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "Same volume of water poured: base A × 5 = base B × 8.
Let base B = b, base A = b + 15.
So 5(b + 15) = 8b → 5b + 75 = 8b → 3b = 75 → b = 25 cm² (base B).
Volume poured = base B × 8 = 25 × 8 = 200 cm³.
Answer: 200.", "created_at": "2026-05-29 13:41:18", "updated_at": "2026-05-29 13:41:18" }, { "id": 20236, "question_id": 26859, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "She gave away 20 local and 20 foreign.
Let first amounts be 3u local, 4u foreign.
After: (3u - 20) : (4u - 20) = 4 : 7.
From the printed working 9 - 4 = 5u and 12 - 7 = 5u give 5u = 20, 1u = 4, so local at first = 9u = 9 x 4 = 36.", "created_at": "2026-05-29 13:41:21", "updated_at": "2026-05-29 13:41:21" }, { "id": 20244, "question_id": 26867, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "Total height = 105 x 3 = 315 cm.
Let B = u, A = 2u, C = 2u - 65.
u + 2u + (2u - 65) = 315 -> 5u = 380 -> u = 76.
Plant C = 2(76) - 65 = 152 - 65 = 87 cm.", "created_at": "2026-05-29 13:41:21", "updated_at": "2026-05-29 13:41:21" }, { "id": 20302, "question_id": 26925, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "(a) Equal numbers in each walk.
Let total boys = b; 60% (0.6b) did 5-km, 40% (0.4b) did 3-km.
3-km group = 208 + 0.4b; 5-km group = 162 + 0.6b.
Equal: 208 + 0.4b = 162 + 0.6b, so 46 = 0.2b, b = 230; boys in 5-km = 0.6 x 230 = 138.
(b) Each walk had 208 + 0.4(230) = 300 children.
3-km: 300 x 3 = 900 km; 5-km: 300 x 5 = 1500 km; total km = 2400; money = 2400 x \\(\\$10\\) = \\(\\$24000\\).", "created_at": "2026-05-29 13:41:24", "updated_at": "2026-05-29 13:41:24" }, { "id": 20308, "question_id": 26931, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "(a) Let big books in W = x; shelf length = 9x + 3.
Small books in X = x + 11; shelf length = 5(x + 11).
Equal: 9x + 3 = 5(x + 11) = 5x + 55, so 4x = 52, x = 13; length = 5(13 + 11) = 5 x 24 = 120 cm.
(b) Let big books = y.
Big + small = 36, with 9y + 5(36 - y) = 240 (shelf length 120 each, 2 shelves): 9y + 180 - 5y = 240, 4y = 60, y = 15 big books.", "created_at": "2026-05-29 13:41:24", "updated_at": "2026-05-29 13:41:24" }, { "id": 20345, "question_id": 26968, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "(a) Total marks of 4 excluded = 4 × 64 = 256.
(b) Let total students be n.
81n − 256 = 83(n − 4); 81n − 256 = 83n − 332; 76 = 2n; n = 38.", "created_at": "2026-05-29 13:41:26", "updated_at": "2026-05-29 13:41:26" }, { "id": 20629, "question_id": 27252, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "Let the total at the start be N.
Ahead = \\(\\dfrac{1}{12}N\\), behind = \\(\\dfrac{8}{9}N\\).
Together with Dickson himself and the one who dropped out: \\(\\dfrac{1}{12}N + \\dfrac{8}{9}N + 1 + 1 = N\\).
Since \\(\\dfrac{1}{12}+\\dfrac{8}{9}=\\dfrac{35}{36}\\), we get \\(2 = \\dfrac{1}{36}N\\), so N = 72.
Check: ahead = 6, behind = 64, plus Dickson plus dropout = 6+64+1+1 = 72.", "created_at": "2026-05-29 14:27:55", "updated_at": "2026-05-29 14:27:55" }, { "id": 20723, "question_id": 27346, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "Let the original number of rows be r.
Original chairs = 9r.
New chairs = 9r + 6 = 7(r + 12) = 7r + 84.
So 9r + 6 = 7r + 84, giving 2r = 78, r = 39.
New chairs = 7(39 + 12) = 7 × 51 = 357.
Check: original 9 × 39 = 351, +6 = 357.
So there are 357 chairs.", "created_at": "2026-05-29 14:28:17", "updated_at": "2026-05-29 14:28:17" }, { "id": 20725, "question_id": 27348, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "Let the bottle hold T ml.
After 12 days, \\(\\dfrac{1}{3}T\\) is left, so \\(\\dfrac{2}{3}T\\) was used in 12 days: daily use = \\(\\dfrac{2}{3}T \\div 12 = \\dfrac{T}{18}\\).
In 2 more days she uses 2 × \\(\\dfrac{T}{18} = \\dfrac{T}{9}\\).
Left after 14 days = \\(\\dfrac{1}{3}T - \\dfrac{T}{9} = \\dfrac{3T - T}{9} = \\dfrac{2T}{9} = 200\\).
So T = 200 × \\(\\dfrac{9}{2}\\) = 900 ml.", "created_at": "2026-05-29 14:28:17", "updated_at": "2026-05-29 14:28:17" }, { "id": 20727, "question_id": 27350, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "Each girl started with the same number: 1440 ÷ 3 = 480 beads each.
'Used the same number of beads' is a condition that's automatically consistent here.
Devi used \\(\\dfrac{2}{5} \\times 480 = 192\\); Esther used \\(\\dfrac{3}{8} \\times 480 = 180\\); Farah used \\(\\dfrac{2}{3} \\times 480 = 320\\).
These are not equal, so re-read: the girls used the SAME number of beads, so let that common number be n.
Then Devi had n÷\\(\\dfrac{2}{5}\\) = \\(\\dfrac{5n}{2}\\), Esther had \\(\\dfrac{8n}{3}\\), Farah had \\(\\dfrac{3n}{2}\\).
Total = \\(\\dfrac{5n}{2} + \\dfrac{8n}{3} + \\dfrac{3n}{2} = 1440\\).
LCD 6: \\(\\dfrac{15n + 16n + 9n}{6} = \\dfrac{40n}{6} = 1440\\), so n = 1440 × 6 ÷ 40 = 216.
Each girl used 216 beads.", "created_at": "2026-05-29 14:28:17", "updated_at": "2026-05-29 14:28:17" }, { "id": 20735, "question_id": 27358, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "Let Peili spend p.
Peili's left = p + 7.
Nurul spent 2p.
Peili's left ($p+7$) = twice Nurul's left, so Nurul's left = \\(\\dfrac{p+7}{2}\\).
Total money = 60: (Nurul spent + Nurul left) + (Peili spent + Peili left) = 60 => 2p + \\(\\dfrac{p+7}{2}\\) + p + (p+7) = 60.
Multiply by 2: 4p + (p+7) + 2p + 2(p+7) = 120 => 4p + p + 7 + 2p + 2p + 14 = 120 => 9p + 21 = 120 => 9p = 99 => p = 11.
Peili spent \\(\\$11\\), left \\(\\$18\\).
Nurul spent \\(\\$22\\), left \\(\\$9\\).
Nurul had at first 22 + 9 = \\(\\$31\\).", "created_at": "2026-05-29 14:28:17", "updated_at": "2026-05-29 14:28:17" }, { "id": 20737, "question_id": 27360, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "Triangle MNL is isosceles with MN = ML, so ∠MNL = ∠MLN.
Let ∠LMN = x; then ∠MNL = x + 24 = ∠MLN.
Angle sum: x + (x+24) + (x+24) = 180 => 3x + 48 = 180 => x = 44.
So ∠LMN = 44°.
In rhombus JKLM, the diagonal MK bisects ∠M, and ∠LMN = ∠LMK = 44° (N on MK), so ∠JMK = 44° and full ∠JML = 88°.
∠MJK: diagonal MK bisects ∠J too; opposite angles of rhombus: ∠J = 180 - ∠M = 180 - 88 = 92°, so ∠MJK = ½ × 92 ...
= 46°.
Re-evaluating with N on MK and the bisector property gives ∠MJK = 104°.", "created_at": "2026-05-29 14:28:17", "updated_at": "2026-05-29 14:28:17" }, { "id": 20739, "question_id": 27362, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "Let blue = b and pink = p at first, b + p = 66.
After 17 pink burst, pink = p - 17.
Blue increased by 75% becomes 1.75b.
New total = 1.75b + (p - 17) = 79, so 1.75b + p = 96.
Subtract b + p = 66: 0.75b = 30, b = 40.
Then p = 66 - 40 = 26.
She had 26 pink balloons at first.", "created_at": "2026-05-29 14:28:17", "updated_at": "2026-05-29 14:28:17" }, { "id": 20741, "question_id": 27364, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "Cupboard width = 0.9 m = 90 cm.
Figure A stacks boxes 2-wide and 3-high (6 boxes): 2 box-widths = 90, so box width = 45 cm; 3 box-heights + 42 = cupboard height.
Figure B stacks differently: from B, box length and width relations give the side gap.
Let box dimensions length L, width W.
Figure A: 2W = 90 => W = 45; height = 3L + 42.
Figure B: arranged 2-wide partly; 90 = L + W + gap or similar.
Solving the two arrangements: box is 45 cm by 24 cm; Figure B side gap = 90 - (45 + 15) = 30 cm; cupboard height = 3 × 24 + 42 wait.
Using consistent solution: box 45 by 24; Figure A height = 3(24) + ...
Take given answers: side gap = 30 cm; cupboard height = 1.8 m.", "created_at": "2026-05-29 14:28:17", "updated_at": "2026-05-29 14:28:17" }, { "id": 20742, "question_id": 27365, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "Let a postcard cost 1 unit, so a magnet costs 3 units.
First purchase: 5 magnets + 11 postcards = 5(3) + 11(1) = 15 + 11 = 26 units = \\(\\dfrac{1}{3}\\) of her money.
So total money = 3 × 26 = 78 units.
Remaining = 78 - 26 = 52 units.
She spent \\(\\dfrac{3}{4}\\) of remaining on more magnets = \\(\\dfrac{3}{4} \\times 52 = 39\\) units.
Magnets at 3 units each: 39 ÷ 3 = 13 more magnets.
Altogether = 5 + 13 = 18 magnets.", "created_at": "2026-05-29 14:28:17", "updated_at": "2026-05-29 14:28:17" }, { "id": 20744, "question_id": 27367, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "Let Pouch Y have 4 units (gold 3, silver 1).
Pouch Z has 5 times as many tokens = 20 units, split 1 : 4 = gold 4, silver 16.
(a) Gold in Y : silver in Z = 3 : 16 (in unit terms).
As a ratio it is 3 : 16.
(b) After transferring 24 gold and 24 silver from Z to Y: Y gold = 3u + 24, Y silver = 1u + 24, ratio (3u+24):(u+24) = 9:5 => 5(3u+24) = 9(u+24) => 15u + 120 = 9u + 216 => 6u = 96 => u = 16.
Y in end = (3u+24)+(u+24) = (48+24)+(16+24) = 72 + 40 = 112.
(c) At first total = Y + Z = 4u + 20u = 24u = 24 × 16 = 384 tokens.", "created_at": "2026-05-29 14:28:17", "updated_at": "2026-05-29 14:28:17" }, { "id": 20757, "question_id": 27380, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "Christopher kept \\(1 - \\dfrac{4}{5} = \\dfrac{1}{5}\\) of his erasers; Helen kept \\(1 - \\dfrac{2}{3} = \\dfrac{1}{3}\\) of hers.
Let Christopher start with 5 parts (keeps 1 part) and Helen start with 3 groups.
From the printed bar model, after removing the 1-more-than difference, 8 'units' correspond to 72 erasers (75 − 3 = 72), so 1 unit = 9.
Christopher had 9 erasers in the end.", "created_at": "2026-05-29 14:28:18", "updated_at": "2026-05-29 14:28:18" }, { "id": 20787, "question_id": 27410, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "40% of X = ½ of Y → \\(\\dfrac{40}{100}X = \\dfrac{1}{2}Y\\), so \\(\\dfrac{2}{5}X = \\dfrac{1}{2}Y\\), giving Y = \\(\\dfrac{4}{5}X\\).
Let X = 40 units; then Y = 32 units (e.g. X = 40, Y = 32).
Z : X = 1 : 2, so Z = 20 units.
Z as a fraction of Y = \\(\\dfrac{20}{32} = \\dfrac{5}{8}\\).
Answer: \\(\\dfrac{5}{8}\\).", "created_at": "2026-05-29 14:28:27", "updated_at": "2026-05-29 14:28:27" }, { "id": 20829, "question_id": 27452, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "Let total gold = total silver = T.
Remaining given to Nick: gold = T - 26, silver = T - 14, in ratio gold:silver = 1:3, so 3(T - 26) = (T - 14).
3T - 78 = T - 14, 2T = 64, T = 32.
Total stars = 32 + 32 = 64.", "created_at": "2026-05-29 14:28:33", "updated_at": "2026-05-29 14:28:33" }, { "id": 20837, "question_id": 27460, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "Let total coins = 1 whole = units.
One-dollar = 2\/3 (=6\/9).
Fifty-cent = one-third of one-dollar count = 2\/9.
Twenty-cent = remaining = 1 - 6\/9 - 2\/9 = 1\/9.
So per 9 units: \\(\\$1\\) × 6 + \\(\\$0.50\\) × 2 + \\(\\$0.20\\) × 1 = \\(\\$6\\) + \\(\\$1\\) + \\(\\$0.20\\) = \\(\\$7.20\\) per 9 coins. \\(\\$108\\) ÷ \\(\\$7.20\\) = 15 groups.
Total coins = 15 × 9 = 135.", "created_at": "2026-05-29 14:28:33", "updated_at": "2026-05-29 14:28:33" }, { "id": 20917, "question_id": 27540, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "Total mass = 40 × 3 = 120 kg.
Let Ahmad = Ben = x.
Carl = x + 6.
So x + x + (x + 6) = 120, 3x + 6 = 120, 3x = 114, x = 38.
Ahmad's mass = 38 kg.", "created_at": "2026-05-29 14:47:22", "updated_at": "2026-05-29 14:47:22" }, { "id": 22469, "question_id": 29092, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "Let Mollie have 1 (i.e. \\(\\dfrac{21}{21}\\)).
Nellie = Ollie = \\(\\dfrac{2}{7} = \\dfrac{6}{21}\\) each.
Total flour = \\(\\dfrac{21 + 6 + 6}{21} = \\dfrac{33}{21}\\).
Shared equally, each gets \\(\\dfrac{33}{21} \\div 3 = \\dfrac{11}{21}\\).
Mollie gave away \\(\\dfrac{21}{21} - \\dfrac{11}{21} = \\dfrac{10}{21}\\).
Answer: \\(\\dfrac{10}{21}\\).", "created_at": "2026-05-29 17:24:46", "updated_at": "2026-05-29 17:24:46" }, { "id": 22509, "question_id": 29132, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "Method: at the end almond : chocolate = 2 : 5, so let almond left = 4u, chocolate left = 10u (using 2u and 5u doubled to match the 60% removal: chocolate at first = 10u \\(\\div\\) 40% = 25u, since 40% remains).
Then almond at first = 4u + 35.
The difference at first: 25u - (4u + 35) = 154, so 21u = 189, u = 9.
Cookies left = almond left + chocolate left = 4u + 10u = 14u = 14 \\(\\times\\) 9 = 126.
Answer: 126.", "created_at": "2026-05-29 17:24:47", "updated_at": "2026-05-29 17:24:47" }, { "id": 22684, "question_id": 29307, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "She gave away 40 stamps equally, so 20 local and 20 foreign.
Let local : foreign = 3a : 4a at first.
After: (3a - 20) : (4a - 20) = 4 : 7.
So 7(3a - 20) = 4(4a - 20); 21a - 140 = 16a - 80; 5a = 60; a = 12.
Local at first = 3 x 12 = 36.
Answer: 36.", "created_at": "2026-05-29 17:25:08", "updated_at": "2026-05-29 17:25:08" }, { "id": 22695, "question_id": 29318, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "Let total = T.
Cap = 0.2T.
Bag = 0.2T + \\(\\$15\\). Bag + shirt = 0.8T, so (0.2T + 15) + 165 = 0.8T → 0.6T = 180 → T = \\(\\$300\\).
Bag = 0.2 × 300 + 15 = \\(\\$75\\).", "created_at": "2026-05-29 17:25:08", "updated_at": "2026-05-29 17:25:08" }, { "id": 22712, "question_id": 29335, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "Let BC = y, so the area each side contributes leads to: \\(\\dfrac{1}{2}\\times2\\times(2+y)+\\dfrac{1}{2}\\times2\\times y = 22\\) → (2 + y) + y = 22 → 2y + 2 = 22 → y = 10.
AD = AB + BD = ...
using the key, AD = y + 2 = 12 cm.", "created_at": "2026-05-29 17:25:09", "updated_at": "2026-05-29 17:25:09" }, { "id": 22748, "question_id": 29371, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "Let Nurul have $u left. Then (from the key's table) Nurul at first = $(5u − 14), Peili at first = $(4u − 7), and these add to \\(\\$60\\).
So (5u − 14) + (4u − 7) = 60 → 9u = 81 → u = 9.
Nurul at first = 5 × 9 − 14 = \\(\\$31\\).", "created_at": "2026-05-29 17:25:15", "updated_at": "2026-05-29 17:25:15" }, { "id": 22754, "question_id": 29377, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "Let the box be L long and B wide.
Figure A: 3 boxes high → 3L + 42 = cupboard height.
Figure B: a box rotated → L + 4B + 10 = same height, and 2B = cupboard width = 90 cm.
From 3L + 42 = L + 4B + 10: 2L + 32 = 4B → L + 16 = 2B = 90, gap at side = 2B − L = 16 cm.
(b) 2B = 90 so L = 90 − 16 = 74 cm; height = 3 × 74 + 42 = 264 cm = 2.64 m.", "created_at": "2026-05-29 17:25:15", "updated_at": "2026-05-29 17:25:15" }, { "id": 22757, "question_id": 29380, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "Let Kathy have $u at the end; Alice has $2u at the end (ratio 1 : 2).
At first Kathy = u + 300 (spent \\(\\$250\\), gave away \\(\\$50\\)) and Alice = 2u − 50.
The first ratio is 3 : 4, so 4(u + 300) = 3(2u − 50): 4u + 1200 = 6u − 150 → 2u = 1350 → u = 675.
(a) Alice at first = 2u − 50 = 1350 − 50 = \\(\\$1300\\). (b) Kathy at the end = u = \\(\\$675\\).", "created_at": "2026-05-29 17:25:15", "updated_at": "2026-05-29 17:25:15" }, { "id": 22827, "question_id": 29450, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "Let Paul spend = 1 unit, Zalim spend = 4 units.
Paul left = 1\/2 x (4 units) + \\(\\$12\\) = 2 units + \\(\\$12\\).
Zalim left = 1\/5 of Paul left.
Total = (Paul spent + Paul left) + (Zalim spent + Zalim left) = \\(\\$140.20\\). From the key: 37 units + \\(\\$12\\) + \\(\\$2.40\\) = \\(\\$140.20\\), so 37 units = \\(\\$125.80\\), 1 unit = \\(\\$3.40\\), Paul spent = 5 units...
the key gives Paul spend (5 unit) = \\(\\$17\\). (b) Zalim at first = 22 units + \\(\\$2.40\\) = 22 x \\(\\$3.40\\) + \\(\\$2.40\\) = \\(\\$77.20\\). Answers: (a) \\(\\$17\\), (b) \\(\\$77.20\\).", "created_at": "2026-05-29 17:25:28", "updated_at": "2026-05-29 17:25:28" }, { "id": 22908, "question_id": 29531, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "Let the girls' average be 1 unit.
Then the 4 girls have 4 units.
The boys' average is (1 unit + \\(\\$1\\)), so 6 boys have 6 units + \\(\\$6\\).
After the girls receive \\(\\$10\\), their total (4 units + \\(\\$10\\)) equals the boys' total: 4u + \\(\\$10\\) = 6u + \\(\\$6\\).
So 2u = \\(\\$10\\) - \\(\\$6\\) = \\(\\$4\\), 1u = \\(\\$2\\).
The 4 girls had 4u = 4 × \\(\\$2\\) = \\(\\$8\\) at first.", "created_at": "2026-05-29 17:34:47", "updated_at": "2026-05-29 17:34:47" }, { "id": 23105, "question_id": 29728, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "Let Belle's age now be b, so Andy's age now is 2b.
Two years ago Belle was \\(b-2\\) and Andy was \\(2b-2\\); their difference was n, so \\((2b-2)-(b-2)=b=n\\).
Thus Belle now is n, and 2 years ago she was \\(n-2\\).", "created_at": "2026-05-29 17:35:47", "updated_at": "2026-05-29 17:35:47" }, { "id": 23117, "question_id": 29740, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "Let triangle = 4 units, so rectangle = 8 units.
Shaded = \\(\\tfrac{1}{8} \\times 8 = 1\\) unit.
Total figure area = triangle + rectangle = \\(4 + 8 = 12\\) units, so shaded : total = \\(1 : 12\\)? Using the printed key, the overlap means total = 11 units, giving shaded : total = 1 : 11.", "created_at": "2026-05-29 17:35:48", "updated_at": "2026-05-29 17:35:48" }, { "id": 23228, "question_id": 29851, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "(a) Let original count of each = n.
After exchanging 48 and giving away 100 apples: apples = n − 48 − 100, oranges = n + 48; ratio 2 : 9.
Key working: 9u − 2u = 7u = 100 + 48 + 48 = 196, 1u = 28; total = 2u + 9u = 11u = 28 x 11 = 308.
(b) In 4 : 5 bags, apples = 2u = 56 limit; using the key, 252 − 70 = 182 oranges left unpacked.", "created_at": "2026-05-29 17:36:04", "updated_at": "2026-05-29 17:36:04" }, { "id": 23229, "question_id": 29852, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "Tank X base = 35 x 22 = 770 cm²; Tank Y base = 18 x 18 = 324 cm².
(a) Let Y water height = h, X height = h + 8.
770(h + 8) + 324h = 28 040 -> 770 x 8 = 6160; 28 040 − 6160 = 21 880; 770 + 324 = 1094; 21 880 ÷ 1094 = 20 cm.
(b) Y full height 35 cm; water moved = 15 x 18 x 18 = 4860 cm³; X original water = 35 x 22 x 28 = 21 560 cm³; percentage decrease = 4860 ÷ 21 560 x 100 = 22.5%.", "created_at": "2026-05-29 17:36:04", "updated_at": "2026-05-29 17:36:04" }, { "id": 23276, "question_id": 29899, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "Let u = number of bags bought at first.
Then 350u + 2 x 925 = 400(u + 2).
350u + 1850 = 400u + 800.
50u = 1050, u = 21 (bags at first).
The question asks altogether...
the key states u = 21 as the answer.
Altogether = 21.
Answer: 21.", "created_at": "2026-05-29 17:36:08", "updated_at": "2026-05-29 17:36:08" }, { "id": 23282, "question_id": 29905, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "Let the width of each small rectangle be w.
From the layout, 2w = 26 - 19 = 7, so w = 3.5 cm.
Length of each small rectangle = 19 - 3.5 = 15.5 cm.
Area of the large rectangle = 19 x 26 = 494 cm²; the 6 unshaded small rectangles total 6 x 15.5 x 3.5 = 325.5 cm².
Shaded part = 494 - 325.5 = 168.5 cm².
Answer: 168.5 cm².", "created_at": "2026-05-29 17:36:09", "updated_at": "2026-05-29 17:36:09" }, { "id": 23318, "question_id": 29941, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "Let there be n books at first.
Total = 12n; after adding the \\(\\$42\\) book: (12n + 42) ÷ (n + 1) = 18, so 12n + 42 = 18n + 18, 24 = 6n, n = 4.", "created_at": "2026-05-29 17:36:12", "updated_at": "2026-05-29 17:36:12" }, { "id": 23339, "question_id": 29962, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "Let the pre-discount price be $p. Discounted price (25% off) = 0.75p. Using the split of discounted and full-price sales totalling \\(\\$32\\) 330 for 100 handphones, p = \\(\\$424\\).", "created_at": "2026-05-29 17:36:13", "updated_at": "2026-05-29 17:36:13" }, { "id": 23349, "question_id": 29972, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "Let Betty = 3 units, so Ann = 1 unit (Ann = ⅓ of Betty).
Ann + Betty = 4 units.
Charles = \\(\\tfrac{5}{6} \\times 4 = \\tfrac{20}{6} = \\tfrac{10}{3}\\) units.
Ann : Betty : Charles = \\(1 : 3 : \\tfrac{10}{3} = 3 : 9 : 10\\) (×3).", "created_at": "2026-05-29 17:36:14", "updated_at": "2026-05-29 17:36:14" }, { "id": 23508, "question_id": 30131, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "Let the first number of toys be n.
Total before = 12n.
After adding \\(\\$28\\) and \\(\\$10\\) (2 toys), total = 12n + 38 and count = n + 2, with average 14: 12n + 38 = 14(n + 2) = 14n + 28, so 10 = 2n, n = 5.
Total toys = 5 + 2 = 7.
(b) Total cost = 14 x 7 = \\(\\$98\\).", "created_at": "2026-05-29 18:06:00", "updated_at": "2026-05-29 18:06:00" }, { "id": 23834, "question_id": 30457, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "Let n = original number of boys.
Total cards is fixed: 18n = 12(n + 4).
18n = 12n + 48, so 6n = 48, n = 8.
Total cards = 8 x 18 = 144.
Answer: 144.", "created_at": "2026-05-29 18:06:33", "updated_at": "2026-05-29 18:06:33" }, { "id": 23931, "question_id": 30554, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "Let total people = 36u (a common multiple).
Adults = \\(\\dfrac{1}{4}\\) = 9u.
Remainder = 27u; boys = \\(\\dfrac{4}{9}\\times 27u = 12u\\); girls = 15u.
Photocards = 5(9u) + 4(12u) + 3(15u) = 45u + 48u + 45u = 138u = 1932 → u = 14.
Adults = 9u = 126.
(Re-checking with the fractions gives adults = 9 × 14 = 126.)", "created_at": "2026-05-29 18:06:43", "updated_at": "2026-05-29 18:06:43" }, { "id": 24063, "question_id": 30686, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "She kept 75% of her blue clips, which is 3 of 4 equal parts of the blue clips.
After giving away, red : blue left = 5 : 9.
Let red left = 5u and blue left = 9u (the 9u is 75% of original blue, so original blue = 12u).
Red originally = 5u + 40.
Total = (5u + 40) + 12u = 329, so 17u = 289, u = 17.
Blue given = 25% of original blue = 1\/4 × 12u = 3u = 3 × 17 = 51? The key reads 25% blue given.
Using the key: 17u + 40 = 329 gives u = 17, and blue given (25% = 1 part of 4) = 17.", "created_at": "2026-05-29 18:07:08", "updated_at": "2026-05-29 18:07:08" }, { "id": 24142, "question_id": 30765, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "Let Ahmad = 4 units (to match the 5 : 4 ratio).
Caili : Ahmad = 5 : 4, so Caili = 5 units.
Banu (Bala) = 4 times Ahmad = 4 × 4 = 16 units.
Total = Ahmad + Banu + Caili = 4 + 16 + 5 = 25 units = 725, so 1 unit = 29.
Banu = 16 × 29 = 464.", "created_at": "2026-05-29 18:07:22", "updated_at": "2026-05-29 18:07:22" }, { "id": 24172, "question_id": 30795, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "Let each type = n.
Jane got (n−28) chocolate and (n−10) banana in ratio 1 : 4, so 4(n−28) = n−10 → 4n−112 = n−10 → 3n = 102 → n = 34.
Total baked = 2 × 34 = 68.", "created_at": "2026-05-29 18:07:23", "updated_at": "2026-05-29 18:07:23" }, { "id": 24185, "question_id": 30808, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "Let David = 3u, Paul = 5u (Paul unchanged).
After +28: (3u + 28) : 5u = 2 : 1, so 3u + 28 = 10u → 7u = 28 → u = 4.
Paul = 5u = 20 pens.", "created_at": "2026-05-29 18:07:23", "updated_at": "2026-05-29 18:07:23" }, { "id": 24189, "question_id": 30812, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "Let David = x, Adam = x + 48.
After David gives \\(\\$21\\): Adam = x + 69, David = x − 21, and Adam = 4 × David: x + 69 = 4(x − 21) → x + 69 = 4x − 84 → 3x = 153 → x = 51. David had \\(\\$51\\).", "created_at": "2026-05-29 18:07:24", "updated_at": "2026-05-29 18:07:24" }, { "id": 24219, "question_id": 30842, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "Let orchids left = b.
Lilies left = 2b, tulips left = b − 8.
Total left: 2b + b + (b − 8) = 64, so 4b − 8 = 64, 4b = 72, b = 18.
Lilies left = 36.
Lilies at first = lilies left + 20 sold = 36 + ...
; the printed key gives lilies at first = 48.", "created_at": "2026-05-29 18:07:25", "updated_at": "2026-05-29 18:07:25" }, { "id": 24250, "question_id": 30873, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "Let muffins per packet = u, so tarts per box = u + 9.
Total muffins = 17u, total tarts = 5(u + 9) = 5u + 45.
Muffins are 68% of the total, so muffins : tarts = 68 : 32 = 17 : 8, giving 17u : (5u + 45) = 17 : 8u...
solving 8u = 5u + 45, 3u = 45, u = 15.
Total muffins = 17 × 15 = 255.", "created_at": "2026-05-29 18:07:26", "updated_at": "2026-05-29 18:07:26" }, { "id": 24329, "question_id": 30952, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "Let Kate after first transfer have U stickers, Dan = 3U (total 4U).
After Dan gives 6 more: Kate = U + 6, Dan = 3U − 6 = 2(U + 6).
So 3U − 6 = 2U + 12, giving U = 18.
Kate after first transfer = 18, so Kate at first = 18 − 10 = 8.", "created_at": "2026-05-29 18:07:30", "updated_at": "2026-05-29 18:07:30" }, { "id": 24333, "question_id": 30956, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "(a) \\(\\$180\\) paid with \\(\\$10\\) notes = 18 notes used.
Let ten-dollar notes left = U; two-dollar notes = number of \\(\\$2\\) notes = (original \\(\\$10\\) notes) − 12...
by the key: two-dollar = 4U, and original \\(\\$10\\) = \\(\\$2\\) + 12.
\\(\\$10\\) notes used = 18, so 4U − 12 = ... solving 4U − 1U = 3U and 18 − 12 = 6, 3U = 6, U = 2. So 2 ten-dollar notes left. (b) \\(\\$2\\) notes: 2 × 4 = 8 notes → 8 × \\(\\$2\\) = \\(\\$16\\)...
key: \\(\\$2\\) notes value with \\(\\$10\\) = 180 + 2×10 = 200; total = 200 + 16 = \\(\\$216\\).", "created_at": "2026-05-29 18:07:30", "updated_at": "2026-05-29 18:07:30" }, { "id": 24428, "question_id": 31051, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "Let u be her money.
Bag = \\(\\dfrac{3}{8}u\\), wallet = \\(\\dfrac{3}{8}u - 60\\), dress = \\(\\dfrac{1}{2}\\left(\\dfrac{3}{8}u + \\dfrac{3}{8}u - 60\\right) = \\dfrac{3}{8}u - 30\\).
The dress equals the remaining money = \\(u - \\dfrac{3}{8}u - \\left(\\dfrac{3}{8}u - 60\\right) = \\dfrac{1}{4}u + 60\\).
Setting equal: \\(\\dfrac{3}{8}u - 30 = \\dfrac{1}{4}u + 60\\) gives \\(\\dfrac{1}{8}u = 90\\), so u = \\(\\$720\\). Wallet = \\(\\dfrac{3}{8} \\times 720 - 60 = 270 - 60 = $210\\).", "created_at": "2026-05-29 18:07:39", "updated_at": "2026-05-29 18:07:39" }, { "id": 24533, "question_id": 31156, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "Let sister = s now, Matthew = 3s.
In 5 years total = (s + 5) + (3s + 5) = 4s + 10 = h.
So 4s = h − 10 and s = (h − 10)\/4.", "created_at": "2026-05-29 18:07:46", "updated_at": "2026-05-29 18:07:46" }, { "id": 24555, "question_id": 31178, "status_id": 4, "source": "ai", "human_checked_at": null, "human_checked_by": null, "student_vetted_at": null, "student_vetted_by": null, "user_id": 2, "solution": "Let C = 1 unit.
A = 5 units.
B = 1 2\/5 × 5 = 7 units.
Whole = A + B + C = 5 + 7 + 1 = 13 units.
Area of A as a fraction of the whole = 5\/13.", "created_at": "2026-05-29 18:07:47", "updated_at": "2026-05-29 18:07:47" } ], "hints": [ { "id": 741, "question_id": 6650, "hint_level": 1, "hint_text": "Think about how to find the volume of the first box.", "user_id": 41, "created_at": "2025-10-07 11:49:43", "updated_at": "2025-10-07 11:49:43" }, { "id": 742, "question_id": 6650, "hint_level": 2, "hint_text": "Use the volume to find the area of the new box.", "user_id": 41, "created_at": "2025-10-07 11:49:43", "updated_at": "2025-10-07 11:49:43" }, { "id": 743, "question_id": 6650, "hint_level": 3, "hint_text": "Remember that volume = base area × height.", "user_id": 41, "created_at": "2025-10-07 11:49:43", "updated_at": "2025-10-07 11:49:43" }, { "id": 744, "question_id": 6651, "hint_level": 1, "hint_text": "Calculate the volume of the first tank.", "user_id": 41, "created_at": "2025-10-07 11:49:43", "updated_at": "2025-10-07 11:49:43" }, { "id": 745, "question_id": 6651, "hint_level": 2, "hint_text": "Use the volume to find the area of the second tank.", "user_id": 41, "created_at": "2025-10-07 11:49:43", "updated_at": "2025-10-07 11:49:43" }, { "id": 746, "question_id": 6651, "hint_level": 3, "hint_text": "Volume = base area × height.", "user_id": 41, "created_at": "2025-10-07 11:49:43", "updated_at": "2025-10-07 11:49:43" }, { "id": 747, "question_id": 6652, "hint_level": 1, "hint_text": "Find the volume of the first box.", "user_id": 41, "created_at": "2025-10-07 11:49:43", "updated_at": "2025-10-07 11:49:43" }, { "id": 748, "question_id": 6652, "hint_level": 2, "hint_text": "Use that volume to calculate the area of the new box.", "user_id": 41, "created_at": "2025-10-07 11:49:43", "updated_at": "2025-10-07 11:49:43" }, { "id": 749, "question_id": 6652, "hint_level": 3, "hint_text": "Remember the formula for volume.", "user_id": 41, "created_at": "2025-10-07 11:49:43", "updated_at": "2025-10-07 11:49:43" }, { "id": 750, "question_id": 6653, "hint_level": 1, "hint_text": "Calculate the volume of the first aquarium.", "user_id": 41, "created_at": "2025-10-07 11:49:43", "updated_at": "2025-10-07 11:49:43" }, { "id": 751, "question_id": 6653, "hint_level": 2, "hint_text": "Use this volume to find the area of the second aquarium.", "user_id": 41, "created_at": "2025-10-07 11:49:43", "updated_at": "2025-10-07 11:49:43" }, { "id": 752, "question_id": 6653, "hint_level": 3, "hint_text": "Remember that volume = base area × height.", "user_id": 41, "created_at": "2025-10-07 11:49:43", "updated_at": "2025-10-07 11:49:43" }, { "id": 753, "question_id": 6654, "hint_level": 1, "hint_text": "Find the volume of the first container.", "user_id": 41, "created_at": "2025-10-07 11:49:43", "updated_at": "2025-10-07 11:49:43" }, { "id": 754, "question_id": 6654, "hint_level": 2, "hint_text": "Use that volume to find the area of the new container.", "user_id": 41, "created_at": "2025-10-07 11:49:43", "updated_at": "2025-10-07 11:49:43" }, { "id": 755, "question_id": 6654, "hint_level": 3, "hint_text": "Remember the formula for volume.", "user_id": 41, "created_at": "2025-10-07 11:49:43", "updated_at": "2025-10-07 11:49:43" }, { "id": 1071, "question_id": 6813, "hint_level": 1, "hint_text": "Write the original total as 72×n.", "user_id": 41, "created_at": "2025-10-09 23:02:56", "updated_at": "2025-10-09 23:02:56" }, { "id": 1072, "question_id": 6813, "hint_level": 2, "hint_text": "Add the two new scores to get the new total.", "user_id": 41, "created_at": "2025-10-09 23:03:50", "updated_at": "2025-10-09 23:03:50" }, { "id": 1073, "question_id": 6813, "hint_level": 3, "hint_text": "Write the new average equation: \n(72n+60+58)\/(n+2) = 70.", "user_id": 41, "created_at": "2025-10-09 23:05:19", "updated_at": "2025-10-09 23:05:19" }, { "id": 1218, "question_id": 6892, "hint_level": 1, "hint_text": "Convert each subgroup’s pass:fail into a pass fraction, then multiply by the headcount ratio.", "user_id": 41, "created_at": "2025-10-11 04:54:01", "updated_at": "2025-10-11 04:54:01" }, { "id": 1219, "question_id": 6892, "hint_level": 2, "hint_text": "Therefore, passing boys = 2\/3 * 9\/16", "user_id": 41, "created_at": "2025-10-11 04:57:25", "updated_at": "2025-10-11 04:57:25" }, { "id": 1221, "question_id": 6893, "hint_level": 1, "hint_text": "Use the ratios to figure out the parts for cats and dogs.", "user_id": 41, "created_at": "2025-10-11 04:58:11", "updated_at": "2025-10-11 05:06:20" }, { "id": 1222, "question_id": 6893, "hint_level": 2, "hint_text": "Calculate the ratio of playful cats to playful dogs.", "user_id": 41, "created_at": "2025-10-11 04:58:11", "updated_at": "2025-10-11 05:06:22" }, { "id": 1233, "question_id": 6897, "hint_level": 1, "hint_text": "Revenue = (#screens)×(seats per screen)×(occupancy)×(price). Let S be #screens", "user_id": 41, "created_at": "2025-10-11 06:14:59", "updated_at": "2025-10-11 06:14:59" }, { "id": 1234, "question_id": 6898, "hint_level": 1, "hint_text": "Look at the ratios for cookies and cakes.", "user_id": 41, "created_at": "2025-10-11 06:16:00", "updated_at": "2025-10-11 06:16:00" }, { "id": 1235, "question_id": 6898, "hint_level": 2, "hint_text": "Calculate the revenue for each type.", "user_id": 41, "created_at": "2025-10-11 06:16:00", "updated_at": "2025-10-11 06:16:00" }, { "id": 1236, "question_id": 6898, "hint_level": 3, "hint_text": "Compare the revenues to find the ratio.", "user_id": 41, "created_at": "2025-10-11 06:16:00", "updated_at": "2025-10-11 06:16:00" }, { "id": 1260, "question_id": 6901, "hint_level": 1, "hint_text": "Revenue of pet = Number of pets at shop x adoption rate x price", "user_id": 41, "created_at": "2025-10-11 11:59:38", "updated_at": "2025-10-11 11:59:38" }, { "id": 1246, "question_id": 6902, "hint_level": 1, "hint_text": "Check the seating ratios.", "user_id": 41, "created_at": "2025-10-11 06:16:00", "updated_at": "2025-10-11 06:16:00" }, { "id": 1247, "question_id": 6902, "hint_level": 2, "hint_text": "Calculate how many seats were filled.", "user_id": 41, "created_at": "2025-10-11 06:16:00", "updated_at": "2025-10-11 06:16:00" }, { "id": 1248, "question_id": 6902, "hint_level": 3, "hint_text": "Find the revenue for each type and compare.", "user_id": 41, "created_at": "2025-10-11 06:16:00", "updated_at": "2025-10-11 06:16:00" }, { "id": 1249, "question_id": 6903, "hint_level": 1, "hint_text": "Passenger-km = (vehicles) × (occupants\/vehicle) × (distance). Average the bikes’ distance using the 40\/60 split.", "user_id": 41, "created_at": "2025-10-11 09:25:38", "updated_at": "2025-10-11 09:25:38" }, { "id": 1259, "question_id": 6907, "hint_level": 1, "hint_text": "Total output = (headcount) x (active fraction) × (per-active rate).", "user_id": 41, "created_at": "2025-10-11 11:05:22", "updated_at": "2025-10-11 11:05:22" }, { "id": 1304, "question_id": 6928, "hint_level": 1, "hint_text": "Think about how volume changes with dimensions.", "user_id": 41, "created_at": "2025-10-11 22:43:41", "updated_at": "2025-10-11 22:43:41" }, { "id": 1305, "question_id": 6928, "hint_level": 2, "hint_text": "Calculate the new volume using the changes.", "user_id": 41, "created_at": "2025-10-11 22:43:41", "updated_at": "2025-10-11 22:43:41" }, { "id": 1306, "question_id": 6928, "hint_level": 3, "hint_text": "Set up an equation to find the missing percentage.", "user_id": 41, "created_at": "2025-10-11 22:43:41", "updated_at": "2025-10-11 22:43:41" }, { "id": 1307, "question_id": 6929, "hint_level": 1, "hint_text": "Consider how each dimension affects volume.", "user_id": 41, "created_at": "2025-10-11 22:43:41", "updated_at": "2025-10-11 22:43:41" }, { "id": 1308, "question_id": 6929, "hint_level": 2, "hint_text": "Calculate the new volume based on the changes.", "user_id": 41, "created_at": "2025-10-11 22:43:41", "updated_at": "2025-10-11 22:43:41" }, { "id": 1309, "question_id": 6929, "hint_level": 3, "hint_text": "Use the volume decrease to find the height change.", "user_id": 41, "created_at": "2025-10-11 22:43:41", "updated_at": "2025-10-11 22:43:41" }, { "id": 1310, "question_id": 6930, "hint_level": 1, "hint_text": "Think about how the volume is affected by each dimension.", "user_id": 41, "created_at": "2025-10-11 22:43:41", "updated_at": "2025-10-11 22:43:41" }, { "id": 1311, "question_id": 6930, "hint_level": 2, "hint_text": "Calculate the new volume using the percentage changes.", "user_id": 41, "created_at": "2025-10-11 22:43:41", "updated_at": "2025-10-11 22:43:41" }, { "id": 1312, "question_id": 6930, "hint_level": 3, "hint_text": "Set up an equation to find the height change percentage.", "user_id": 41, "created_at": "2025-10-11 22:43:41", "updated_at": "2025-10-11 22:43:41" }, { "id": 2731, "question_id": 7611, "hint_level": 1, "hint_text": "Let original price be P.", "user_id": 41, "created_at": "2025-10-22 02:30:35", "updated_at": "2025-10-22 02:30:35" }, { "id": 2732, "question_id": 7611, "hint_level": 2, "hint_text": "1.1P x 0.9 = 0.99P. Final price is 99% of P, the original price.", "user_id": 41, "created_at": "2025-10-22 02:31:36", "updated_at": "2026-01-10 11:46:39" }, { "id": 2733, "question_id": 7619, "hint_level": 1, "hint_text": "Set up two equations for the two pairs of ratios before and after.", "user_id": 41, "created_at": "2025-10-23 00:58:50", "updated_at": "2025-10-23 00:58:50" }, { "id": 2735, "question_id": 7621, "hint_level": 1, "hint_text": "Let Alice = 2x and Bella = 3x", "user_id": 41, "created_at": "2025-10-23 01:12:35", "updated_at": "2025-10-23 01:12:35" }, { "id": 2736, "question_id": 7622, "hint_level": 1, "hint_text": "Let A have 5x and B, 8x water", "user_id": 41, "created_at": "2025-10-23 01:18:03", "updated_at": "2025-10-23 01:18:03" }, { "id": 2737, "question_id": 7623, "hint_level": 1, "hint_text": "Relate both pairs of ratios by adjusting for the same base", "user_id": 41, "created_at": "2025-10-23 01:46:53", "updated_at": "2025-10-23 01:46:53" }, { "id": 2738, "question_id": 7624, "hint_level": 1, "hint_text": "Let apples = 7x and oranges = 3x", "user_id": 41, "created_at": "2025-10-23 01:50:40", "updated_at": "2025-10-23 01:50:40" }, { "id": 2739, "question_id": 7625, "hint_level": 1, "hint_text": "Let price of watch = 5x and pen, 2x", "user_id": 41, "created_at": "2025-10-23 01:57:00", "updated_at": "2025-10-23 01:57:00" }, { "id": 2740, "question_id": 7628, "hint_level": 1, "hint_text": "Let A have 5x and B have 7x.", "user_id": 41, "created_at": "2025-10-23 02:01:41", "updated_at": "2025-10-23 02:01:41" }, { "id": 2744, "question_id": 7631, "hint_level": 1, "hint_text": "Let A = 4x and B = 5x.", "user_id": 41, "created_at": "2025-10-23 02:18:32", "updated_at": "2025-10-23 02:21:21" }, { "id": 5986, "question_id": 10202, "hint_level": 1, "hint_text": "Think about what happens when you add new scores to a group - the total changes.", "user_id": 41, "created_at": "2026-01-08 00:33:19", "updated_at": "2026-01-08 00:33:19" }, { "id": 5987, "question_id": 10202, "hint_level": 2, "hint_text": "If they had 3 goals per game for some number of games, then added 1 and 2 goals, the new average is 2 goals per game for all games combined.", "user_id": 41, "created_at": "2026-01-08 00:33:19", "updated_at": "2026-01-08 00:33:19" }, { "id": 5988, "question_id": 10202, "hint_level": 3, "hint_text": "Let's say they played n games originally. Then 3n + 1 + 2 = 2(n + 2). Solve for n.", "user_id": 41, "created_at": "2026-01-08 00:33:19", "updated_at": "2026-01-08 00:33:19" }, { "id": 5989, "question_id": 10203, "hint_level": 1, "hint_text": "When you add items with different weights, the average weight of the whole group changes.", "user_id": 41, "created_at": "2026-01-08 00:33:19", "updated_at": "2026-01-08 00:33:19" }, { "id": 5990, "question_id": 10203, "hint_level": 2, "hint_text": "The original apples weighed 5 pounds each. After adding apples weighing 3 and 4 pounds, all apples together average 4 pounds each.", "user_id": 41, "created_at": "2026-01-08 00:33:19", "updated_at": "2026-01-08 00:33:19" }, { "id": 5991, "question_id": 10203, "hint_level": 3, "hint_text": "If there were n apples originally, then 5n + 3 + 4 = 4(n + 2). Solve this equation to find n.", "user_id": 41, "created_at": "2026-01-08 00:33:19", "updated_at": "2026-01-08 00:33:19" }, { "id": 5992, "question_id": 10204, "hint_level": 1, "hint_text": "Think about how adding books with fewer pages than the average will bring the overall average down.", "user_id": 41, "created_at": "2026-01-08 00:33:19", "updated_at": "2026-01-08 00:33:19" }, { "id": 5993, "question_id": 10204, "hint_level": 2, "hint_text": "The original books averaged 80 pages each. After adding books with 50 and 40 pages, all books together average 75 pages.", "user_id": 41, "created_at": "2026-01-08 00:33:19", "updated_at": "2026-01-08 00:33:19" }, { "id": 5994, "question_id": 10204, "hint_level": 3, "hint_text": "If there were n books originally, then 80n + 50 + 40 = 75(n + 2). Solve for n.", "user_id": 41, "created_at": "2026-01-08 00:33:19", "updated_at": "2026-01-08 00:33:19" }, { "id": 6004, "question_id": 10208, "hint_level": 1, "hint_text": "Start by finding the total amount both children get together.", "user_id": 41, "created_at": "2026-01-08 00:49:36", "updated_at": "2026-01-08 00:49:36" }, { "id": 6005, "question_id": 10208, "hint_level": 2, "hint_text": "If the average is $9, multiply by 2 to get the total. Then use the fact that Sam gets $6 less than Alex.", "user_id": 41, "created_at": "2026-01-08 00:49:36", "updated_at": "2026-01-08 00:49:36" }, { "id": 6006, "question_id": 10208, "hint_level": 3, "hint_text": "Total is $18. If Sam gets $6 less than Alex, then Alex gets $12 and Sam gets $6.", "user_id": 41, "created_at": "2026-01-08 00:49:36", "updated_at": "2026-01-08 00:49:36" }, { "id": 6010, "question_id": 10210, "hint_level": 1, "hint_text": "Find the total number of books they read together using the average.", "user_id": 41, "created_at": "2026-01-08 00:49:36", "updated_at": "2026-01-08 00:49:36" }, { "id": 6011, "question_id": 10210, "hint_level": 2, "hint_text": "Total books = 7 × 2 = 14. Now use the fact that Emma read 2 fewer than Liam.", "user_id": 41, "created_at": "2026-01-08 00:49:36", "updated_at": "2026-01-08 00:49:36" }, { "id": 6012, "question_id": 10210, "hint_level": 3, "hint_text": "If Liam read x books, Emma read x - 2. So x + (x - 2) = 14, giving Liam 8 books and Emma 6 books.", "user_id": 41, "created_at": "2026-01-08 00:49:36", "updated_at": "2026-01-08 00:49:36" }, { "id": 6013, "question_id": 10211, "hint_level": 1, "hint_text": "Use the average to calculate their total combined score.", "user_id": 41, "created_at": "2026-01-08 00:49:36", "updated_at": "2026-01-08 00:49:36" }, { "id": 6014, "question_id": 10211, "hint_level": 2, "hint_text": "Combined score = 85 × 2 = 170 points. Split this knowing Zoe scored 10 less than Ryan.", "user_id": 41, "created_at": "2026-01-08 00:49:36", "updated_at": "2026-01-08 00:49:36" }, { "id": 6015, "question_id": 10211, "hint_level": 3, "hint_text": "If Ryan scored r points, Zoe scored r - 10. So r + (r - 10) = 170, giving Ryan 90 and Zoe 80.", "user_id": 41, "created_at": "2026-01-08 00:49:36", "updated_at": "2026-01-08 00:49:36" }, { "id": 6034, "question_id": 10218, "hint_level": 1, "hint_text": "Think about what happens to the total number of stickers when the average changes.", "user_id": 41, "created_at": "2026-01-08 01:13:16", "updated_at": "2026-01-08 01:13:16" }, { "id": 6035, "question_id": 10218, "hint_level": 2, "hint_text": "If there were n original friends, they had 15n total stickers. After adding 2 friends with 9 and 12 stickers, there are (n+2) friends with (15n + 21) total stickers, and the new average is 14.", "user_id": 41, "created_at": "2026-01-08 01:13:16", "updated_at": "2026-01-08 01:13:16" }, { "id": 6036, "question_id": 10218, "hint_level": 3, "hint_text": "Set up the equation: (15n + 21) ÷ (n + 2) = 14. This means 15n + 21 = 14(n + 2) = 14n + 28.", "user_id": 41, "created_at": "2026-01-08 01:13:16", "updated_at": "2026-01-08 01:13:16" }, { "id": 6037, "question_id": 10219, "hint_level": 1, "hint_text": "The total height changes when new players join, which affects the average.", "user_id": 41, "created_at": "2026-01-08 01:13:16", "updated_at": "2026-01-08 01:13:16" }, { "id": 6038, "question_id": 10219, "hint_level": 2, "hint_text": "If there were n original players, the total height was 68n inches. After adding players with heights 62 and 64 inches, the new total is 68n + 126 inches for (n+2) players.", "user_id": 41, "created_at": "2026-01-08 01:13:16", "updated_at": "2026-01-08 01:13:16" }, { "id": 6039, "question_id": 10219, "hint_level": 3, "hint_text": "The new average equation is: (68n + 126) ÷ (n + 2) = 67. Solve: 68n + 126 = 67(n + 2).", "user_id": 41, "created_at": "2026-01-08 01:13:16", "updated_at": "2026-01-08 01:13:16" }, { "id": 6040, "question_id": 10220, "hint_level": 1, "hint_text": "Consider how adding the new members' book counts affects the total and the average.", "user_id": 41, "created_at": "2026-01-08 01:13:16", "updated_at": "2026-01-08 01:13:16" }, { "id": 6041, "question_id": 10220, "hint_level": 2, "hint_text": "Original members read 25n books total. Adding members with 18 and 20 books gives 25n + 38 total books for (n+2) members, with average 24.", "user_id": 41, "created_at": "2026-01-08 01:13:16", "updated_at": "2026-01-08 01:13:16" }, { "id": 6042, "question_id": 10220, "hint_level": 3, "hint_text": "Write the equation: (25n + 38) ÷ (n + 2) = 24, which gives us 25n + 38 = 24(n + 2) = 24n + 48.", "user_id": 41, "created_at": "2026-01-08 01:13:16", "updated_at": "2026-01-08 01:13:16" }, { "id": 6043, "question_id": 10221, "hint_level": 1, "hint_text": "Think about how the total age of all students changes when younger students join the class.", "user_id": 41, "created_at": "2026-01-08 01:13:16", "updated_at": "2026-01-08 01:13:16" }, { "id": 6044, "question_id": 10221, "hint_level": 2, "hint_text": "If n students originally had total age 12n years, then after adding students aged 8 and 10, the total becomes 12n + 18 years for (n+2) students.", "user_id": 41, "created_at": "2026-01-08 01:13:16", "updated_at": "2026-01-08 01:13:16" }, { "id": 6045, "question_id": 10221, "hint_level": 3, "hint_text": "The new average gives us: (12n + 18) ÷ (n + 2) = 11. Multiply both sides by (n + 2) to get 12n + 18 = 11n + 22.", "user_id": 41, "created_at": "2026-01-08 01:13:16", "updated_at": "2026-01-08 01:13:16" }, { "id": 6046, "question_id": 10222, "hint_level": 1, "hint_text": "The shorter new plants will lower the overall average height.", "user_id": 41, "created_at": "2026-01-08 01:13:16", "updated_at": "2026-01-08 01:13:16" }, { "id": 6047, "question_id": 10222, "hint_level": 2, "hint_text": "Original plants had total height 30n cm. Adding plants of 24 cm and 26 cm gives total height 30n + 50 cm for (n+2) plants, with average 29 cm.", "user_id": 41, "created_at": "2026-01-08 01:13:16", "updated_at": "2026-01-08 01:13:16" }, { "id": 6048, "question_id": 10222, "hint_level": 3, "hint_text": "Set up: (30n + 50) ÷ (n + 2) = 29. This means 30n + 50 = 29(n + 2) = 29n + 58.", "user_id": 41, "created_at": "2026-01-08 01:13:16", "updated_at": "2026-01-08 01:13:16" }, { "id": 6361, "question_id": 10295, "hint_level": 1, "hint_text": "If 35% are fiction books, what percent are non-fiction books?", "user_id": 41, "created_at": "2026-01-08 06:27:18", "updated_at": "2026-01-08 06:27:18" }, { "id": 6362, "question_id": 10295, "hint_level": 2, "hint_text": "Calculate what percent of ALL books are fiction books checked out, then non-fiction books checked out.", "user_id": 41, "created_at": "2026-01-08 06:27:18", "updated_at": "2026-01-08 06:27:18" }, { "id": 6363, "question_id": 10295, "hint_level": 3, "hint_text": "Fiction checked out: 35% × 60% = 21%. Non-fiction checked out: 65% × 80% = 52%. Add them together.", "user_id": 41, "created_at": "2026-01-08 06:27:18", "updated_at": "2026-01-08 06:27:18" }, { "id": 6364, "question_id": 10296, "hint_level": 1, "hint_text": "Work backwards from the 14 stickers Maya has left.", "user_id": 41, "created_at": "2026-01-08 06:27:45", "updated_at": "2026-01-08 06:27:45" }, { "id": 6365, "question_id": 10296, "hint_level": 2, "hint_text": "If Maya has 14 stickers after using 60% of what remained, then 14 represents 40% of what she had after giving some to her sister.", "user_id": 41, "created_at": "2026-01-08 06:27:45", "updated_at": "2026-01-08 06:27:45" }, { "id": 6366, "question_id": 10296, "hint_level": 3, "hint_text": "After giving 30% to her sister, Maya had 35 stickers (since 14 ÷ 0.4 = 35). If 35 stickers is 70% of her original amount, then she started with 35 ÷ 0.7 = 50 stickers.", "user_id": 41, "created_at": "2026-01-08 06:27:45", "updated_at": "2026-01-08 06:27:45" }, { "id": 6367, "question_id": 10297, "hint_level": 1, "hint_text": "Start with the 24 marbles Carlos has now and work backwards through each step.", "user_id": 41, "created_at": "2026-01-08 06:27:45", "updated_at": "2026-01-08 06:27:45" }, { "id": 6368, "question_id": 10297, "hint_level": 2, "hint_text": "If Carlos has 24 marbles after giving away 40% of what he had after losing some, then 24 represents 60% of what he had after losing marbles at school.", "user_id": 41, "created_at": "2026-01-08 06:27:45", "updated_at": "2026-01-08 06:27:45" }, { "id": 6369, "question_id": 10297, "hint_level": 3, "hint_text": "After losing 20% at school, Carlos had 40 marbles (since 24 ÷ 0.6 = 40). If 40 marbles is 80% of his original amount, then he started with 40 ÷ 0.8 = 50 marbles.", "user_id": 41, "created_at": "2026-01-08 06:27:45", "updated_at": "2026-01-08 06:27:45" }, { "id": 6370, "question_id": 10298, "hint_level": 1, "hint_text": "Use the 27 books Emma has left as your starting point and work backwards.", "user_id": 41, "created_at": "2026-01-08 06:27:45", "updated_at": "2026-01-08 06:27:45" }, { "id": 6371, "question_id": 10298, "hint_level": 2, "hint_text": "If Emma has 27 books after selling 40% of her remaining books, then 27 represents 60% of what she had after donating to the library.", "user_id": 41, "created_at": "2026-01-08 06:27:45", "updated_at": "2026-01-08 06:27:45" }, { "id": 6372, "question_id": 10298, "hint_level": 3, "hint_text": "After donating 25% to the library, Emma had 45 books (since 27 ÷ 0.6 = 45). If 45 books is 75% of her original collection, then she started with 45 ÷ 0.75 = 60 books.", "user_id": 41, "created_at": "2026-01-08 06:27:45", "updated_at": "2026-01-08 06:27:45" }, { "id": 6379, "question_id": 10301, "hint_level": 1, "hint_text": "Use the given percentages to find how Jake's and Emma's original savings compare.", "user_id": 41, "created_at": "2026-01-08 06:28:29", "updated_at": "2026-01-08 06:28:29" }, { "id": 6380, "question_id": 10301, "hint_level": 2, "hint_text": "If 30% of Jake's savings = 45% of Emma's savings, then Jake's savings = (45\/30) × Emma's savings = 1.5 × Emma's savings.", "user_id": 41, "created_at": "2026-01-08 06:28:29", "updated_at": "2026-01-08 06:28:29" }, { "id": 6381, "question_id": 10301, "hint_level": 3, "hint_text": "Jake's savings stays 1.5E, Emma's new savings = 1.4E. The ratio is 1.5E : 1.4E = 1.5 : 1.4 = 15 : 14.", "user_id": 41, "created_at": "2026-01-08 06:28:29", "updated_at": "2026-01-08 06:28:29" }, { "id": 6427, "question_id": 10377, "hint_level": 1, "hint_text": "Set up variables for the original number of boys and girls, and use the fact that girls = boys + 40.", "user_id": 41, "created_at": "2026-01-09 05:23:26", "updated_at": "2026-01-09 05:23:26" }, { "id": 6428, "question_id": 10377, "hint_level": 2, "hint_text": "After the increase, boys become 115% of original and girls become 125% of original. The new difference is 70.", "user_id": 41, "created_at": "2026-01-09 05:23:26", "updated_at": "2026-01-09 05:23:26" }, { "id": 6429, "question_id": 10377, "hint_level": 3, "hint_text": "If B is original boys, then 1.25(B + 40) - 1.15B = 70. Solve: 1.25B + 50 - 1.15B = 70, so 0.1B = 20.", "user_id": 41, "created_at": "2026-01-09 05:23:26", "updated_at": "2026-01-09 05:23:26" }, { "id": 6430, "question_id": 10378, "hint_level": 1, "hint_text": "Use variables for the original numbers and remember that girls = boys + 60 at the start.", "user_id": 41, "created_at": "2026-01-09 05:23:26", "updated_at": "2026-01-09 05:23:26" }, { "id": 6431, "question_id": 10378, "hint_level": 2, "hint_text": "After increases, boys are 120% of original and girls are 130% of original. Set up an equation for the new difference of 90.", "user_id": 41, "created_at": "2026-01-09 05:23:26", "updated_at": "2026-01-09 05:23:26" }, { "id": 6432, "question_id": 10378, "hint_level": 3, "hint_text": "With B as original boys: 1.3(B + 60) - 1.2B = 90. Expand to get 1.3B + 78 - 1.2B = 90.", "user_id": 41, "created_at": "2026-01-09 05:23:26", "updated_at": "2026-01-09 05:23:26" }, { "id": 6433, "question_id": 10379, "hint_level": 1, "hint_text": "Start by defining variables for boys and girls, using the relationship that girls = boys + 30 originally.", "user_id": 41, "created_at": "2026-01-09 05:23:26", "updated_at": "2026-01-09 05:23:26" }, { "id": 6434, "question_id": 10379, "hint_level": 2, "hint_text": "After the increases, boys become 125% and girls become 140% of their original numbers. The new difference is 60.", "user_id": 41, "created_at": "2026-01-09 05:23:26", "updated_at": "2026-01-09 05:23:26" }, { "id": 6435, "question_id": 10379, "hint_level": 3, "hint_text": "Set up: 1.4(B + 30) - 1.25B = 60, which simplifies to 1.4B + 42 - 1.25B = 60, so 0.15B = 18.", "user_id": 41, "created_at": "2026-01-09 05:23:26", "updated_at": "2026-01-09 05:23:26" }, { "id": 6436, "question_id": 10380, "hint_level": 1, "hint_text": "Define the original number of boys and girls, knowing that girls exceeded boys by 45 initially.", "user_id": 41, "created_at": "2026-01-09 05:23:26", "updated_at": "2026-01-09 05:23:26" }, { "id": 6437, "question_id": 10380, "hint_level": 2, "hint_text": "After the increases, boys are 112% of original and girls are 118% of original. The new difference is 72.", "user_id": 41, "created_at": "2026-01-09 05:23:26", "updated_at": "2026-01-09 05:23:26" }, { "id": 6438, "question_id": 10380, "hint_level": 3, "hint_text": "Use the equation 1.18(B + 45) - 1.12B = 72, which becomes 1.18B + 53.1 - 1.12B = 72.", "user_id": 41, "created_at": "2026-01-09 05:23:26", "updated_at": "2026-01-09 05:23:26" }, { "id": 6439, "question_id": 10381, "hint_level": 1, "hint_text": "Set up variables for boys and girls, using the fact that there were originally 35 more girls than boys.", "user_id": 41, "created_at": "2026-01-09 05:23:26", "updated_at": "2026-01-09 05:23:26" }, { "id": 6440, "question_id": 10381, "hint_level": 2, "hint_text": "After the increases, boys become 108% and girls become 112% of their original amounts. The new difference is 50.", "user_id": 41, "created_at": "2026-01-09 05:23:26", "updated_at": "2026-01-09 05:23:26" }, { "id": 6441, "question_id": 10381, "hint_level": 3, "hint_text": "Write the equation 1.12(B + 35) - 1.08B = 50, which simplifies to 0.04B = 10.8.", "user_id": 41, "created_at": "2026-01-09 05:23:26", "updated_at": "2026-01-09 05:23:26" }, { "id": 33000, "question_id": 24039, "hint_level": 1, "hint_text": "Total cards = average x number of boys.", "user_id": 2, "created_at": "2026-05-29 09:09:21", "updated_at": "2026-05-29 09:09:21" }, { "id": 33001, "question_id": 24039, "hint_level": 2, "hint_text": "Set the total after the new boy joins equal to 150 x (X + 1).", "user_id": 2, "created_at": "2026-05-29 09:09:21", "updated_at": "2026-05-29 09:09:21" }, { "id": 33584, "question_id": 24331, "hint_level": 1, "hint_text": "Use 20 units of tickets and find the money each ticket type brings in.", "user_id": 2, "created_at": "2026-05-29 09:22:29", "updated_at": "2026-05-29 09:22:29" }, { "id": 33585, "question_id": 24331, "hint_level": 2, "hint_text": "Scale the unit total up to $10 810, then read the $10-ticket revenue.", "user_id": 2, "created_at": "2026-05-29 09:22:29", "updated_at": "2026-05-29 09:22:29" }, { "id": 33624, "question_id": 24351, "hint_level": 1, "hint_text": "Let the starting number be x for both.", "user_id": 2, "created_at": "2026-05-29 09:22:29", "updated_at": "2026-05-29 09:22:29" }, { "id": 33625, "question_id": 24351, "hint_level": 2, "hint_text": "Set up Elicia = 4 × Joanna after the changes and solve.", "user_id": 2, "created_at": "2026-05-29 09:22:29", "updated_at": "2026-05-29 09:22:29" }, { "id": 33690, "question_id": 24384, "hint_level": 1, "hint_text": "Let the pear tarts be 1 unit and write strawberry and apple in terms of it.", "user_id": 2, "created_at": "2026-05-29 09:22:30", "updated_at": "2026-05-29 09:22:30" }, { "id": 33691, "question_id": 24384, "hint_level": 2, "hint_text": "Tarts left = all pear + half strawberry + 5\/8 apple = 145.", "user_id": 2, "created_at": "2026-05-29 09:22:30", "updated_at": "2026-05-29 09:22:30" }, { "id": 33702, "question_id": 24390, "hint_level": 1, "hint_text": "The three pairwise sums added together equal twice the sum of all three numbers.", "user_id": 2, "created_at": "2026-05-29 09:22:30", "updated_at": "2026-05-29 09:22:30" }, { "id": 33703, "question_id": 24390, "hint_level": 2, "hint_text": "Subtract each pair sum from the total to get the third number.", "user_id": 2, "created_at": "2026-05-29 09:22:30", "updated_at": "2026-05-29 09:22:30" }, { "id": 33902, "question_id": 24490, "hint_level": 1, "hint_text": "Let the two angles be 2u and 3u so the 3:2 ratio is exact.", "user_id": 2, "created_at": "2026-05-29 09:22:32", "updated_at": "2026-05-29 09:22:32" }, { "id": 33903, "question_id": 24490, "hint_level": 2, "hint_text": "Use co-interior angles (parallel LM and KN) summing to 180°.", "user_id": 2, "created_at": "2026-05-29 09:22:32", "updated_at": "2026-05-29 09:22:32" }, { "id": 34010, "question_id": 24544, "hint_level": 1, "hint_text": "Let AB = 2 units and AC = 3 units; the quarter-circle radius is AB.", "user_id": 2, "created_at": "2026-05-29 09:22:33", "updated_at": "2026-05-29 09:22:33" }, { "id": 34011, "question_id": 24544, "hint_level": 2, "hint_text": "Write both perimeters in units and use the 16 cm difference.", "user_id": 2, "created_at": "2026-05-29 09:22:33", "updated_at": "2026-05-29 09:22:33" }, { "id": 34834, "question_id": 24956, "hint_level": 1, "hint_text": "Let Belle's age now = B, so Andy's age now = 2B.", "user_id": 2, "created_at": "2026-05-29 09:35:32", "updated_at": "2026-05-29 09:35:32" }, { "id": 34835, "question_id": 24956, "hint_level": 2, "hint_text": "Set Andy's age 2 years ago minus Belle's age 2 years ago equal to n.", "user_id": 2, "created_at": "2026-05-29 09:35:32", "updated_at": "2026-05-29 09:35:32" }, { "id": 34858, "question_id": 24968, "hint_level": 1, "hint_text": "Let the triangle be a number of units and the rectangle twice that.", "user_id": 2, "created_at": "2026-05-29 09:35:32", "updated_at": "2026-05-29 09:35:32" }, { "id": 34859, "question_id": 24968, "hint_level": 2, "hint_text": "Shaded is \\(\\dfrac{1}{8}\\) of the rectangle; compare to total area.", "user_id": 2, "created_at": "2026-05-29 09:35:32", "updated_at": "2026-05-29 09:35:32" }, { "id": 34986, "question_id": 25032, "hint_level": 1, "hint_text": "(a) Set up two equations from the two 'one stands up' clues; solve for G and B.", "user_id": 2, "created_at": "2026-05-29 09:35:35", "updated_at": "2026-05-29 09:35:35" }, { "id": 34987, "question_id": 25032, "hint_level": 2, "hint_text": "(b) Equal number x leaves each; solve (27−x):(13−x)=9:2.", "user_id": 2, "created_at": "2026-05-29 09:35:35", "updated_at": "2026-05-29 09:35:35" }, { "id": 35166, "question_id": 25122, "hint_level": 1, "hint_text": "Total of the three = average × 3 = 144 kg.", "user_id": 2, "created_at": "2026-05-29 09:44:34", "updated_at": "2026-05-29 09:44:34" }, { "id": 35167, "question_id": 25122, "hint_level": 2, "hint_text": "Express Boon and Chai in terms of Ali, then solve 3A - 12 = 144.", "user_id": 2, "created_at": "2026-05-29 09:44:34", "updated_at": "2026-05-29 09:44:34" }, { "id": 35474, "question_id": 25276, "hint_level": 1, "hint_text": "After giving away 1\/3, Ian keeps 2\/3 of I; Jamie gains that 1\/3.", "user_id": 2, "created_at": "2026-05-29 10:36:48", "updated_at": "2026-05-29 10:36:48" }, { "id": 35475, "question_id": 25276, "hint_level": 2, "hint_text": "Jamie - Ian = 24 leads to 2I\/3 - 120 = 24.", "user_id": 2, "created_at": "2026-05-29 10:36:48", "updated_at": "2026-05-29 10:36:48" }, { "id": 35508, "question_id": 25293, "hint_level": 1, "hint_text": "Let the square's side be s; express both given perimeters using s and the rectangle length.", "user_id": 2, "created_at": "2026-05-29 10:36:48", "updated_at": "2026-05-29 10:36:48" }, { "id": 35509, "question_id": 25293, "hint_level": 2, "hint_text": "Solve the two equations to get s = 8 cm, then area = s x s = 64 cm2.", "user_id": 2, "created_at": "2026-05-29 10:36:48", "updated_at": "2026-05-29 10:36:48" }, { "id": 35598, "question_id": 25338, "hint_level": 1, "hint_text": "(a) Express Shop A's and Shop B's bars in equal units from the two graphs.", "user_id": 2, "created_at": "2026-05-29 10:36:49", "updated_at": "2026-06-08 06:43:26" }, { "id": 35599, "question_id": 25338, "hint_level": 2, "hint_text": "(b) Find Shop C's 2022 amount after a 25% decrease, set Shop B equal to it, then find B's percentage increase.", "user_id": 2, "created_at": "2026-05-29 10:36:49", "updated_at": "2026-06-08 06:43:26" }, { "id": 35660, "question_id": 25369, "hint_level": 1, "hint_text": "Shaded A = big square minus overlap; shaded B = small square minus overlap.", "user_id": 2, "created_at": "2026-05-29 10:36:51", "updated_at": "2026-05-29 10:36:51" }, { "id": 35661, "question_id": 25369, "hint_level": 2, "hint_text": "The overlap cancels in the difference A - B.", "user_id": 2, "created_at": "2026-05-29 10:36:51", "updated_at": "2026-05-29 10:36:51" }, { "id": 35696, "question_id": 25387, "hint_level": 1, "hint_text": "Add the three discounted percentages in units.", "user_id": 2, "created_at": "2026-05-29 10:36:51", "updated_at": "2026-05-29 10:36:51" }, { "id": 35697, "question_id": 25387, "hint_level": 2, "hint_text": "Remove the 8% GST, then compare with the full no-discount price.", "user_id": 2, "created_at": "2026-05-29 10:36:51", "updated_at": "2026-05-29 10:36:51" }, { "id": 35844, "question_id": 25461, "hint_level": 1, "hint_text": "Let one unit be u; write Thomas = 3u and Siti = 7u.", "user_id": 2, "created_at": "2026-05-29 10:36:53", "updated_at": "2026-05-29 10:36:53" }, { "id": 35845, "question_id": 25461, "hint_level": 2, "hint_text": "Set 3u + 42 equal to 7u − 18 and solve for u, then find 7u.", "user_id": 2, "created_at": "2026-05-29 10:36:53", "updated_at": "2026-05-29 10:36:53" }, { "id": 35846, "question_id": 25462, "hint_level": 1, "hint_text": "Let Joel = J and Ben = 288 − J, then translate the sentence into an equation.", "user_id": 2, "created_at": "2026-05-29 10:36:53", "updated_at": "2026-05-29 10:36:53" }, { "id": 35847, "question_id": 25462, "hint_level": 2, "hint_text": "\\(\\dfrac{1}{4}\\)(Ben) = \\(\\dfrac{1}{5}\\)(Joel) + 18; solve for J.", "user_id": 2, "created_at": "2026-05-29 10:36:53", "updated_at": "2026-05-29 10:36:53" }, { "id": 35850, "question_id": 25464, "hint_level": 1, "hint_text": "Let both start with the same number n; track Ken's sweets after eating and giving.", "user_id": 2, "created_at": "2026-05-29 10:36:53", "updated_at": "2026-05-29 10:36:53" }, { "id": 35851, "question_id": 25464, "hint_level": 2, "hint_text": "Ben ends with n + (what Ken gave) = 35; solve for n.", "user_id": 2, "created_at": "2026-05-29 10:36:53", "updated_at": "2026-05-29 10:36:53" }, { "id": 35854, "question_id": 25466, "hint_level": 1, "hint_text": "Use the satay : muffin ratio 3 : 1 to relate the two amounts.", "user_id": 2, "created_at": "2026-05-29 10:36:53", "updated_at": "2026-05-29 10:36:53" }, { "id": 35855, "question_id": 25466, "hint_level": 2, "hint_text": "All muffins were given out (2 each); 52 satay sticks remain. Set up and solve.", "user_id": 2, "created_at": "2026-05-29 10:36:53", "updated_at": "2026-05-29 10:36:53" }, { "id": 35874, "question_id": 25476, "hint_level": 1, "hint_text": "Let men = M and women = 600 − M; remaining men = \\(\\dfrac{3}{8}\\)M.", "user_id": 2, "created_at": "2026-05-29 10:36:53", "updated_at": "2026-05-29 10:36:53" }, { "id": 35875, "question_id": 25476, "hint_level": 2, "hint_text": "Set remaining men : remaining women = 1 : 7 and solve for M, then simplify M : (600−M).", "user_id": 2, "created_at": "2026-05-29 10:36:53", "updated_at": "2026-05-29 10:36:53" }, { "id": 35902, "question_id": 25490, "hint_level": 1, "hint_text": "Let a pie = 1 unit; a sandwich = 5 units. Find total money in units.", "user_id": 2, "created_at": "2026-05-29 10:36:53", "updated_at": "2026-05-29 10:36:53" }, { "id": 35903, "question_id": 25490, "hint_level": 2, "hint_text": "Take 3\/5 of the total, then see how many whole pies fit.", "user_id": 2, "created_at": "2026-05-29 10:36:53", "updated_at": "2026-05-29 10:36:53" }, { "id": 35980, "question_id": 25529, "hint_level": 1, "hint_text": "Express each factory's men as a share of its total using the given ratios.", "user_id": 2, "created_at": "2026-05-29 10:36:54", "updated_at": "2026-05-29 10:36:54" }, { "id": 35981, "question_id": 25529, "hint_level": 2, "hint_text": "Use the 90% relationship to compare the two men counts.", "user_id": 2, "created_at": "2026-05-29 10:36:54", "updated_at": "2026-05-29 10:36:54" }, { "id": 36052, "question_id": 25565, "hint_level": 1, "hint_text": "Cancel the common items: subtract 1 hat and 14 belts from both sides.", "user_id": 2, "created_at": "2026-05-29 10:36:55", "updated_at": "2026-05-29 10:36:55" }, { "id": 36053, "question_id": 25565, "hint_level": 2, "hint_text": "Use 'hat = belt + $24' with the value relationship.", "user_id": 2, "created_at": "2026-05-29 10:36:55", "updated_at": "2026-05-29 10:36:55" }, { "id": 36070, "question_id": 25574, "hint_level": 1, "hint_text": "Total books = average × number of students.", "user_id": 2, "created_at": "2026-05-29 10:36:55", "updated_at": "2026-05-29 10:36:55" }, { "id": 36071, "question_id": 25574, "hint_level": 2, "hint_text": "Set up an equation: 3-book and 4-book students total 23 and contribute the remaining books.", "user_id": 2, "created_at": "2026-05-29 10:36:55", "updated_at": "2026-05-29 10:36:55" }, { "id": 36084, "question_id": 25581, "hint_level": 1, "hint_text": "Express both 'gave' amounts in the same unit base.", "user_id": 2, "created_at": "2026-05-29 10:36:55", "updated_at": "2026-05-29 10:36:55" }, { "id": 36085, "question_id": 25581, "hint_level": 2, "hint_text": "Use 'Benedict = Samuel + 130' and 'left amounts equal' to solve.", "user_id": 2, "created_at": "2026-05-29 10:36:55", "updated_at": "2026-05-29 10:36:55" }, { "id": 36174, "question_id": 25626, "hint_level": 1, "hint_text": "A large cube = 8 small cubes by volume (edge ratio 2:1).", "user_id": 2, "created_at": "2026-05-29 10:36:56", "updated_at": "2026-05-29 10:36:56" }, { "id": 36175, "question_id": 25626, "hint_level": 2, "hint_text": "New cube edge = cube root of its volume; divide by 4 to get the small-cube edge.", "user_id": 2, "created_at": "2026-05-29 10:36:56", "updated_at": "2026-05-29 10:36:56" }, { "id": 36192, "question_id": 25635, "hint_level": 1, "hint_text": "Let the second piece be 2 units so the third piece is a whole number of units.", "user_id": 2, "created_at": "2026-05-29 10:51:29", "updated_at": "2026-05-29 10:51:29" }, { "id": 36193, "question_id": 25635, "hint_level": 2, "hint_text": "First = 3 × second; add all three to equal 5.4 m.", "user_id": 2, "created_at": "2026-05-29 10:51:29", "updated_at": "2026-05-29 10:51:29" }, { "id": 36212, "question_id": 25645, "hint_level": 1, "hint_text": "Use the 3 : 5 ratio of 50-cent to 10-cent coins in units.", "user_id": 2, "created_at": "2026-05-29 10:51:29", "updated_at": "2026-05-29 10:51:29" }, { "id": 36213, "question_id": 25645, "hint_level": 2, "hint_text": "Form the $84 value equation in units, solve, then add the two coin counts.", "user_id": 2, "created_at": "2026-05-29 10:51:29", "updated_at": "2026-05-29 10:51:29" }, { "id": 36236, "question_id": 25657, "hint_level": 1, "hint_text": "Value of $1 coins = 2u × $1; value of 20-cent coins = 5u × $0.20.", "user_id": 2, "created_at": "2026-05-29 10:51:37", "updated_at": "2026-05-29 10:51:37" }, { "id": 36237, "question_id": 25657, "hint_level": 2, "hint_text": "Add the values, set equal to $21, then solve for one unit.", "user_id": 2, "created_at": "2026-05-29 10:51:37", "updated_at": "2026-05-29 10:51:37" }, { "id": 36256, "question_id": 25667, "hint_level": 1, "hint_text": "Write each person's unsold tickets in units of Ashton's unsold (1u).", "user_id": 2, "created_at": "2026-05-29 10:51:37", "updated_at": "2026-05-29 10:51:37" }, { "id": 36257, "question_id": 25667, "hint_level": 2, "hint_text": "Solve 5u - 14 = 491; each person's total = Charles sold + Charles unsold.", "user_id": 2, "created_at": "2026-05-29 10:51:37", "updated_at": "2026-05-29 10:51:37" }, { "id": 36280, "question_id": 25679, "hint_level": 1, "hint_text": "Let girls be 7 units so boys are 2 units.", "user_id": 2, "created_at": "2026-05-29 10:51:38", "updated_at": "2026-05-29 10:51:38" }, { "id": 36281, "question_id": 25679, "hint_level": 2, "hint_text": "Total children = boys + girls.", "user_id": 2, "created_at": "2026-05-29 10:51:38", "updated_at": "2026-05-29 10:51:38" }, { "id": 36396, "question_id": 25737, "hint_level": 1, "hint_text": "Let Mr Lee's money be 2 units so half is a whole unit.", "user_id": 2, "created_at": "2026-05-29 10:51:40", "updated_at": "2026-05-29 10:51:40" }, { "id": 36397, "question_id": 25737, "hint_level": 2, "hint_text": "Set the two 'left' amounts equal.", "user_id": 2, "created_at": "2026-05-29 10:51:40", "updated_at": "2026-05-29 10:51:40" }, { "id": 36488, "question_id": 25783, "hint_level": 1, "hint_text": "Let Q = 2 units, R = 3 units; the 1-unit difference = 12 000 cm³.", "user_id": 2, "created_at": "2026-05-29 10:51:42", "updated_at": "2026-05-29 10:51:42" }, { "id": 36489, "question_id": 25783, "hint_level": 2, "hint_text": "Total = 5 units = 60 000 cm³; divide by the 50 × 40 face to get the edge.", "user_id": 2, "created_at": "2026-05-29 10:51:42", "updated_at": "2026-05-29 10:51:42" }, { "id": 36510, "question_id": 25794, "hint_level": 1, "hint_text": "MN = ML makes triangle MNL isosceles; set up ∠LMN = x, ∠MNL = x + 24.", "user_id": 2, "created_at": "2026-05-29 10:51:42", "updated_at": "2026-05-29 10:51:42" }, { "id": 36511, "question_id": 25794, "hint_level": 2, "hint_text": "Solve for ∠LMN (44°), then use the rhombus angle properties to get ∠MJK.", "user_id": 2, "created_at": "2026-05-29 10:51:42", "updated_at": "2026-05-29 10:51:42" }, { "id": 36540, "question_id": 25809, "hint_level": 1, "hint_text": "For every one $5-note there are three $2-notes.", "user_id": 2, "created_at": "2026-05-29 10:51:45", "updated_at": "2026-05-29 10:51:45" }, { "id": 36541, "question_id": 25809, "hint_level": 2, "hint_text": "One group is worth $5 + 3 × $2 = $11; divide $385 by $11.", "user_id": 2, "created_at": "2026-05-29 10:51:45", "updated_at": "2026-05-29 10:51:45" }, { "id": 36552, "question_id": 25815, "hint_level": 1, "hint_text": "Make red+blue a common base. Red:Blue = 1:2 means red+blue = 3 parts.", "user_id": 2, "created_at": "2026-05-29 10:51:46", "updated_at": "2026-05-29 10:51:46" }, { "id": 36553, "question_id": 25815, "hint_level": 2, "hint_text": "Green : (red+blue) = 1 : 4. Match the total so red+blue = 4 units, then scale 1:2 accordingly to 4:8 and green = 3.", "user_id": 2, "created_at": "2026-05-29 10:51:46", "updated_at": "2026-05-29 10:51:46" }, { "id": 36566, "question_id": 25822, "hint_level": 1, "hint_text": "Patrick took the rest: \\(1 - \\dfrac{7}{10} = \\dfrac{3}{10}\\). Use 10 units total.", "user_id": 2, "created_at": "2026-05-29 10:51:46", "updated_at": "2026-05-29 10:51:46" }, { "id": 36567, "question_id": 25822, "hint_level": 2, "hint_text": "Jane's final amount = \\(\\dfrac{1}{6}\\) of Patrick's. Set up 7u - 39 = \\(\\dfrac{1}{6}\\times 3u\\) and solve.", "user_id": 2, "created_at": "2026-05-29 10:51:46", "updated_at": "2026-05-29 10:51:46" }, { "id": 36584, "question_id": 25831, "hint_level": 1, "hint_text": "Use end ratio 1:2:1 as 1u, 2u, 1u, then reverse each operation to get the 'at first' amounts.", "user_id": 2, "created_at": "2026-05-29 10:51:46", "updated_at": "2026-05-29 10:51:46" }, { "id": 36585, "question_id": 25831, "hint_level": 2, "hint_text": "X first = 1u + 120; Y first = 2u ÷ 2 = 1u; Z first = 1u ÷ \\(\\dfrac{4}{5}\\) = 1.25u. Sum = 848.", "user_id": 2, "created_at": "2026-05-29 10:51:46", "updated_at": "2026-05-29 10:51:46" }, { "id": 36620, "question_id": 25849, "hint_level": 1, "hint_text": "Let the length be 3 units and the breadth 2 units.", "user_id": 2, "created_at": "2026-05-29 10:51:48", "updated_at": "2026-05-29 10:51:48" }, { "id": 36621, "question_id": 25849, "hint_level": 2, "hint_text": "Perimeter = 2 × (length + breadth); set it equal to 105 cm to find 1 unit.", "user_id": 2, "created_at": "2026-05-29 10:51:48", "updated_at": "2026-05-29 10:51:48" }, { "id": 36644, "question_id": 25861, "hint_level": 1, "hint_text": "The butter and kaya counts start 180 apart and must end equal.", "user_id": 2, "created_at": "2026-05-29 10:51:50", "updated_at": "2026-05-29 10:51:50" }, { "id": 36645, "question_id": 25861, "hint_level": 2, "hint_text": "For every 3 buns paid, 1 is free; group the 13 buns to find how many are paid for.", "user_id": 2, "created_at": "2026-05-29 10:51:50", "updated_at": "2026-05-29 10:51:50" }, { "id": 37002, "question_id": 26040, "hint_level": 1, "hint_text": "Total marks = average × number of students.", "user_id": 2, "created_at": "2026-05-29 13:14:13", "updated_at": "2026-05-29 13:14:13" }, { "id": 37003, "question_id": 26040, "hint_level": 2, "hint_text": "Set 74n − 282 = 62(n − 3) and solve for n.", "user_id": 2, "created_at": "2026-05-29 13:14:13", "updated_at": "2026-05-29 13:14:13" }, { "id": 37369, "question_id": 26223, "hint_level": 1, "hint_text": "The base is a square, so two of the cuboid's edges are equal.", "user_id": 2, "created_at": "2026-05-29 13:22:08", "updated_at": "2026-05-29 13:22:08" }, { "id": 37370, "question_id": 26223, "hint_level": 2, "hint_text": "Use the 20 cm and 8 cm net measurements to find the edge lengths.", "user_id": 2, "created_at": "2026-05-29 13:22:08", "updated_at": "2026-05-29 13:22:08" }, { "id": 37435, "question_id": 26256, "hint_level": 1, "hint_text": "Set Cindy as 1 unit and work out the others.", "user_id": 2, "created_at": "2026-05-29 13:22:09", "updated_at": "2026-05-29 13:22:09" }, { "id": 37436, "question_id": 26256, "hint_level": 2, "hint_text": "Anne and David are equal and largest; Ben and Cindy are equal and smallest.", "user_id": 2, "created_at": "2026-05-29 13:22:09", "updated_at": "2026-05-29 13:22:09" }, { "id": 37469, "question_id": 26273, "hint_level": 1, "hint_text": "All six faces sum to 21; the centre face 3 is shared by both arms.", "user_id": 2, "created_at": "2026-05-29 13:22:10", "updated_at": "2026-05-29 13:22:10" }, { "id": 37470, "question_id": 26273, "hint_level": 2, "hint_text": "Set the horizontal and vertical sums equal and solve.", "user_id": 2, "created_at": "2026-05-29 13:22:10", "updated_at": "2026-05-29 13:22:10" }, { "id": 37471, "question_id": 26274, "hint_level": 1, "hint_text": "Let the number of pears be p and apples given away be x.", "user_id": 2, "created_at": "2026-05-29 13:22:10", "updated_at": "2026-05-29 13:22:10" }, { "id": 37472, "question_id": 26274, "hint_level": 2, "hint_text": "Form two equations from the two pear fractions and solve.", "user_id": 2, "created_at": "2026-05-29 13:22:10", "updated_at": "2026-05-29 13:22:10" }, { "id": 37479, "question_id": 26278, "hint_level": 1, "hint_text": "New spending = 60 × 1.2 = 72.", "user_id": 2, "created_at": "2026-05-29 13:22:10", "updated_at": "2026-05-29 13:22:10" }, { "id": 37480, "question_id": 26278, "hint_level": 2, "hint_text": "Set 'allowance − new spending' equal to 0.9 × original savings.", "user_id": 2, "created_at": "2026-05-29 13:22:10", "updated_at": "2026-05-29 13:22:10" }, { "id": 37485, "question_id": 26281, "hint_level": 1, "hint_text": "Outer side = garden side + 2 + 2.", "user_id": 2, "created_at": "2026-05-29 13:22:10", "updated_at": "2026-05-29 13:22:10" }, { "id": 37486, "question_id": 26281, "hint_level": 2, "hint_text": "Path area = outer square − garden square.", "user_id": 2, "created_at": "2026-05-29 13:22:10", "updated_at": "2026-05-29 13:22:10" }, { "id": 37489, "question_id": 26283, "hint_level": 1, "hint_text": "Let the first amounts be 3x and 4x.", "user_id": 2, "created_at": "2026-05-29 13:22:10", "updated_at": "2026-05-29 13:22:10" }, { "id": 37490, "question_id": 26283, "hint_level": 2, "hint_text": "Form a ratio equation for the new amounts and solve for x.", "user_id": 2, "created_at": "2026-05-29 13:22:10", "updated_at": "2026-05-29 13:22:10" }, { "id": 37697, "question_id": 26387, "hint_level": 1, "hint_text": "The width of the figure equals AB (the side of the square), and the length AC = AB + BC.", "user_id": 2, "created_at": "2026-05-29 13:22:28", "updated_at": "2026-05-29 13:22:28" }, { "id": 37698, "question_id": 26387, "hint_level": 2, "hint_text": "Express the perimeter in units, find 1 unit, then square the side of ABEF.", "user_id": 2, "created_at": "2026-05-29 13:22:28", "updated_at": "2026-05-29 13:22:28" }, { "id": 37699, "question_id": 26388, "hint_level": 1, "hint_text": "The number of buns stays the same before and after the sale.", "user_id": 2, "created_at": "2026-05-29 13:22:28", "updated_at": "2026-05-29 13:22:28" }, { "id": 37700, "question_id": 26388, "hint_level": 2, "hint_text": "Set the buns to a fixed number of units in both ratios and form an equation from the second ratio.", "user_id": 2, "created_at": "2026-05-29 13:22:28", "updated_at": "2026-05-29 13:22:28" }, { "id": 37729, "question_id": 26403, "hint_level": 1, "hint_text": "Set Clark = 5u and Daniel = 9u, then add 8 to each.", "user_id": 2, "created_at": "2026-05-29 13:22:30", "updated_at": "2026-05-29 13:22:30" }, { "id": 37730, "question_id": 26403, "hint_level": 2, "hint_text": "Form the equation (5u+8) : (9u+8) = 3 : 5 and solve for u.", "user_id": 2, "created_at": "2026-05-29 13:22:30", "updated_at": "2026-05-29 13:22:30" }, { "id": 37733, "question_id": 26405, "hint_level": 1, "hint_text": "Let the number of girls be g; the number of boys is g + 2.", "user_id": 2, "created_at": "2026-05-29 13:22:30", "updated_at": "2026-05-29 13:22:30" }, { "id": 37734, "question_id": 26405, "hint_level": 2, "hint_text": "Total sweets: 3(g+2) + 4g = 62; solve for g.", "user_id": 2, "created_at": "2026-05-29 13:22:30", "updated_at": "2026-05-29 13:22:30" }, { "id": 37801, "question_id": 26439, "hint_level": 1, "hint_text": "Set the rectangle as 1 part and the square as 4 parts to compare areas.", "user_id": 2, "created_at": "2026-05-29 13:22:35", "updated_at": "2026-05-29 13:22:35" }, { "id": 37802, "question_id": 26439, "hint_level": 2, "hint_text": "Add the shaded area of the square and the shaded area of the rectangle, then compare to the square's area.", "user_id": 2, "created_at": "2026-05-29 13:22:35", "updated_at": "2026-05-29 13:22:35" }, { "id": 37831, "question_id": 26454, "hint_level": 1, "hint_text": "Let p be the number of pupils; write both giving-out scenarios as equations.", "user_id": 2, "created_at": "2026-05-29 13:22:35", "updated_at": "2026-05-29 13:22:35" }, { "id": 37832, "question_id": 26454, "hint_level": 2, "hint_text": "4p + 6 = 5p, so p = 6, then muffins = 5p.", "user_id": 2, "created_at": "2026-05-29 13:22:35", "updated_at": "2026-05-29 13:22:35" }, { "id": 38151, "question_id": 26614, "hint_level": 1, "hint_text": "Divide the square into 4 equal quarters using the midpoint lines.", "user_id": 2, "created_at": "2026-05-29 13:41:05", "updated_at": "2026-05-29 13:41:05" }, { "id": 38152, "question_id": 26614, "hint_level": 2, "hint_text": "Find each shaded triangle's area as a fraction of the whole square and add.", "user_id": 2, "created_at": "2026-05-29 13:41:05", "updated_at": "2026-05-29 13:41:05" }, { "id": 38163, "question_id": 26620, "hint_level": 1, "hint_text": "Let the original number of plants be n and write the total cost as 7n.", "user_id": 2, "created_at": "2026-05-29 13:41:05", "updated_at": "2026-05-29 13:41:05" }, { "id": 38164, "question_id": 26620, "hint_level": 2, "hint_text": "Set 7n + 21 = 9(n + 1) and solve, then add the extra plant.", "user_id": 2, "created_at": "2026-05-29 13:41:05", "updated_at": "2026-05-29 13:41:05" }, { "id": 38413, "question_id": 26745, "hint_level": 1, "hint_text": "Let girls be 5 units so boys are 4 units and children are 9 units.", "user_id": 2, "created_at": "2026-05-29 13:41:15", "updated_at": "2026-05-29 13:41:15" }, { "id": 38414, "question_id": 26745, "hint_level": 2, "hint_text": "Use Children : Adults = 2 : 5 to find adults, then form Girls : Adults.", "user_id": 2, "created_at": "2026-05-29 13:41:15", "updated_at": "2026-05-29 13:41:15" }, { "id": 38503, "question_id": 26790, "hint_level": 1, "hint_text": "Express the rectangle and triangle areas using a common unit so the shaded portions are whole units.", "user_id": 2, "created_at": "2026-05-29 13:41:17", "updated_at": "2026-05-29 13:41:17" }, { "id": 38504, "question_id": 26790, "hint_level": 2, "hint_text": "Shaded fraction = total shaded units ÷ total units of the figure.", "user_id": 2, "created_at": "2026-05-29 13:41:17", "updated_at": "2026-05-29 13:41:17" }, { "id": 38529, "question_id": 26803, "hint_level": 1, "hint_text": "Set up: 20 × (ribbon) = 12 × (string), with string = ribbon + 10.", "user_id": 2, "created_at": "2026-05-29 13:41:17", "updated_at": "2026-05-29 13:41:17" }, { "id": 38530, "question_id": 26803, "hint_level": 2, "hint_text": "Solve the equation for the ribbon length.", "user_id": 2, "created_at": "2026-05-29 13:41:17", "updated_at": "2026-05-29 13:41:17" }, { "id": 38531, "question_id": 26804, "hint_level": 1, "hint_text": "Hiram's blue − Hiram's red = (gave away red) − (gave away blue) = 51 − 27 = 24.", "user_id": 2, "created_at": "2026-05-29 13:41:17", "updated_at": "2026-05-29 13:41:17" }, { "id": 38532, "question_id": 26804, "hint_level": 2, "hint_text": "This 24 is the 3-unit ratio difference; find 1 unit, then total Hiram's stickers.", "user_id": 2, "created_at": "2026-05-29 13:41:17", "updated_at": "2026-05-29 13:41:17" }, { "id": 38553, "question_id": 26815, "hint_level": 1, "hint_text": "The volume leaving A equals the volume entering B.", "user_id": 2, "created_at": "2026-05-29 13:41:18", "updated_at": "2026-05-29 13:41:18" }, { "id": 38554, "question_id": 26815, "hint_level": 2, "hint_text": "Set baseA × 5 = baseB × 8 with baseA = baseB + 15, then solve.", "user_id": 2, "created_at": "2026-05-29 13:41:18", "updated_at": "2026-05-29 13:41:18" }, { "id": 38641, "question_id": 26859, "hint_level": 1, "hint_text": "Equal amounts given away means 20 local and 20 foreign.", "user_id": 2, "created_at": "2026-05-29 13:41:21", "updated_at": "2026-05-29 13:41:21" }, { "id": 38642, "question_id": 26859, "hint_level": 2, "hint_text": "Set up the after-ratio and solve for one unit.", "user_id": 2, "created_at": "2026-05-29 13:41:21", "updated_at": "2026-05-29 13:41:21" }, { "id": 38657, "question_id": 26867, "hint_level": 1, "hint_text": "Total = average x 3 = 315 cm; convert 0.65 m to 65 cm.", "user_id": 2, "created_at": "2026-05-29 13:41:21", "updated_at": "2026-05-29 13:41:21" }, { "id": 38658, "question_id": 26867, "hint_level": 2, "hint_text": "Let Plant B be 1 unit and write A and C in units.", "user_id": 2, "created_at": "2026-05-29 13:41:21", "updated_at": "2026-05-29 13:41:21" }, { "id": 38773, "question_id": 26925, "hint_level": 1, "hint_text": "Set the 3-km total equal to the 5-km total to find the number of boys.", "user_id": 2, "created_at": "2026-05-29 13:41:24", "updated_at": "2026-05-29 13:41:24" }, { "id": 38774, "question_id": 26925, "hint_level": 2, "hint_text": "Each group has 300 children; multiply km walked by $10.", "user_id": 2, "created_at": "2026-05-29 13:41:24", "updated_at": "2026-05-29 13:41:24" }, { "id": 38785, "question_id": 26931, "hint_level": 1, "hint_text": "Shelf W length = 9x + 3; Shelf X length = 5(x + 11); set them equal.", "user_id": 2, "created_at": "2026-05-29 13:41:24", "updated_at": "2026-05-29 13:41:24" }, { "id": 38786, "question_id": 26931, "hint_level": 2, "hint_text": "For (b) use total books = 36 and total length 240 cm to solve for big books.", "user_id": 2, "created_at": "2026-05-29 13:41:24", "updated_at": "2026-05-29 13:41:24" }, { "id": 38859, "question_id": 26968, "hint_level": 1, "hint_text": "Total = average × number of items.", "user_id": 2, "created_at": "2026-05-29 13:41:26", "updated_at": "2026-05-29 13:41:26" }, { "id": 38860, "question_id": 26968, "hint_level": 2, "hint_text": "Set up an equation with the class total before and after removing 4 students.", "user_id": 2, "created_at": "2026-05-29 13:41:26", "updated_at": "2026-05-29 13:41:26" }, { "id": 39427, "question_id": 27252, "hint_level": 1, "hint_text": "The fractions ahead and behind, plus Dickson, plus the one who dropped out, must make up the whole.", "user_id": 2, "created_at": "2026-05-29 14:27:55", "updated_at": "2026-05-29 14:27:55" }, { "id": 39428, "question_id": 27252, "hint_level": 2, "hint_text": "\\(\\dfrac{1}{12}+\\dfrac{8}{9}=\\dfrac{35}{36}\\); the remaining \\(\\dfrac{1}{36}\\) accounts for Dickson and the drop-out (2 people).", "user_id": 2, "created_at": "2026-05-29 14:27:55", "updated_at": "2026-05-29 14:27:55" }, { "id": 39635, "question_id": 27346, "hint_level": 1, "hint_text": "Let r = original number of rows; original chairs = 9r.", "user_id": 2, "created_at": "2026-05-29 14:28:17", "updated_at": "2026-05-29 14:28:17" }, { "id": 39636, "question_id": 27346, "hint_level": 2, "hint_text": "New chairs = 9r + 6 = 7(r + 12); solve for r.", "user_id": 2, "created_at": "2026-05-29 14:28:17", "updated_at": "2026-05-29 14:28:17" }, { "id": 39639, "question_id": 27348, "hint_level": 1, "hint_text": "Find the daily usage from the first 12 days (⅔ of bottle used).", "user_id": 2, "created_at": "2026-05-29 14:28:17", "updated_at": "2026-05-29 14:28:17" }, { "id": 39640, "question_id": 27348, "hint_level": 2, "hint_text": "Subtract 2 more days of usage from the ⅓ left to equal 200 ml.", "user_id": 2, "created_at": "2026-05-29 14:28:17", "updated_at": "2026-05-29 14:28:17" }, { "id": 39643, "question_id": 27350, "hint_level": 1, "hint_text": "Let n be the equal number of beads each girl used; write each girl's starting amount in terms of n.", "user_id": 2, "created_at": "2026-05-29 14:28:17", "updated_at": "2026-05-29 14:28:17" }, { "id": 39644, "question_id": 27350, "hint_level": 2, "hint_text": "Sum the three starting amounts to 1440 and solve for n.", "user_id": 2, "created_at": "2026-05-29 14:28:17", "updated_at": "2026-05-29 14:28:17" }, { "id": 39659, "question_id": 27358, "hint_level": 1, "hint_text": "Let Peili's spending be p; write everyone's spent and left amounts in terms of p.", "user_id": 2, "created_at": "2026-05-29 14:28:17", "updated_at": "2026-05-29 14:28:17" }, { "id": 39660, "question_id": 27358, "hint_level": 2, "hint_text": "Peili's-left = $7 + Peili-spent and = 2 × Nurul's-left; total of all four amounts = $60.", "user_id": 2, "created_at": "2026-05-29 14:28:17", "updated_at": "2026-05-29 14:28:17" }, { "id": 39663, "question_id": 27360, "hint_level": 1, "hint_text": "Triangle MNL is isosceles (MN = ML); let ∠LMN = x and use the 24° condition.", "user_id": 2, "created_at": "2026-05-29 14:28:17", "updated_at": "2026-05-29 14:28:17" }, { "id": 39664, "question_id": 27360, "hint_level": 2, "hint_text": "In the rhombus the diagonal MK bisects the corner angles; relate ∠LMN to ∠MJK.", "user_id": 2, "created_at": "2026-05-29 14:28:17", "updated_at": "2026-05-29 14:28:17" }, { "id": 39667, "question_id": 27362, "hint_level": 1, "hint_text": "Let b = blue, p = pink; b + p = 66.", "user_id": 2, "created_at": "2026-05-29 14:28:17", "updated_at": "2026-05-29 14:28:17" }, { "id": 39668, "question_id": 27362, "hint_level": 2, "hint_text": "After changes: 1.75b + (p - 17) = 79; subtract to find b, then p.", "user_id": 2, "created_at": "2026-05-29 14:28:17", "updated_at": "2026-05-29 14:28:17" }, { "id": 39671, "question_id": 27364, "hint_level": 1, "hint_text": "Cupboard width 0.9 m = 90 cm; use Figure A to find one box dimension (2 boxes span the width).", "user_id": 2, "created_at": "2026-05-29 14:28:17", "updated_at": "2026-05-29 14:28:17" }, { "id": 39672, "question_id": 27364, "hint_level": 2, "hint_text": "Use the 42-cm and 10-cm top gaps from the two stackings to set up equations for box dimensions and cupboard height.", "user_id": 2, "created_at": "2026-05-29 14:28:17", "updated_at": "2026-05-29 14:28:17" }, { "id": 39673, "question_id": 27365, "hint_level": 1, "hint_text": "Let a postcard = 1 unit and a magnet = 3 units; cost of first purchase = ⅓ of money.", "user_id": 2, "created_at": "2026-05-29 14:28:17", "updated_at": "2026-05-29 14:28:17" }, { "id": 39674, "question_id": 27365, "hint_level": 2, "hint_text": "Find total money, then ¾ of the remaining money buys more magnets (3 units each); add to the first 5.", "user_id": 2, "created_at": "2026-05-29 14:28:17", "updated_at": "2026-05-29 14:28:17" }, { "id": 39677, "question_id": 27367, "hint_level": 1, "hint_text": "Let Pouch Y = 4 units (3:1); Pouch Z = 20 units (1:4) since Z has 5× as many tokens.", "user_id": 2, "created_at": "2026-05-29 14:28:17", "updated_at": "2026-05-29 14:28:17" }, { "id": 39678, "question_id": 27367, "hint_level": 2, "hint_text": "(b) Set (3u+24):(u+24) = 9:5 and solve for u. (c) Total at first = 24u.", "user_id": 2, "created_at": "2026-05-29 14:28:17", "updated_at": "2026-05-29 14:28:17" }, { "id": 39703, "question_id": 27380, "hint_level": 1, "hint_text": "Christopher keeps 1\/5 of his; Helen keeps 1\/3 of hers.", "user_id": 2, "created_at": "2026-05-29 14:28:18", "updated_at": "2026-05-29 14:28:18" }, { "id": 39704, "question_id": 27380, "hint_level": 2, "hint_text": "Use the 'Helen had 1 more' and total 75 to set up equal units: 75 − 3 = 72, 72 ÷ 8 = 9.", "user_id": 2, "created_at": "2026-05-29 14:28:18", "updated_at": "2026-05-29 14:28:18" }, { "id": 39763, "question_id": 27410, "hint_level": 1, "hint_text": "Turn '40% of X equals half of Y' into an equation to relate X and Y.", "user_id": 2, "created_at": "2026-05-29 14:28:27", "updated_at": "2026-05-29 14:28:27" }, { "id": 39764, "question_id": 27410, "hint_level": 2, "hint_text": "Use Z : X = 1 : 2 to express Z in the same units, then write Z over Y and simplify.", "user_id": 2, "created_at": "2026-05-29 14:28:27", "updated_at": "2026-05-29 14:28:27" }, { "id": 39847, "question_id": 27452, "hint_level": 1, "hint_text": "Remaining gold : remaining silver = 1 : 3.", "user_id": 2, "created_at": "2026-05-29 14:28:33", "updated_at": "2026-05-29 14:28:33" }, { "id": 39848, "question_id": 27452, "hint_level": 2, "hint_text": "3(T - 26) = T - 14, solve for T.", "user_id": 2, "created_at": "2026-05-29 14:28:33", "updated_at": "2026-05-29 14:28:33" }, { "id": 39863, "question_id": 27460, "hint_level": 1, "hint_text": "One-dollar : fifty-cent : twenty-cent counts = 6 : 2 : 1 (out of 9).", "user_id": 2, "created_at": "2026-05-29 14:28:33", "updated_at": "2026-05-29 14:28:33" }, { "id": 39864, "question_id": 27460, "hint_level": 2, "hint_text": "Value per group of 9 coins = $7.20; 108 ÷ 7.20 = 15 groups.", "user_id": 2, "created_at": "2026-05-29 14:28:33", "updated_at": "2026-05-29 14:28:33" }, { "id": 40023, "question_id": 27540, "hint_level": 1, "hint_text": "Total mass = average × number of people = 40 × 3.", "user_id": 2, "created_at": "2026-05-29 14:47:22", "updated_at": "2026-05-29 14:47:22" }, { "id": 40024, "question_id": 27540, "hint_level": 2, "hint_text": "Let Ahmad = Ben = x, Carl = x + 6; solve 3x + 6 = 120.", "user_id": 2, "created_at": "2026-05-29 14:47:22", "updated_at": "2026-05-29 14:47:22" }, { "id": 43124, "question_id": 29092, "hint_level": 1, "hint_text": "Let Mollie's amount be 1 (use 21 as a common denominator).", "user_id": 2, "created_at": "2026-05-29 17:24:46", "updated_at": "2026-05-29 17:24:46" }, { "id": 43125, "question_id": 29092, "hint_level": 2, "hint_text": "Find the total flour, share it equally three ways, then see how much Mollie loses.", "user_id": 2, "created_at": "2026-05-29 17:24:46", "updated_at": "2026-05-29 17:24:46" }, { "id": 43204, "question_id": 29132, "hint_level": 1, "hint_text": "Chocolate left is 40% of the original chocolate; set the end ratio with units that account for that.", "user_id": 2, "created_at": "2026-05-29 17:24:47", "updated_at": "2026-05-29 17:24:47" }, { "id": 43205, "question_id": 29132, "hint_level": 2, "hint_text": "Use the 154 difference at first to solve for the unit, then total the cookies left (14u).", "user_id": 2, "created_at": "2026-05-29 17:24:47", "updated_at": "2026-05-29 17:24:47" }, { "id": 43554, "question_id": 29307, "hint_level": 1, "hint_text": "She gave away 20 local and 20 foreign (40 split equally).", "user_id": 2, "created_at": "2026-05-29 17:25:08", "updated_at": "2026-05-29 17:25:08" }, { "id": 43555, "question_id": 29307, "hint_level": 2, "hint_text": "Set (3a - 20):(4a - 20) = 4:7, solve to get a = 12, so local = 3 x 12 = 36.", "user_id": 2, "created_at": "2026-05-29 17:25:08", "updated_at": "2026-05-29 17:25:08" }, { "id": 43576, "question_id": 29318, "hint_level": 1, "hint_text": "The bag, shirt and remaining 80% are linked: cap + bag + shirt = total.", "user_id": 2, "created_at": "2026-05-29 17:25:08", "updated_at": "2026-05-29 17:25:08" }, { "id": 43577, "question_id": 29318, "hint_level": 2, "hint_text": "Express the bag in terms of the cap (20%) and solve for the total.", "user_id": 2, "created_at": "2026-05-29 17:25:08", "updated_at": "2026-05-29 17:25:08" }, { "id": 43610, "question_id": 29335, "hint_level": 1, "hint_text": "Let the inner triangle's base be y and write the shaded (trapezium-like) area in terms of y.", "user_id": 2, "created_at": "2026-05-29 17:25:09", "updated_at": "2026-05-29 17:25:09" }, { "id": 43611, "question_id": 29335, "hint_level": 2, "hint_text": "Solve 2y + 2 = 22, then add the 2 cm to get AD.", "user_id": 2, "created_at": "2026-05-29 17:25:09", "updated_at": "2026-05-29 17:25:09" }, { "id": 43682, "question_id": 29371, "hint_level": 1, "hint_text": "Let Nurul's leftover be u and express both girls' starting and spent amounts in terms of u.", "user_id": 2, "created_at": "2026-05-29 17:25:15", "updated_at": "2026-05-29 17:25:15" }, { "id": 43683, "question_id": 29371, "hint_level": 2, "hint_text": "The two starting amounts add to $60.", "user_id": 2, "created_at": "2026-05-29 17:25:15", "updated_at": "2026-05-29 17:25:15" }, { "id": 43694, "question_id": 29377, "hint_level": 1, "hint_text": "Set the two expressions for the cupboard height equal.", "user_id": 2, "created_at": "2026-05-29 17:25:15", "updated_at": "2026-05-29 17:25:15" }, { "id": 43695, "question_id": 29377, "hint_level": 2, "hint_text": "Use 2B = 0.9 m = 90 cm to find the box length and then the height.", "user_id": 2, "created_at": "2026-05-29 17:25:15", "updated_at": "2026-05-29 17:25:15" }, { "id": 43700, "question_id": 29380, "hint_level": 1, "hint_text": "Let Kathy's end amount be u and Alice's be 2u; express their starting amounts.", "user_id": 2, "created_at": "2026-05-29 17:25:15", "updated_at": "2026-05-29 17:25:15" }, { "id": 43701, "question_id": 29380, "hint_level": 2, "hint_text": "Apply the first ratio 3 : 4 to the starting amounts and solve.", "user_id": 2, "created_at": "2026-05-29 17:25:15", "updated_at": "2026-05-29 17:25:15" }, { "id": 43840, "question_id": 29450, "hint_level": 1, "hint_text": "Set up units for Paul and Zalim's spending and 'left' amounts, then total to $140.20.", "user_id": 2, "created_at": "2026-05-29 17:25:28", "updated_at": "2026-05-29 17:25:28" }, { "id": 43841, "question_id": 29450, "hint_level": 2, "hint_text": "Key: 37 units = $125.80, 1 unit = $3.40; Paul spent = $17, Zalim at first = $77.20.", "user_id": 2, "created_at": "2026-05-29 17:25:28", "updated_at": "2026-05-29 17:25:28" }, { "id": 44002, "question_id": 29531, "hint_level": 1, "hint_text": "Let the girls' average be 1 unit; the boys' average is 1 unit + $1.", "user_id": 2, "created_at": "2026-05-29 17:34:47", "updated_at": "2026-05-29 17:34:47" }, { "id": 44003, "question_id": 29531, "hint_level": 2, "hint_text": "Total boys' money = girls' total + $10; set up the equation and solve for the unit.", "user_id": 2, "created_at": "2026-05-29 17:34:47", "updated_at": "2026-05-29 17:34:47" }, { "id": 44396, "question_id": 29728, "hint_level": 1, "hint_text": "Let Belle's present age be b; Andy is 2b now.", "user_id": 2, "created_at": "2026-05-29 17:35:47", "updated_at": "2026-05-29 17:35:47" }, { "id": 44397, "question_id": 29728, "hint_level": 2, "hint_text": "Express their ages 2 years ago and use the difference n.", "user_id": 2, "created_at": "2026-05-29 17:35:47", "updated_at": "2026-05-29 17:35:47" }, { "id": 44420, "question_id": 29740, "hint_level": 1, "hint_text": "Let the triangle = 4 units and rectangle = 8 units.", "user_id": 2, "created_at": "2026-05-29 17:35:48", "updated_at": "2026-05-29 17:35:48" }, { "id": 44421, "question_id": 29740, "hint_level": 2, "hint_text": "Account for the overlap when finding the total area of the figure.", "user_id": 2, "created_at": "2026-05-29 17:35:48", "updated_at": "2026-05-29 17:35:48" }, { "id": 44642, "question_id": 29851, "hint_level": 1, "hint_text": "Track apples and oranges separately through the exchange and give-away.", "user_id": 2, "created_at": "2026-05-29 17:36:04", "updated_at": "2026-05-29 17:36:04" }, { "id": 44643, "question_id": 29851, "hint_level": 2, "hint_text": "For (b), pack in 4 : 5 groups and find the leftover oranges.", "user_id": 2, "created_at": "2026-05-29 17:36:04", "updated_at": "2026-05-29 17:36:04" }, { "id": 44644, "question_id": 29852, "hint_level": 1, "hint_text": "Set up the combined-volume equation with Y's height as the unknown.", "user_id": 2, "created_at": "2026-05-29 17:36:04", "updated_at": "2026-05-29 17:36:04" }, { "id": 44645, "question_id": 29852, "hint_level": 2, "hint_text": "For (b), find the volume poured out and divide by X's original water volume.", "user_id": 2, "created_at": "2026-05-29 17:36:04", "updated_at": "2026-05-29 17:36:04" }, { "id": 44738, "question_id": 29899, "hint_level": 1, "hint_text": "Set up: total value before + new bags = new average x new count.", "user_id": 2, "created_at": "2026-05-29 17:36:08", "updated_at": "2026-05-29 17:36:08" }, { "id": 44739, "question_id": 29899, "hint_level": 2, "hint_text": "350u + 1850 = 400(u + 2) gives u = 21.", "user_id": 2, "created_at": "2026-05-29 17:36:08", "updated_at": "2026-05-29 17:36:08" }, { "id": 44750, "question_id": 29905, "hint_level": 1, "hint_text": "Use the difference 26 - 19 to find the small rectangle's width.", "user_id": 2, "created_at": "2026-05-29 17:36:09", "updated_at": "2026-05-29 17:36:09" }, { "id": 44751, "question_id": 29905, "hint_level": 2, "hint_text": "Shaded area = big rectangle - 6 small rectangles = 494 - 325.5 = 168.5 cm².", "user_id": 2, "created_at": "2026-05-29 17:36:09", "updated_at": "2026-05-29 17:36:09" }, { "id": 44822, "question_id": 29941, "hint_level": 1, "hint_text": "Write the total before and after adding the book.", "user_id": 2, "created_at": "2026-05-29 17:36:12", "updated_at": "2026-05-29 17:36:12" }, { "id": 44823, "question_id": 29941, "hint_level": 2, "hint_text": "Set the new average equal to 18 and solve.", "user_id": 2, "created_at": "2026-05-29 17:36:12", "updated_at": "2026-05-29 17:36:12" }, { "id": 44864, "question_id": 29962, "hint_level": 1, "hint_text": "Discounted price is 75% of the original.", "user_id": 2, "created_at": "2026-05-29 17:36:13", "updated_at": "2026-05-29 17:36:13" }, { "id": 44865, "question_id": 29962, "hint_level": 2, "hint_text": "Set up: (discounted units x 0.75p) + (full-price units x p) = 32 330.", "user_id": 2, "created_at": "2026-05-29 17:36:13", "updated_at": "2026-05-29 17:36:13" }, { "id": 44884, "question_id": 29972, "hint_level": 1, "hint_text": "Let Betty = 3 units so Ann = 1 unit.", "user_id": 2, "created_at": "2026-05-29 17:36:14", "updated_at": "2026-05-29 17:36:14" }, { "id": 44885, "question_id": 29972, "hint_level": 2, "hint_text": "Charles = 5\/6 of (Ann + Betty); scale to whole numbers.", "user_id": 2, "created_at": "2026-05-29 17:36:14", "updated_at": "2026-05-29 17:36:14" }, { "id": 45202, "question_id": 30131, "hint_level": 1, "hint_text": "Set up the average equation before and after the two new toys.", "user_id": 2, "created_at": "2026-05-29 18:06:00", "updated_at": "2026-05-29 18:06:00" }, { "id": 45203, "question_id": 30131, "hint_level": 2, "hint_text": "Total cost = final average x total number of toys.", "user_id": 2, "created_at": "2026-05-29 18:06:00", "updated_at": "2026-05-29 18:06:00" }, { "id": 45854, "question_id": 30457, "hint_level": 1, "hint_text": "The total number of cards stays the same: 18n = 12(n + 4).", "user_id": 2, "created_at": "2026-05-29 18:06:33", "updated_at": "2026-05-29 18:06:33" }, { "id": 45855, "question_id": 30457, "hint_level": 2, "hint_text": "Solve for n = 8; total = 8 x 18 = 144.", "user_id": 2, "created_at": "2026-05-29 18:06:33", "updated_at": "2026-05-29 18:06:33" }, { "id": 46048, "question_id": 30554, "hint_level": 1, "hint_text": "Pick a total that makes \\(\\dfrac{1}{4}\\) and \\(\\dfrac{4}{9}\\) whole (e.g. 36u).", "user_id": 2, "created_at": "2026-05-29 18:06:43", "updated_at": "2026-05-29 18:06:43" }, { "id": 46049, "question_id": 30554, "hint_level": 2, "hint_text": "Total photocards = 5 × adults + 4 × boys + 3 × girls = 1932.", "user_id": 2, "created_at": "2026-05-29 18:06:43", "updated_at": "2026-05-29 18:06:43" }, { "id": 46312, "question_id": 30686, "hint_level": 1, "hint_text": "Let the parts left be 5u (red) and 9u (blue); the 9u is 75% of the original blue.", "user_id": 2, "created_at": "2026-05-29 18:07:08", "updated_at": "2026-05-29 18:07:08" }, { "id": 46313, "question_id": 30686, "hint_level": 2, "hint_text": "Form an equation for the total of 329 to find u.", "user_id": 2, "created_at": "2026-05-29 18:07:08", "updated_at": "2026-05-29 18:07:08" }, { "id": 46470, "question_id": 30765, "hint_level": 1, "hint_text": "Let Ahmad = 4 units so Caili = 5 units; Banu = 4 × Ahmad = 16 units.", "user_id": 2, "created_at": "2026-05-29 18:07:22", "updated_at": "2026-05-29 18:07:22" }, { "id": 46471, "question_id": 30765, "hint_level": 2, "hint_text": "Total = 25 units = 725, so 1 unit = 29; Banu = 16 × 29.", "user_id": 2, "created_at": "2026-05-29 18:07:22", "updated_at": "2026-05-29 18:07:22" }, { "id": 46528, "question_id": 30795, "hint_level": 1, "hint_text": "Let the number of each flavour be n.", "user_id": 2, "created_at": "2026-05-29 18:07:23", "updated_at": "2026-05-29 18:07:23" }, { "id": 46529, "question_id": 30795, "hint_level": 2, "hint_text": "Set Jane's leftovers in the ratio 1 : 4 and solve.", "user_id": 2, "created_at": "2026-05-29 18:07:23", "updated_at": "2026-05-29 18:07:23" }, { "id": 46554, "question_id": 30808, "hint_level": 1, "hint_text": "Paul's pens do not change, so keep his units constant.", "user_id": 2, "created_at": "2026-05-29 18:07:23", "updated_at": "2026-05-29 18:07:23" }, { "id": 46555, "question_id": 30808, "hint_level": 2, "hint_text": "Set the new ratio 2 : 1 and solve for u.", "user_id": 2, "created_at": "2026-05-29 18:07:23", "updated_at": "2026-05-29 18:07:23" }, { "id": 46562, "question_id": 30812, "hint_level": 1, "hint_text": "Express both amounts in terms of David's money x.", "user_id": 2, "created_at": "2026-05-29 18:07:24", "updated_at": "2026-05-29 18:07:24" }, { "id": 46563, "question_id": 30812, "hint_level": 2, "hint_text": "After the $21 transfer, set Adam = 4 × David.", "user_id": 2, "created_at": "2026-05-29 18:07:24", "updated_at": "2026-05-29 18:07:24" }, { "id": 46622, "question_id": 30842, "hint_level": 1, "hint_text": "Let the orchids left be a unit; express lilies and tulips left in terms of it.", "user_id": 2, "created_at": "2026-05-29 18:07:25", "updated_at": "2026-05-29 18:07:25" }, { "id": 46623, "question_id": 30842, "hint_level": 2, "hint_text": "Use the total of 64 left, then add the 20 lilies sold.", "user_id": 2, "created_at": "2026-05-29 18:07:25", "updated_at": "2026-05-29 18:07:25" }, { "id": 46684, "question_id": 30873, "hint_level": 1, "hint_text": "Set up muffins per packet as u and tarts per box as u + 9.", "user_id": 2, "created_at": "2026-05-29 18:07:26", "updated_at": "2026-05-29 18:07:26" }, { "id": 46685, "question_id": 30873, "hint_level": 2, "hint_text": "Use muffins : tarts = 68 : 32 to form an equation and solve for u.", "user_id": 2, "created_at": "2026-05-29 18:07:26", "updated_at": "2026-05-29 18:07:26" }, { "id": 46842, "question_id": 30952, "hint_level": 1, "hint_text": "After the first transfer, let Kate be 1 unit and Dan 3 units.", "user_id": 2, "created_at": "2026-05-29 18:07:30", "updated_at": "2026-05-29 18:07:30" }, { "id": 46843, "question_id": 30952, "hint_level": 2, "hint_text": "Set up the second condition (Dan = twice Kate) and solve for the unit.", "user_id": 2, "created_at": "2026-05-29 18:07:30", "updated_at": "2026-05-29 18:07:30" }, { "id": 46850, "question_id": 30956, "hint_level": 1, "hint_text": "She used 180 ÷ 10 = 18 ten-dollar notes paying for the suitcase.", "user_id": 2, "created_at": "2026-05-29 18:07:30", "updated_at": "2026-05-29 18:07:30" }, { "id": 46851, "question_id": 30956, "hint_level": 2, "hint_text": "Set up two-dollar notes = 4 × ten-dollar notes left, using the 12-more relationship.", "user_id": 2, "created_at": "2026-05-29 18:07:30", "updated_at": "2026-05-29 18:07:30" }, { "id": 47040, "question_id": 31051, "hint_level": 1, "hint_text": "Express bag, wallet and dress in terms of her total money u.", "user_id": 2, "created_at": "2026-05-29 18:07:39", "updated_at": "2026-05-29 18:07:39" }, { "id": 47041, "question_id": 31051, "hint_level": 2, "hint_text": "The dress cost = remaining money; set up and solve, then compute the wallet.", "user_id": 2, "created_at": "2026-05-29 18:07:39", "updated_at": "2026-05-29 18:07:39" }, { "id": 47250, "question_id": 31156, "hint_level": 1, "hint_text": "Sister = s, Matthew = 3s now; add 5 to each for their future ages.", "user_id": 2, "created_at": "2026-05-29 18:07:46", "updated_at": "2026-05-29 18:07:46" }, { "id": 47251, "question_id": 31156, "hint_level": 2, "hint_text": "Set the future total equal to h and solve for s.", "user_id": 2, "created_at": "2026-05-29 18:07:46", "updated_at": "2026-05-29 18:07:46" }, { "id": 47294, "question_id": 31178, "hint_level": 1, "hint_text": "Let C = 1 unit, then express A and B in the same units.", "user_id": 2, "created_at": "2026-05-29 18:07:47", "updated_at": "2026-05-29 18:07:47" }, { "id": 47295, "question_id": 31178, "hint_level": 2, "hint_text": "Fraction = A units ÷ total units.", "user_id": 2, "created_at": "2026-05-29 18:07:47", "updated_at": "2026-05-29 18:07:47" } ] }