{
"10237": {
"question": {
"id": 10237,
"status_id": 3,
"type_id": 2,
"correct_answer": null
},
"solutions": [
{
"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"
}
],
"hints": []
},
"10238": {
"question": {
"id": 10238,
"status_id": 3,
"type_id": 2,
"correct_answer": null
},
"solutions": [
{
"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"
}
],
"hints": []
},
"10239": {
"question": {
"id": 10239,
"status_id": 3,
"type_id": 2,
"correct_answer": null
},
"solutions": [
{
"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"
}
],
"hints": []
},
"10240": {
"question": {
"id": 10240,
"status_id": 3,
"type_id": 2,
"correct_answer": null
},
"solutions": [
{
"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"
}
],
"hints": []
},
"10244": {
"question": {
"id": 10244,
"status_id": 3,
"type_id": 2,
"correct_answer": null
},
"solutions": [
{
"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"
}
],
"hints": []
},
"10245": {
"question": {
"id": 10245,
"status_id": 3,
"type_id": 2,
"correct_answer": null
},
"solutions": [
{
"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"
}
],
"hints": []
},
"10251": {
"question": {
"id": 10251,
"status_id": 3,
"type_id": 2,
"correct_answer": null
},
"solutions": [
{
"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"
}
],
"hints": []
},
"10295": {
"question": {
"id": 10295,
"status_id": 3,
"type_id": 2,
"correct_answer": 0
},
"solutions": [
{
"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"
}
],
"hints": [
{
"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"
}
]
},
"10376": {
"question": {
"id": 10376,
"status_id": 3,
"type_id": 2,
"correct_answer": null
},
"solutions": [
{
"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"
}
],
"hints": []
},
"10378": {
"question": {
"id": 10378,
"status_id": 3,
"type_id": 2,
"correct_answer": 0
},
"solutions": [
{
"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"
}
],
"hints": [
{
"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"
}
]
},
"10438": {
"question": {
"id": 10438,
"status_id": 3,
"type_id": 2,
"correct_answer": null
},
"solutions": [
{
"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"
}
],
"hints": []
},
"10440": {
"question": {
"id": 10440,
"status_id": 3,
"type_id": 2,
"correct_answer": null
},
"solutions": [
{
"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"
}
],
"hints": []
},
"10441": {
"question": {
"id": 10441,
"status_id": 3,
"type_id": 2,
"correct_answer": null
},
"solutions": [
{
"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"
}
],
"hints": []
},
"10443": {
"question": {
"id": 10443,
"status_id": 3,
"type_id": 2,
"correct_answer": null
},
"solutions": [
{
"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"
}
],
"hints": []
},
"10445": {
"question": {
"id": 10445,
"status_id": 3,
"type_id": 2,
"correct_answer": null
},
"solutions": [
{
"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"
}
],
"hints": []
}
}