{ "4155": { "sol_id": 3411, "source": "human", "user_id": 41, "sol_status": 1, "q_status": 3, "type": 2, "q": "At first, Nathan and Jack had the same amount water in each of their water bottles. Then, Nathan drank 150ml and and Jack drank 80ml from their water bottles. After that, Jack's water bottle contained thrice as much water as Nathan's water bottle. How much water did each have in their water bottles initially? Answer : ml", "a": [ "185", null, null, null ], "correct": 185, "sol": "Given: Nathan (at first) = Jack (at first) Nathan drank = 150 ml Jack drank = 80 ml Jack (end) = 3 × Nathan (end) Step 1: Express amounts at the end Let starting amount for each = S Nathan (end) = S − 150 Jack (end) = S − 80 Step 2: Set up equation Jack (end) = 3 × Nathan (end) S − 80 = 3 × (S − 150) S − 80 = 3S − 450 Step 3: Solve for S S − 80 = 3S − 450 −80 + 450 = 3S − S 370 = 2S S = 185 Step 4: Verify Nathan (at first) = 185 ml Jack (at first) = 185 ml Nathan (end) = 185 − 150 = 35 ml Jack (end) = 185 − 80 = 105 ml Jack (end) = 3 × Nathan (end): 105 = 3 × 35 ✓ Answer: 185 ml", "all_sols": [ { "id": 3411, "source": "human", "user_id": 41, "status_id": 1 } ], "hint_users": [] }, "4156": { "sol_id": 3412, "source": "human", "user_id": 41, "sol_status": 1, "q_status": 3, "type": 2, "q": "Five days ago, Jed's plant and Einstein's plant were of the same height. Now, Jed's plant has grown taller by 4 cm but Einstein's plant has grown taller by 24 cm. Einstein's plant is now thrice as tall as Jed's plant. How tall was Einstein's plant five days ago? Answer : cm", "a": [ "6", null, null, null ], "correct": 6, "sol": "Given: Jed (5 days ago) = Einstein (5 days ago) Jed grew = 4 cm Einstein grew = 24 cm Einstein (now) = 3 × Jed (now) Step 1: Express heights now Let starting height for each = S Jed (now) = S + 4 Einstein (now) = S + 24 Step 2: Set up equation Einstein (now) = 3 × Jed (now) S + 24 = 3 × (S + 4) S + 24 = 3S + 12 Step 3: Solve for S S + 24 = 3S + 12 24 − 12 = 3S − S 12 = 2S S = 6 Step 4: Verify Jed (5 days ago) = 6 cm Einstein (5 days ago) = 6 cm Jed (now) = 6 + 4 = 10 cm Einstein (now) = 6 + 24 = 30 cm Einstein (now) = 3 × Jed (now): 30 = 3 × 10 ✓ Answer: 6 cm", "all_sols": [ { "id": 3412, "source": "human", "user_id": 41, "status_id": 1 } ], "hint_users": [] }, "4197": { "sol_id": 3413, "source": "human", "user_id": 41, "sol_status": 1, "q_status": 3, "type": 2, "q": "In 2008, the sum of the ages of Mr. Chung and his son Andrew was 47 years. Fourteen years from 2008, Mr. Chung will be twice as old as Andrew. Andrew was years old in 2008.", "a": [ "11", null, null, null ], "correct": 11, "sol": "Non-algebraic Solution #1 Given: Mr. Chung + Andrew = 47 years (in 2008) Mr. Chung = 2 × Andrew (in 2022, 14 years later) Step 1: Find sum of ages in 2022 Both age by 14 years Total increase = 14 + 14 = 28 years Sum in 2022 = 47 + 28 = 75 years Step 2: Find ages in 2022 In 2022: Mr. Chung = 2 × Andrew Draw a model: Andrew (2022): [____] Mr. Chung (2022): [____][____] Total units = 3 3 units = 75 years 1 unit = 75 ÷ 3 = 25 years Andrew (2022) = 1 unit = 25 years Mr. Chung (2022) = 2 units = 50 years Step 3: Find Andrew's age in 2008 = 25 − 14 = 11 years Step 4: Verify Andrew (2008) = 11 years Mr. Chung (2008) = 47 − 11 = 36 years Andrew (2022) = 11 + 14 = 25 years Mr. Chung (2022) = 36 + 14 = 50 years Mr. Chung = 2 × Andrew: 50 = 2 × 25 ✓ Answer: 11 years old Algebraic Solution #2 Given: Mr. Chung + Andrew = 47 years (in 2008) Mr. Chung = 2 × Andrew (in 2022, 14 years later) Step 1: Define variables Let Andrew's age in 2008 = A Mr. Chung's age in 2008 = 47 − A Step 2: Express ages in 2022 (14 years later) Andrew (2022) = A + 14 Mr. Chung (2022) = (47 − A) + 14 = 61 − A Step 3: Set up equation Mr. Chung (2022) = 2 × Andrew (2022) 61 − A = 2 × (A + 14) 61 − A = 2A + 28 Step 4: Solve for A 61 − A = 2A + 28 61 − 28 = 2A + A 33 = 3A A = 11 Step 5: Verify Andrew (2008) = 11 years Mr. Chung (2008) = 47 − 11 = 36 years Andrew (2022) = 11 + 14 = 25 years Mr. Chung (2022) = 36 + 14 = 50 years Mr. Chung = 2 × Andrew: 50 = 2 × 25 ✓ Answer: 11 years old", "all_sols": [ { "id": 3413, "source": "human", "user_id": 41, "status_id": 1 } ], "hint_users": [] }, "4322": { "sol_id": 4068, "source": "human", "user_id": 41, "sol_status": 1, "q_status": 3, "type": 2, "q": "Wendy spent $\\frac{2}{9}$ of her money on an assessment book and had \\(\\$14\\) left. How much money did she have at first? Answer : $", "a": [ "18", null, null, null ], "correct": 0, "sol": "Money left = 1−29=791 - \\frac{2}{9} = \\frac{7}{9}1−92​=97​ 79\\frac{7}{9}97​ of money = 14 dollars Money at first = 14 ÷ 7\/9 = 14 × 9\/7 = 18 dollars ✓", "all_sols": [ { "id": 4068, "source": "human", "user_id": 41, "status_id": 1 } ], "hint_users": [] }, "4330": { "sol_id": 4078, "source": "human", "user_id": 41, "sol_status": 1, "q_status": 3, "type": 1, "q": "Cherry has 1000 dollars. She gives $\\frac{1}{5}$ of her money to her daughter and spends $\\frac{1}{4}$ of the remainder on groceries. She then saves $\\frac{2}{3}$ of what is left in the bank. How much (in dollars) does she save in the bank?", "a": [ "700", "300", "400", "500" ], "correct": 2, "sol": "Let me verify: After giving to daughter: \\(\\$1000\\) - \\frac{1}{5} \\times 1000 = 1000 - 200 = 800$ Spent on groceries: $\\frac{1}{4} \\times 800 = 200$ After groceries: \\(\\$800\\) - 200 = 600$ Saved in bank: $\\frac{2}{3} \\times 600 = 400$", "all_sols": [ { "id": 4078, "source": "human", "user_id": 41, "status_id": 1 } ], "hint_users": [] }, "4343": { "sol_id": 4182, "source": "human", "user_id": 41, "sol_status": 1, "q_status": 3, "type": 2, "q": "Ali had some money. He spent $\\frac{1}{6}$ of it on a watch. Then, he spent $\\frac{3}{5}$ of the remainder on a toy. He had 15 dollars left. How much more did he spend on the toy than the watch? Answer : $", "a": [ "15", null, null, null ], "correct": 15, "sol": "Let total money = 6 units (since $\\frac{1}{6}$ spent on watch) Spent on watch = $\\frac{1}{6}$ × 6 units = 1 unit Remainder = 6 − 1 = 5 units Spent on toy = $\\frac{3}{5}$ × 5 units = 3 units Left = 5 − 3 = 2 units = \\(\\$15\\) 1 unit = \\(\\$7.50\\) Watch = 1 unit = \\(\\$7.50\\) Toy = 3 units = \\(\\$22.50\\) Difference = 22.50 − 7.50 = **\\(\\$15\\)** ✓ Check: Total = 6 units = \\(\\$45\\) Watch = $\\frac{1}{6}$ × 45 = \\(\\$7.50\\) ✓ Remainder = 45 − 7.50 = \\(\\$37.50\\) Toy = $\\frac{3}{5}$ × 37.50 = \\(\\$22.50\\) ✓ Left = 37.50 − 22.50 = \\(\\$15\\) ✓", "all_sols": [ { "id": 4182, "source": "human", "user_id": 41, "status_id": 1 } ], "hint_users": [] }, "4363": { "sol_id": 4107, "source": "human", "user_id": 41, "sol_status": 1, "q_status": 3, "type": 2, "q": "$\\frac{1}{9}$ of X is equal to $\\frac{1}{10}$ of Y. If Y is greater than X by 100, what is the sum of X and Y? The sum of X and Y is .", "a": [ "1900", null, null, null ], "correct": 1900, "sol": "$\\frac{1}{9}$X = $\\frac{1}{10}$Y Y = $\\frac{10}{9}$X Y − X = 100 $\\frac{10}{9}$X − X = 100 $\\frac{1}{9}$X = 100 X = 900 Y = $\\frac{10}{9}$ × 900 = 1000 Sum = 900 + 1000 = 1900 ✓", "all_sols": [ { "id": 4107, "source": "human", "user_id": 41, "status_id": 1 } ], "hint_users": [] }, "4367": { "sol_id": 4111, "source": "human", "user_id": 41, "sol_status": 1, "q_status": 3, "type": 2, "q": "At first, $\\frac{2}{7}$ of the pupils in a class were girls. Then, 12 girls from another class came over and that made $\\frac{1}{2}$ of the pupils girls. How many pupils were there in the class at first? There were pupils in the class at first.", "a": [ "28", null, null, null ], "correct": 28, "sol": "Let total pupils at first = T Girls at first = $\\frac{2}{7}$T After 12 girls joined: Total pupils = T + 12 Girls = $\\frac{2}{7}$T + 12 $\\frac{2}{7}$T + 12 = $\\frac{1}{2}$(T + 12) $\\frac{2}{7}$T + 12 = $\\frac{1}{2}$T + 6 12 − 6 = $\\frac{1}{2}$T − $\\frac{2}{7}$T 6 = $\\frac{7}{14}$T − $\\frac{4}{14}$T 6 = $\\frac{3}{14}$T T = \\(\\$6\\) × \\frac{14}{3}$ = 28 ✓", "all_sols": [ { "id": 4111, "source": "human", "user_id": 41, "status_id": 1 } ], "hint_users": [] }, "4368": { "sol_id": 4112, "source": "human", "user_id": 41, "sol_status": 1, "q_status": 3, "type": 1, "q": "Janet read $\\frac{1}{5}$ of a novel on Saturday and $\\frac{1}{4}$ of the novel on Sunday. If she is able to read $\\frac{1}{9}$ of the novel every day from Monday onwards, which day will she complete reading the novel?.", "a": [ "Friday", "Tuesday", "Wednesday", "Thursday" ], "correct": 0, "sol": "Total after Sunday: 15+14=920\\frac{1}{5} + \\frac{1}{4} = \\frac{9}{20}51​+41​=209​ Remaining: 1120\\frac{11}{20}2011​ Convert to common denominator with 9: use 180 Remaining: 1120=99180\\frac{11}{20} = \\frac{99}{180}2011​=18099​ Each day: 19=20180\\frac{1}{9} = \\frac{20}{180}91​=18020​ Monday: 99180−20180=79180\\frac{99}{180} - \\frac{20}{180} = \\frac{79}{180}18099​−18020​=18079​ Tuesday: 79180−20180=59180\\frac{79}{180} - \\frac{20}{180} = \\frac{59}{180}18079​−18020​=18059​ Wednesday: 59180−20180=39180\\frac{59}{180} - \\frac{20}{180} = \\frac{39}{180}18059​−18020​=18039​ Thursday: 39180−20180=19180\\frac{39}{180} - \\frac{20}{180} = \\frac{19}{180}18039​−18020​=18019​ Friday: 19180−20180=−1180\\frac{19}{180} - \\frac{20}{180} = -\\frac{1}{180}18019​−18020​=−1801​ She completes on Friday! ✓", "all_sols": [ { "id": 4112, "source": "human", "user_id": 41, "status_id": 1 } ], "hint_users": [] }, "4369": { "sol_id": 4113, "source": "human", "user_id": 41, "sol_status": 1, "q_status": 3, "type": 2, "q": "In a class, $\\frac{1}{3}$ of the pupils needed glasses. Then, 3 pupils who needed glasses were transferred out of the class and the fraction of the pupils who needed glasses dropped to $\\frac{1}{4}$. How many pupils were there in the class in the end? Answer :", "a": [ "24", null, null, null ], "correct": 24, "sol": "Let total pupils at first = T Pupils who needed glasses at first = $\\frac{1}{3}$T After 3 pupils who needed glasses left: Total pupils = T − 3 Pupils who needed glasses = $\\frac{1}{3}$T − 3 $\\frac{1}{3}$T − 3 = $\\frac{1}{4}$(T − 3) $\\frac{1}{3}$T − 3 = $\\frac{1}{4}$T − $\\frac{3}{4}$ $\\frac{1}{3}$T − $\\frac{1}{4}$T = 3 − $\\frac{3}{4}$ $\\frac{4}{12}$T − $\\frac{3}{12}$T = $\\frac{12}{4} - \\frac{3}{4}$ $\\frac{1}{12}$T = $\\frac{9}{4}$ T = $\\frac{9}{4}$ × 12 = 27 Pupils in the end = 27 − 3 = 24 ✓ Check: At first: 27 pupils, $\\frac{1}{3}$ × 27 = 9 needed glasses After: 24 pupils, 9 − 3 = 6 needed glasses $\\frac{6}{24} = \\frac{1}{4}$ ✓", "all_sols": [ { "id": 4113, "source": "human", "user_id": 41, "status_id": 1 } ], "hint_users": [] }, "4374": { "sol_id": 4118, "source": "human", "user_id": 41, "sol_status": 1, "q_status": 3, "type": 2, "q": "Lionel had some marbles. He gave $\\frac{1}{3}$ of them to Paul. He then gave $\\frac{1}{4}$ of the remainder to Han and $\\frac{1}{6}$ of the remainder to Nick. He kept the rest of the marbles. If Han got 12 marbles, how many marbles did Lionel have at first? Answer :", "a": [ "72", null, null, null ], "correct": 72, "sol": "Let total marbles at first = T Given to Paul: $\\frac{1}{3}$T Remainder after Paul: \\(\\$1\\) - \\frac{1}{3} = \\frac{2}{3}$T Given to Han: $\\frac{1}{4}$ of remainder = $\\frac{1}{4} \\times \\frac{2}{3}$T = $\\frac{2}{12}$T = $\\frac{1}{6}$T Han got 12 marbles: $\\frac{1}{6}$T = 12 T = 72 ✓", "all_sols": [ { "id": 4118, "source": "human", "user_id": 41, "status_id": 1 } ], "hint_users": [] }, "4376": { "sol_id": 4122, "source": "human", "user_id": 41, "sol_status": 1, "q_status": 3, "type": 2, "q": "Now Mabel's age is $\\frac{1}{2}$ of her sister's age. 4 years from now, her age will be $\\frac{2}{3}$ of her sister's age. How old will Mabel's sister be in 4 years? Mabel's sister will be years' old in 4 years.", "a": [ "12", null, null, null ], "correct": 12, "sol": "Solution (algebraic): Let Mabel's current age = M Let Sister's current age = S Now: M = $\\frac{1}{2}$S 4 years from now: M + 4 = $\\frac{2}{3}$(S + 4) Substitute M = $\\frac{1}{2}$S into the second equation: $\\frac{1}{2}$S + 4 = $\\frac{2}{3}$(S + 4) $\\frac{1}{2}$S + 4 = $\\frac{2}{3}$S + $\\frac{8}{3}$ 4 − $\\frac{8}{3}$ = $\\frac{2}{3}$S − $\\frac{1}{2}$S $\\frac{12}{3}$ − $\\frac{8}{3}$ = $\\frac{4}{6}$S − $\\frac{3}{6}$S $\\frac{4}{3}$ = $\\frac{1}{6}$S S = $\\frac{4}{3}$ × 6 = 8 Sister's current age = 8 years Sister's age in 4 years = 8 + 4 = **12 years**", "all_sols": [ { "id": 4121, "source": "human", "user_id": 41, "status_id": 1 }, { "id": 4122, "source": "human", "user_id": 41, "status_id": 1 } ], "hint_users": [] }, "4378": { "sol_id": 4126, "source": "human", "user_id": 41, "sol_status": 1, "q_status": 3, "type": 2, "q": "At first, Eddy had $\\frac{2}{7}$ as much money as Caleb. Then Caleb gave 20 dollars to Eddy. Now, Eddy has $\\frac{1}{2}$ as much money as Caleb. How much money did Eddy have at first? Eddy had $ at first.", "a": [ "40", null, null, null ], "correct": 40, "sol": "Solution (algebraic): Let Eddy's money at first = E Let Caleb's money at first = C At first: E = $\\frac{2}{7}$C After Caleb gave \\(\\$20\\) to Eddy: Eddy has: E + 20 Caleb has: C − 20 E + 20 = $\\frac{1}{2}$(C − 20) Substitute E = $\\frac{2}{7}$C: $\\frac{2}{7}$C + 20 = $\\frac{1}{2}$(C − 20) $\\frac{2}{7}$C + 20 = $\\frac{1}{2}$C − 10 20 + 10 = $\\frac{1}{2}$C − $\\frac{2}{7}$C 30 = $\\frac{7}{14}$C − $\\frac{4}{14}$C 30 = $\\frac{3}{14}$C C = 30 × $\\frac{14}{3}$ = 140 Eddy at first = E = $\\frac{2}{7}$ × 140 = **\\(\\$40\\)** ✓", "all_sols": [ { "id": 4125, "source": "human", "user_id": 41, "status_id": 1 }, { "id": 4126, "source": "human", "user_id": 41, "status_id": 1 } ], "hint_users": [] }, "4379": { "sol_id": 4128, "source": "human", "user_id": 41, "sol_status": 1, "q_status": 3, "type": 2, "q": "Container A and Container B had some water. Container A had $\\frac{7}{10}$ as much water as Container B. Then, 300 ml of water was poured from Container A to Container B. After that, Container A had $\\frac{4}{13}$ as much water as Container B. How much water was in the containers altogether? Answer : ml", "a": [ "1700", null, null, null ], "correct": 1700, "sol": "Solution (algebraic): Let Container A at first = A Let Container B at first = B At first: A = $\\frac{7}{10}$B After 300 ml poured from A to B: Container A has: A − 300 Container B has: B + 300 A − 300 = $\\frac{4}{13}$(B + 300) Substitute A = $\\frac{7}{10}$B: $\\frac{7}{10}$B − 300 = $\\frac{4}{13}$(B + 300) $\\frac{7}{10}$B − 300 = $\\frac{4}{13}$B + $\\frac{1200}{13}$ $\\frac{7}{10}$B − $\\frac{4}{13}$B = 300 + $\\frac{1200}{13}$ $\\frac{91}{130}$B − $\\frac{40}{130}$B = $\\frac{3900}{13}$ + $\\frac{1200}{13}$ $\\frac{51}{130}$B = $\\frac{5100}{13}$ B = $\\frac{5100}{13}$ × $\\frac{130}{51}$ B = $\\frac{5100 × 130}{13 × 51}$ B = $\\frac{5100 × 10}{51}$ B = $\\frac{51000}{51}$ = 1000 ml A = $\\frac{7}{10}$ × 1000 = 700 ml Total = A + B = 700 + 1000 = **1700 ml** ✓", "all_sols": [ { "id": 4127, "source": "human", "user_id": 41, "status_id": 1 }, { "id": 4128, "source": "human", "user_id": 41, "status_id": 1 } ], "hint_users": [] }, "4380": { "sol_id": 4129, "source": "human", "user_id": 41, "sol_status": 1, "q_status": 3, "type": 2, "q": "At first, there were $\\frac{4}{5}$ as many boys as girls on a bus. Then, a boy alighted from the bus and a girl boarded the bus. Now, there are $\\frac{5}{7}$ as many boys as girls on the bus. Find the number of boys and the number of girls on the bus now. Boys : Girls :", "a": [ "15", "21", null, null ], "correct": 15, "sol": "Solution (algebraic): Let Girls at first = G Let Boys at first = B At first: B = $\\frac{4}{5}$G After 1 boy alighted and 1 girl boarded: Boys = B − 1 Girls = G + 1 B − 1 = $\\frac{5}{7}$(G + 1) Substitute B = $\\frac{4}{5}$G: $\\frac{4}{5}$G − 1 = $\\frac{5}{7}$(G + 1) $\\frac{4}{5}$G − 1 = $\\frac{5}{7}$G + $\\frac{5}{7}$ $\\frac{4}{5}$G − $\\frac{5}{7}$G = 1 + $\\frac{5}{7}$ $\\frac{28}{35}$G − $\\frac{25}{35}$G = $\\frac{7}{7}$ + $\\frac{5}{7}$ $\\frac{3}{35}$G = $\\frac{12}{7}$ G = $\\frac{12}{7}$ × $\\frac{35}{3}$ = $\\frac{12 × 35}{7 × 3}$ = $\\frac{12 × 5}{3}$ = 20 B = $\\frac{4}{5}$ × 20 = 16 Boys now = 16 − 1 = **15** ✓ Girls now = 20 + 1 = **21** ✓", "all_sols": [ { "id": 4129, "source": "human", "user_id": 41, "status_id": 1 }, { "id": 4131, "source": "human", "user_id": 41, "status_id": 1 } ], "hint_users": [] }, "4924": { "sol_id": 437, "source": "human", "user_id": 358, "sol_status": 1, "q_status": 3, "type": 2, "q": "UVWX is a trapezium. Find ∠ UXV . ˚", "a": [ "61", null, null, null ], "correct": 61, "sol": "VXW = UVX = 29 VXU = 180 - 90 - 29 = 61", "all_sols": [ { "id": 437, "source": "human", "user_id": 358, "status_id": 1 } ], "hint_users": [] }, "4930": { "sol_id": 440, "source": "human", "user_id": 358, "sol_status": 1, "q_status": 3, "type": 1, "q": "Find ∠ XWY.", "a": [ "14°", "26°", "28°", "34°" ], "correct": 1, "sol": "WYZ = 180 - 76 - 50 = 54 WYX = 180 - 54 = 126 XWY = 180 - 126 - 28 = 26", "all_sols": [ { "id": 440, "source": "human", "user_id": 358, "status_id": 1 } ], "hint_users": [] }, "5285": { "sol_id": 4143, "source": "human", "user_id": 41, "sol_status": 1, "q_status": 3, "type": 1, "q": "The figure shows two rectangles A and B overlapping each other. The area of the shaded part is $\\frac{2}{5}$ of the area of rectangle A. The area of the shaded part is $\\frac{1}{8}$ of the area of rectangle B. What fraction of the figure is shaded?", "a": [ "$\\frac{1}{10}$", "$\\frac{2}{19}$", "$\\frac{3}{19}$", "$\\frac{1}{9}$" ], "correct": 1, "sol": "Let the shaded area = S Shaded area = $\\frac{2}{5}$ of rectangle A Rectangle A = S × $\\frac{5}{2}$ = $\\frac{5S}{2}$ Shaded area = $\\frac{1}{8}$ of rectangle B Rectangle B = 8S Total area of figure = Rectangle A + Rectangle B − Shaded area Total area = $\\frac{5S}{2}$ + 8S − S = $\\frac{5S + 14S}{2}$ = $\\frac{19S}{2}$ Fraction shaded = $\\frac{S}{\\frac{19S}{2}}$ = $\\frac{2}{19}$ ✓", "all_sols": [ { "id": 4143, "source": "human", "user_id": 41, "status_id": 1 } ], "hint_users": [] }, "5286": { "sol_id": 1651, "source": "human", "user_id": 2, "sol_status": 1, "q_status": 3, "type": 1, "q": "$\\frac{1}{4}$ of X is equal to $\\frac{4}{5}$ of Y. What fraction of Y is X?", "a": [ "$\\frac{5}{16}$", "$\\frac{16}{5}$", "$\\frac{1}{5}$", "$\\frac{5}{4}$" ], "correct": 1, "sol": "Given: 14\\dfrac{1}{4}41​ of x is 45\\dfrac{4}{5}54​ of Y. What fraction of Y is x? Step 1: Write the equation 14\\dfrac{1}{4}41​ × x = 45\\dfrac{4}{5}54​ × Y Step 2: Solve for x in terms of Y 14\\dfrac{1}{4}41​x = 45\\dfrac{4}{5}54​Y Step 3: Multiply both sides by 4 x = 4 × 45\\dfrac{4}{5}54​Y Step 4: Simplify x = 165\\dfrac{16}{5}516​Y Answer: x is 165\\dfrac{16}{5}516​ of Y", "all_sols": [ { "id": 1651, "source": "human", "user_id": 2, "status_id": 1 } ], "hint_users": [] }, "5287": { "sol_id": 4144, "source": "human", "user_id": 41, "sol_status": 1, "q_status": 3, "type": 2, "q": "$\\frac{2}{9}$ of P is equal to $\\frac{1}{7}$ of Q. What is the ratio of P to Q? P : Q = :", "a": [ "9", "14", null, null ], "correct": 9, "sol": "29\\frac{2}{9}92​ × P = 17\\frac{1}{7}71​ × Q P = 17\\frac{1}{7}71​ × Q × 92\\frac{9}{2}29​ P = 914\\frac{9}{14}149​ × Q PQ\\frac{P}{Q}QP​ = 914\\frac{9}{14}149​ P : Q = 9 : 14 ✓", "all_sols": [ { "id": 4144, "source": "human", "user_id": 41, "status_id": 1 } ], "hint_users": [] }, "5288": { "sol_id": 4049, "source": "human", "user_id": 41, "sol_status": 1, "q_status": 3, "type": 2, "q": "Alan's height is 5\/6 of Shaun's height. Max's height is half of Alan's height. Express Max's height as a fraction of Shaun's height: A\/B A: B:", "a": [ "5", "12", null, null ], "correct": 5, "sol": "Let Shaun's height = 1 Alan's height = 5\/6 of Shaun's = 5\/6 Max's height = 1\/2 of Alan's = 1\/2 × 5\/6 = **5\/12** A\/B = **5\/12**", "all_sols": [ { "id": 4049, "source": "human", "user_id": 41, "status_id": 1 } ], "hint_users": [] }, "5290": { "sol_id": 4146, "source": "human", "user_id": 41, "sol_status": 1, "q_status": 3, "type": 2, "q": "On a bus, the number of children was $\\frac{5}{7}$ of the number of adults. After a child alighted from the bus and an adult boarded the bus, the number of children became $\\frac{1}{2}$ of the number of adults. How many people were there on the bus? Answer :", "a": [ "72", null, null, null ], "correct": 72, "sol": "Solution (algebraic): Let number of adults at first = A Let number of children at first = C At first: C = $\\frac{5}{7}$A After 6 children alighted and 6 adults boarded: Children = C − 6 Adults = A + 6 C − 6 = $\\frac{1}{2}$(A + 6) Substitute C = $\\frac{5}{7}$A: $\\frac{5}{7}$A − 6 = $\\frac{1}{2}$(A + 6) $\\frac{5}{7}$A − 6 = $\\frac{1}{2}$A + 3 $\\frac{5}{7}$A − $\\frac{1}{2}$A = 6 + 3 $\\frac{10}{14}$A − $\\frac{7}{14}$A = 9 $\\frac{3}{14}$A = 9 A = 9 × $\\frac{14}{3}$ = 42 C = $\\frac{5}{7}$ × 42 = 30 Total = A + C = 42 + 30 = **72 people** ✓", "all_sols": [ { "id": 4145, "source": "human", "user_id": 41, "status_id": 1 }, { "id": 4146, "source": "human", "user_id": 41, "status_id": 1 } ], "hint_users": [] }, "5295": { "sol_id": 4053, "source": "human", "user_id": 41, "sol_status": 1, "q_status": 3, "type": 2, "q": "On a school bus, there were \\(\\$1\\)\\frac{1}{2}$ as many boys as girls. After 6 boys alighted from the bus, there were $\\frac{3}{4}$ as many boys as girls. How many children were there in the bus at first? Answer :", "a": [ "20", null, null, null ], "correct": 34, "sol": "At first: Boys : Girls = 32\\frac{3}{2}23​ : 1 = 3 : 2 After: Boys : Girls = 3 : 4 Make girls equal in both ratios: Before → Boys : Girls = 3 : 2 = 6 : 4 After → Boys : Girls = 3 : 4 Difference in boys = 6 − 3 = 3 units 3 units = 6 boys 1 unit = 2 At first: Boys = 6 units = 12 Girls = 4 units = 8 Total children at first = 12 + 8 = **20 children**", "all_sols": [ { "id": 4053, "source": "human", "user_id": 41, "status_id": 1 } ], "hint_users": [] }, "5313": { "sol_id": 4152, "source": "human", "user_id": 41, "sol_status": 1, "q_status": 3, "type": 2, "q": "At first, there were 94 passengers on a bus. Then, $\\frac{1}{2}$ of the adults and $\\frac{5}{6}$ of the children alighted from the bus. In the end, there were 41 passengers on the bus. How many adults were there on the bus in the end? Answer :", "a": [ "38", null, null, null ], "correct": 38, "sol": "At first: 94 passengers In the end: 41 passengers Alighted: 94 − 41 = 53 passengers Let adults at first = A, children at first = C A + C = 94 Adults alighted = $\\frac{1}{2}$A, so adults remaining = $\\frac{1}{2}$A Children alighted = $\\frac{5}{6}$C, so children remaining = $\\frac{1}{6}$C $\\frac{1}{2}$A + $\\frac{1}{6}$C = 41 Multiply by 6: 3A + C = 246 From A + C = 94: C = 94 − A 3A + (94 − A) = 246 2A = 152 A = 76 adults at first C = 94 − 76 = 18 children at first Adults in the end = $\\frac{1}{2}$ × 76 = **38** ✓ Check: Children in the end = $\\frac{1}{6}$ × 18 = 3 Total in the end = 38 + 3 = 41 ✓", "all_sols": [ { "id": 4152, "source": "human", "user_id": 41, "status_id": 1 }, { "id": 4153, "source": "human", "user_id": 41, "status_id": 1 } ], "hint_users": [] }, "5314": { "sol_id": 4157, "source": "human", "user_id": 41, "sol_status": 1, "q_status": 3, "type": 2, "q": "At first, there were 94 passengers on a bus. Then, $\\frac{1}{2}$ of the adults and $\\frac{5}{6}$ of the children alighted from the bus. In the end, there were 41 passengers on the bus. How many children alighted from the bus?", "a": [ "15", null, null, null ], "correct": 15, "sol": "Solution (non-algebraic using units): Adults remaining = $\\frac{1}{2}$ of adults → Adults at first = 2 units, Adults remaining = 1 unit Children remaining = $\\frac{1}{6}$ of children → Children at first = 6 parts, Children remaining = 1 part At first: 2 units of adults + 6 parts of children = 94 In the end: 1 unit of adults + 1 part of children = 41 Double the \"In the end\" equation: 2 units of adults + 2 parts of children = 82 Subtract from \"At first\" equation: (2 units + 6 parts) − (2 units + 2 parts) = 94 − 82 4 parts of children = 12 1 part = 3 children Children at first = 6 parts = 6 × 3 = 18 children Children alighted = $\\frac{5}{6}$ × 18 = **15** ✓", "all_sols": [ { "id": 4154, "source": "human", "user_id": 41, "status_id": 1 }, { "id": 4157, "source": "human", "user_id": 41, "status_id": 1 } ], "hint_users": [] }, "5316": { "sol_id": 4159, "source": "human", "user_id": 41, "sol_status": 1, "q_status": 3, "type": 2, "q": "In a class, there were 39 pupils. $\\frac{1}{5}$ of the boys and $\\frac{1}{3}$ of the girls wore glasses. 9 pupils wore glasses. How many more boys than girls were there in the class? Answer :", "a": [ "21", null, null, null ], "correct": 21, "sol": "--- Solution (non-algebraic using units): Boys wearing glasses = $\\frac{1}{5}$ of boys → Boys = 5 units, Boys with glasses = 1 unit Girls wearing glasses = $\\frac{1}{3}$ of girls → Girls = 3 parts, Girls with glasses = 1 part Total pupils: 5 units of boys + 3 parts of girls = 39 Pupils with glasses: 1 unit of boys + 1 part of girls = 9 Multiply \"with glasses\" equation by 3: 3 units of boys + 3 parts of girls = 27 Subtract from \"total pupils\" equation: (5 units + 3 parts) − (3 units + 3 parts) = 39 − 27 2 units of boys = 12 1 unit = 6 Boys = 5 units = 5 × 6 = 30 Girls = 39 − 30 = 9 Difference = 30 − 9 = **21 more boys** ✓", "all_sols": [ { "id": 4159, "source": "human", "user_id": 41, "status_id": 1 } ], "hint_users": [] }, "5338": { "sol_id": 4175, "source": "human", "user_id": 41, "sol_status": 1, "q_status": 3, "type": 2, "q": "Mel has $\\frac{6}{7}$ as many marbles as Jay. Zack has $\\frac{1}{8}$ as many marbles as Mel. Jay has 75 more marbles than Zack. Find the ratio of the number of marbles that Mel has to the number of marbles that Jay has to the number of marbles that Zack has. Zack : Mel : Jay = : :", "a": [ "24", "28", "3", null ], "correct": 24, "sol": "Let Jay = 7 units (since Mel = $\\frac{6}{7}$ of Jay) Mel = $\\frac{6}{7}$ × 7 units = 6 units Zack = $\\frac{1}{8}$ × Mel = $\\frac{1}{8}$ × 6 units = $\\frac{6}{8}$ units = $\\frac{3}{4}$ units Jay − Zack = 75 7 units − $\\frac{3}{4}$ units = 75 $\\frac{28}{4}$ units − $\\frac{3}{4}$ units = 75 $\\frac{25}{4}$ units = 75 1 unit = 75 × $\\frac{4}{25}$ = 12 Mel = 6 units = 6 × 12 = 72 marbles Jay = 7 units = 7 × 12 = 84 marbles Zack = $\\frac{3}{4}$ units = $\\frac{3}{4}$ × 12 = 9 marbles Ratio = Mel : Jay : Zack = 72 : 84 : 9 Simplify by dividing by 3: = 24 : 28 : 3 ✓ Check: Jay − Zack = 84 − 9 = 75 ✓ Mel\/Jay = 72\/84 = 6\/7 ✓ Zack\/Mel = 9\/72 = 1\/8 ✓", "all_sols": [ { "id": 4175, "source": "human", "user_id": 41, "status_id": 1 } ], "hint_users": [] }, "5339": { "sol_id": 4176, "source": "human", "user_id": 41, "sol_status": 1, "q_status": 3, "type": 2, "q": "Mel has $\\frac{3}{4}$ as many marbles as Jay. Zack has $\\frac{7}{24}$ as many marbles as Mel. Jay has 75 more marbles than Zack. Jay and Mel want to give some of their marbles to Zack so that in the end, the three of them will each have the same number of marbles. How many marbles must Jay and Mel give to Zack altogether? Answer :", "a": [ "42", null, null, null ], "correct": 42, "sol": "Let Jay = 4 units (since Mel = $\\frac{3}{4}$ of Jay) Mel = $\\frac{3}{4}$ × 4 units = 3 units Zack = $\\frac{7}{24}$ × Mel = $\\frac{7}{24}$ × 3 units = $\\frac{21}{24}$ units = $\\frac{7}{8}$ units Jay − Zack = 75 4 units − $\\frac{7}{8}$ units = 75 $\\frac{32}{8}$ − $\\frac{7}{8}$ = 75 $\\frac{25}{8}$ units = 75 1 unit = 75 × $\\frac{8}{25}$ = 24 At first: Jay = 4 units = 4 × 24 = 96 marbles Mel = 3 units = 3 × 24 = 72 marbles Zack = $\\frac{7}{8}$ units = $\\frac{7}{8}$ × 24 = 21 marbles Total = 96 + 72 + 21 = 189 marbles After equal sharing: Each person = 189 ÷ 3 = 63 marbles Zack receives = 63 − 21 = **42 marbles** ✓ Check: Jay − Zack = 96 − 21 = 75 ✓ Mel\/Jay = 72\/96 = 3\/4 ✓ Zack\/Mel = 21\/72 = 7\/24 ✓", "all_sols": [ { "id": 4176, "source": "human", "user_id": 41, "status_id": 1 } ], "hint_users": [] }, "5372": { "sol_id": 4179, "source": "human", "user_id": 41, "sol_status": 1, "q_status": 3, "type": 2, "q": "Mr Sam's savings is $\\frac{4}{7}$ of Mr Mcdonald's savings. Mr Mcdonald has saved 343 dollars. Find Mr Sam's savings. Answer : $", "a": [ "196", null, null, null ], "correct": 196, "sol": "Mr Mcdonald's savings = \\(\\$343\\) Mr Sam's savings = 47\\frac{4}{7}74​ of Mr Mcdonald's savings Mr Sam's savings = 47\\frac{4}{7}74​ × \\(\\$343\\) = 4×3437\\frac{4 × 343}{7}74×343​ = 13727\\frac{1372}{7}71372​ = **\\(\\$196\\)** ✓ Check: 196343\\frac{196}{343}343196​ = 47\\frac{4}{7}74​ ✓ (since 196 = 4 × 49 and 343 = 7 × 49)", "all_sols": [ { "id": 4179, "source": "human", "user_id": 41, "status_id": 1 } ], "hint_users": [] }, "5382": { "sol_id": 4181, "source": "human", "user_id": 41, "sol_status": 1, "q_status": 3, "type": 1, "q": "Kylie, Kris and Bruce shared some sweets. Kris got thrice as many sweets as Kylie. The number of sweets that Kris got was $\\frac{7}{12}$ of the number of sweets that the children shared. Express the number of sweets that Bruce got as a fraction of the total number of sweets that Kris and Kylie got.", "a": [ "$\\frac{1}{7}$", "$\\frac{2}{7}$", "$\\frac{3}{7}$", "$\\frac{4}{7}$" ], "correct": 1, "sol": "Kris = 3 × Kylie Let Kylie = 1 part, then Kris = 3 parts Kris + Kylie = 4 parts Kris = $\\frac{7}{12}$ of total 3 parts = $\\frac{7}{12}$ of total Total = 3 parts × $\\frac{12}{7}$ = $\\frac{36}{7}$ parts Bruce = Total − (Kris + Kylie) = $\\frac{36}{7}$ parts − 4 parts = $\\frac{36}{7}$ − $\\frac{28}{7}$ = $\\frac{8}{7}$ parts Bruce as fraction of (Kris + Kylie) = $\\frac{8\/7 \\text{ parts}}{4 \\text{ parts}}$ = $\\frac{8}{7}$ × $\\frac{1}{4}$ = $\\frac{8}{28}$ = $\\frac{2}{7}$ ✓ Check: Kylie = 1 part, Kris = 3 parts, Bruce = $\\frac{8}{7}$ parts Total = 4 + $\\frac{8}{7}$ = $\\frac{36}{7}$ parts Kris\/Total = $\\frac{3}{36\/7}$ = $\\frac{3 × 7}{36}$ = $\\frac{21}{36}$ = $\\frac{7}{12}$ ✓", "all_sols": [ { "id": 4181, "source": "human", "user_id": 41, "status_id": 1 } ], "hint_users": [] }, "7046": { "sol_id": 495, "source": "human", "user_id": 41, "sol_status": 3, "q_status": 3, "type": 1, "q": "Write the division sentence for the fraction $\\frac{3}{5}$.", "a": [ "$\\dfrac{3}{5}$ = $3 \\div 5$", "$\\dfrac{3}{5}$ = $5 \\div 3$", "$\\frac{3}{5}$ = 15", "$\\frac{3}{5}$ = 3 and 5" ], "correct": 0, "sol": "Method: standard Steps: 1. Identify the fraction 35\\frac{3}{5}53​. 2. Write it as 3÷53 \\div 53÷5. Final Answer: 35\\dfrac{3}{5}53​ = 3÷53 \\div 53÷5", "all_sols": [ { "id": 495, "source": "human", "user_id": 41, "status_id": 3 } ], "hint_users": [] }, "7086": { "sol_id": 534, "source": "human", "user_id": 41, "sol_status": 3, "q_status": 3, "type": 1, "q": "What is 2 $$\\dfrac{1}{2}$$ + 1 $$\\dfrac{1}{2}$$? Write your answer as a mixed number.", "a": [ "4 $$\\frac{1}{2}$$", "4 $$\\frac{5}{8}$$", "3 $$\\frac{1}{2}$$", "4" ], "correct": 3, "sol": "Method: standard Steps: 1. Add whole numbers: 2 + 1 = 3 2. Convert 34\\frac{3}{4}43​ to 68\\frac{6}{8}86​ 3. Add fractions: 28+68=88\\frac{2}{8} + \\frac{6}{8} = \\frac{8}{8}82​+86​=88​ 4. Combine: Final Answer: 4", "all_sols": [ { "id": 534, "source": "human", "user_id": 41, "status_id": 3 } ], "hint_users": [ { "user_id": 41, "c": 3 } ] }, "7093": { "sol_id": 4052, "source": "human", "user_id": 41, "sol_status": 1, "q_status": 3, "type": 1, "q": "Calculate 6$\\frac{3}{8}$ - 4$\\frac{2}{3}$ and write it as a mixed number in simplest form.", "a": [ "1$\\frac{5}{24}$", "2$\\frac{5}{24}$", "1$\\frac{17}{24}$", "2$\\frac{1}{8}$" ], "correct": 2, "sol": "Step 1: Convert 6386\\frac{3}{8}683​ to an improper fraction: 518\\frac{51}{8}851​ Step 2: Convert 4234\\frac{2}{3}432​ to an improper fraction: 143\\frac{14}{3}314​ Step 3: Find a common denominator (24) Step 4: Rewrite the fractions: 15324−11224\\frac{153}{24} - \\frac{112}{24}24153​−24112​ Step 5: Subtract: 4124\\frac{41}{24}2441​ Step 6: Convert 4124\\frac{41}{24}2441​ to a mixed number: 11724\\mathbf{1\\frac{17}{24}}12417​", "all_sols": [ { "id": 4052, "source": "human", "user_id": 41, "status_id": 1 } ], "hint_users": [ { "user_id": 41, "c": 3 } ] }, "7094": { "sol_id": 541, "source": "human", "user_id": 41, "sol_status": 3, "q_status": 3, "type": 1, "q": "Find the result of 7$\\frac{1}{2}$ - 3$\\frac{3}{5}$ and express it as a mixed number in simplest form.", "a": [ "3$\\frac{1}{10}$", "4$\\frac{1}{10}$", "3$\\frac{3}{10}$", "3$\\frac{9}{10}$" ], "correct": 3, "sol": "Method: standard Steps: 1. Convert 712\\frac{1}{2}21​ to an improper fraction: 15\/2 2. Convert 335\\frac{3}{5}53​ to an improper fraction: 18\/5 3. Find a common denominator (10) 4. Rewrite the fractions: 75\/10 - 36\/10 5. Subtract: 39\/10 6. Convert 39\/10 to a mixed number: 3910\\frac{9}{10}109​", "all_sols": [ { "id": 541, "source": "human", "user_id": 41, "status_id": 3 } ], "hint_users": [ { "user_id": 41, "c": 3 } ] }, "7096": { "sol_id": 543, "source": "human", "user_id": 41, "sol_status": 3, "q_status": 3, "type": 1, "q": "Calculate 9$\\frac{1}{5}$ - 6$\\frac{2}{3}$ and express it as a mixed number in simplest form.", "a": [ "2$\\frac{4}{15}$", "3$\\frac{4}{15}$", "2$\\frac{1}{15}$", "2$\\frac{8}{15}$" ], "correct": 3, "sol": "Method: standard Steps: 1. Convert 915\\frac{1}{5}51​ to an improper fraction: 46\/5 2. Convert 623\\frac{2}{3}32​ to an improper fraction: 20\/3 3. Find a common denominator (15) 4. Rewrite the fractions: 138\/15 - 100\/15 5. Subtract: 38\/15 6. Convert 38\/15 to a mixed number: 2815\\frac{8}{15}158​", "all_sols": [ { "id": 543, "source": "human", "user_id": 41, "status_id": 3 } ], "hint_users": [ { "user_id": 41, "c": 3 } ] }, "7097": { "sol_id": 544, "source": "human", "user_id": 41, "sol_status": 3, "q_status": 3, "type": 1, "q": "What is 10$\\frac{3}{4}$ - 7$\\frac{1}{2}$ expressed as a mixed number in simplest form?", "a": [ "2$\\frac{1}{4}$", "3$\\frac{1}{4}$", "2$\\frac{3}{4}$", "3$\\frac{3}{4}$" ], "correct": 1, "sol": "Method: standard Steps: 1. Convert 1034\\frac{3}{4}43​ to an improper fraction: 43\/4 2. Convert 712\\frac{1}{2}21​ to an improper fraction: 15\/2 3. Find a common denominator (4) 4. Rewrite the fractions: 43\/4 - 30\/4 5. Subtract: 13\/4 6. Convert 13\/4 to a mixed number: 314\\frac{1}{4}41​", "all_sols": [ { "id": 544, "source": "human", "user_id": 41, "status_id": 3 } ], "hint_users": [ { "user_id": 41, "c": 3 } ] }, "7192": { "sol_id": 631, "source": "human", "user_id": 41, "sol_status": 3, "q_status": 3, "type": 1, "q": "A video game costs 1,200 dollars after a 15% discount and 10% tax. What was its original price (rounded to the nearest dollar)?", "a": [ "1300", "1276", "1283", "1294" ], "correct": 2, "sol": "Method: standard Steps: 1. Let original price be y. 2. After a 15% discount, the price is 85% of y. 3. Then, after 10% tax, it becomes 110% of 85% of y. 4. Set up the equation: 1.1 * 0.85 * y = 1200. 5. Solve for y. y=1283.42 Final Answer: 1283 (to nearest dollar)", "all_sols": [ { "id": 631, "source": "human", "user_id": 41, "status_id": 3 } ], "hint_users": [ { "user_id": 41, "c": 3 } ] }, "7193": { "sol_id": 632, "source": "human", "user_id": 41, "sol_status": 3, "q_status": 3, "type": 1, "q": "A tablet is priced at 450 dollars after a 5% discount and 10% sales tax. What was its original price, rounded to the nearest dollar?", "a": [ "500", "451", "431", "650" ], "correct": 2, "sol": "Method: standard Steps: 1. Let original price be z. 2. After a 5% discount, the price is 95% of z. 3. Then, after 10% tax, it becomes 110% of 95% of z. 4. Set up the equation: 1.1 * 0.95 * z = 450. 5. Solve for z.", "all_sols": [ { "id": 632, "source": "human", "user_id": 41, "status_id": 3 } ], "hint_users": [ { "user_id": 41, "c": 3 } ] }, "7194": { "sol_id": 633, "source": "human", "user_id": 41, "sol_status": 3, "q_status": 3, "type": 1, "q": "A pair of shoes costs 720 dollars after a 20% discount and 8% tax. What was the original price, rounded to the nearest dollar?", "a": [ "830", "833", "850", "880" ], "correct": 1, "sol": "Method: standard Steps: 1. Let original price be w. 2. After a 20% discount, the price is 80% of w. 3. Then, after 8% tax, it becomes 108% of 80% of w. 4. Set up the equation: 1.08 * 0.8 * w = 720. 5. Solve for w.", "all_sols": [ { "id": 633, "source": "human", "user_id": 41, "status_id": 3 } ], "hint_users": [ { "user_id": 41, "c": 3 } ] }, "7195": { "sol_id": 634, "source": "human", "user_id": 41, "sol_status": 3, "q_status": 3, "type": 1, "q": "A smartphone is sold for 1,080 dollars after a 10% discount and 12% tax. What was its original price (to the nearest dollar) before any discount or tax?", "a": [ "1200", "1271", "1250", "1280" ], "correct": 1, "sol": "Method: standard Steps: 1. Let original price be v. 2. After a 10% discount, the price is 90% of v. 3. Then, after 12% tax, it becomes 112% of 90% of v. 4. Set up the equation: 1.12 * 0.9 * v = 1080. 5. Solve for v.", "all_sols": [ { "id": 634, "source": "human", "user_id": 41, "status_id": 3 } ], "hint_users": [ { "user_id": 41, "c": 3 } ] }, "7196": { "sol_id": 3574, "source": "human", "user_id": 41, "sol_status": 1, "q_status": 3, "type": 1, "q": "The price of a bag with tax is 165 dollars. Tax is 10 percent. How much was the price before tax?", "a": [ "140", "155", "150", "160" ], "correct": 2, "sol": "Given: Price with tax = \\(\\$165\\) Tax = 10% Step 1: Find percentage of tax-inclusive price Price with tax = 100% + 10% = 110% Step 2: Calculate price before tax 110% = \\(\\$165\\) 1% = 165 ÷ 110 = \\(\\$1.50\\) 100% = 1.50 × 100 = \\(\\$150\\) Step 3: Verify Tax = \\(\\$150\\) × 0.10 = \\(\\$15\\) Price with tax = 150 + 15 = \\(\\$165\\) ✓ Answer: \\(\\$150\\)", "all_sols": [ { "id": 3574, "source": "human", "user_id": 41, "status_id": 1 } ], "hint_users": [] }, "7242": { "sol_id": 664, "source": "human", "user_id": 41, "sol_status": 3, "q_status": 3, "type": 1, "q": "6:_ = 18:15. Find the missing term.", "a": [ "4", "5", "3", "2" ], "correct": 1, "sol": "Method: standard Steps: 1. Set up the ratio: 6\/x = 18\/15 2. Cross multiply: 6 * 15 = 18 * x 3. 90 = 18 * x 4. Divide both sides by 18: x = 90\/18 5. x = 5 Final Answer: 5", "all_sols": [ { "id": 664, "source": "human", "user_id": 41, "status_id": 3 } ], "hint_users": [ { "user_id": 41, "c": 3 } ] }, "7243": { "sol_id": 665, "source": "human", "user_id": 41, "sol_status": 3, "q_status": 3, "type": 1, "q": "8:_ = 32:24. What is the missing number?", "a": [ "4", "6", "5", "3" ], "correct": 1, "sol": "Method: standard Steps: 1. Set up the ratio: 8\/x = 32\/24 2. Cross multiply: 8 * 24 = 32 * x 3. 192 = 32 * x 4. Divide both sides by 32: x = 192\/32 5. x = 6 Final Answer: 6", "all_sols": [ { "id": 665, "source": "human", "user_id": 41, "status_id": 3 } ], "hint_users": [ { "user_id": 41, "c": 3 } ] }, "7245": { "sol_id": 667, "source": "human", "user_id": 41, "sol_status": 3, "q_status": 3, "type": 1, "q": "3:_ = 9:6. What is the missing number?", "a": [ "2", "1", "3", "4" ], "correct": 0, "sol": "Method: standard Steps: 1. Set up the ratio: 3\/x = 9\/6 2. Cross multiply: 3 * 6 = 9 * x 3. 18 = 9 * x 4. Divide both sides by 9: x = 18\/9 5. x = 2 Final Answer: 2", "all_sols": [ { "id": 667, "source": "human", "user_id": 41, "status_id": 3 } ], "hint_users": [ { "user_id": 41, "c": 3 } ] }, "7247": { "sol_id": 669, "source": "human", "user_id": 41, "sol_status": 3, "q_status": 3, "type": 1, "q": "9:_ = 27:18. What is the missing number?", "a": [ "5", "4", "3", "6" ], "correct": 2, "sol": "Method: standard Steps: 1. Set up the ratio: 9\/x = 27\/18 2. Cross multiply: 9 * 18 = 27 * x 3. 162 = 27 * x 4. Divide both sides by 27: x = 162\/27 5. x = 6 Final Answer: 6", "all_sols": [ { "id": 669, "source": "human", "user_id": 41, "status_id": 3 } ], "hint_users": [ { "user_id": 41, "c": 3 } ] }, "7260": { "sol_id": 682, "source": "human", "user_id": 41, "sol_status": 3, "q_status": 3, "type": 1, "q": "At a sports day, there are 6 more girls than boys. If there are 36 participants, what is the ratio of girls to total participants?", "a": [ "1 : 6", "2 : 6", "3 : 6", "7 : 12" ], "correct": 3, "sol": "Method: standard Steps: 1. Let the number of boys be a. 2. Then the number of girls is a + 6. 3. Total participants: a + (a + 6) = 36. 4. 2a + 6 = 36. 5. 2a = 30. 6. a = 15 (boys), so girls = 21. 7. Ratio of girls to total = 21 to 36 = 7 to 12. Final Answer: 7 : 12", "all_sols": [ { "id": 682, "source": "human", "user_id": 41, "status_id": 3 } ], "hint_users": [ { "user_id": 41, "c": 3 } ] }, "9909": { "sol_id": 3387, "source": "human", "user_id": 41, "sol_status": 1, "q_status": 3, "type": 2, "q": "A stadium sold 2845600 tickets across 4 concert nights. The first night sold 725400 tickets, the second night sold 684200 tickets, and the third night sold 892750 tickets. How many tickets were sold on the fourth night? Answer :", "a": [ "543250", null, null, null ], "correct": null, "sol": "Given: Total tickets sold = 2845600 First night = 725400 Second night = 684200 Third night = 892750 Fourth night = unknown Step 1: Calculate total tickets sold on first three nights = 725400 + 684200 + 892750 = 1409600 + 892750 = 2302350 Step 2: Calculate fourth night tickets = 2845600 − 2302350 = 543250 Answer: 543250 tickets", "all_sols": [ { "id": 3387, "source": "human", "user_id": 41, "status_id": 1 } ], "hint_users": [] }, "9919": { "sol_id": 3396, "source": "human", "user_id": 41, "sol_status": 1, "q_status": 3, "type": 2, "q": "A frequent flyer earned 1845000 miles over 3 years. In Year 1, she earned 524000 miles. In Year 2, she earned twice as many miles as Year 1. How many miles did she earn in Year 3? Answer : miles", "a": [ "273000", null, null, null ], "correct": null, "sol": "Given: Total miles = 1845000 Year 1 miles = 524000 Year 2 miles = 2 × Year 1 Year 3 miles = unknown Step 1: Calculate Year 2 miles = 524000 × 2 = 1048000 Step 2: Calculate total miles for Year 1 and Year 2 = 524000 + 1048000 = 1572000 Step 3: Calculate Year 3 miles = 1845000 − 1572000 = 273000 Answer: 273000 miles", "all_sols": [ { "id": 3396, "source": "human", "user_id": 41, "status_id": 1 } ], "hint_users": [] }, "9927": { "sol_id": 3389, "source": "human", "user_id": 41, "sol_status": 1, "q_status": 3, "type": 2, "q": "An orchard harvested 1845000 apples and 2376000 oranges. They packed the apples into boxes of 150 and the oranges into boxes of 180. How many boxes were used in total?", "a": [ "25500", null, null, null ], "correct": null, "sol": "Given: Total apples = 1845000 Total oranges = 2376000 Apples per box = 150 Oranges per box = 180 Step 1: Calculate apple boxes = 1845000 ÷ 150 = 12300 Step 2: Calculate orange boxes = 2376000 ÷ 180 = 13200 Step 3: Calculate total boxes = 12300 + 13200 = 25500 Answer: 25500 boxes", "all_sols": [ { "id": 3389, "source": "human", "user_id": 41, "status_id": 1 } ], "hint_users": [] }, "10022": { "sol_id": 3544, "source": "human", "user_id": 41, "sol_status": 1, "q_status": 3, "type": 2, "q": "The GST-inclusive price of a camera is \\(\\$1090\\). If GST is 9%, what was the price before GST? If the shop had originally marked up the camera by 25% before GST, what was the cost price of the camera? Price before GST : $ Cost price : $", "a": [ "1000", "800", null, null ], "correct": null, "sol": "Given: GST-inclusive price = \\(\\$1090\\) GST = 9% Mark-up = 25% Step 1: Calculate price before GST 109% = \\(\\$1090\\) 1% = 1090 ÷ 109 = 10 100% = 100 x 10 = \\(\\$1000\\) Step 2: Calculate cost price (before mark-up) 125% of cost price = \\(\\$1000\\) 1% = 1000 ÷ 125 = \\(\\$8\\) 100% = 100 x 8 = \\(\\$800\\) Step 3: Verify Cost price = \\(\\$800\\) Mark-up = 800 × 0.25 = \\(\\$200\\) Price before GST = 800 + 200 = \\(\\$1000\\) ✓ GST = 1000 × 0.09 = \\(\\$90\\) GST-inclusive price = 1000 + 90 = \\(\\$1090\\) ✓ Answer: Price before GST = \\(\\$1000\\); Cost price = 800 dollars", "all_sols": [ { "id": 3544, "source": "human", "user_id": 41, "status_id": 1 } ], "hint_users": [] }, "10031": { "sol_id": 3527, "source": "human", "user_id": 41, "sol_status": 1, "q_status": 3, "type": 2, "q": "After a 25% discount and 9% GST, the final price of a television is \\(\\$1635\\). What was the original price before discount and GST? Answer : $", "a": [ "2000", null, null, null ], "correct": null, "sol": "Given: Final price (after discount and GST) = \\(\\$1635\\) Discount = 25% GST = 9% Step 1: Work backwards from final price Final price = Original × 0.75 × 1.09 \\(\\$1635\\) = Original × 0.8175 Step 2: Calculate original price Original = \\(\\$1635\\) ÷ 0.8175 = \\(\\$2000\\) Step 3: Verify Discounted price = 2000 × 0.75 = 2000×0.75=1500 With GST = 1500 × 1.09 = \\(\\$1635\\) ✓ Answer: \\(\\$2000\\)", "all_sols": [ { "id": 3527, "source": "human", "user_id": 41, "status_id": 1 } ], "hint_users": [] }, "10034": { "sol_id": 3530, "source": "human", "user_id": 41, "sol_status": 1, "q_status": 3, "type": 2, "q": "Mr Tan split his savings of \\(\\$60000\\) into three investments. He put 50% in Fund A at 6% simple interest, 30% in Fund B at 5% simple interest, and the rest in Fund C at 4% simple interest. After 2 years, a 10% tax is deducted from his total interest. What is his net interest after tax? Answer : $", "a": [ "5724", null, null, null ], "correct": null, "sol": "Given: Total savings = \\(\\$60000\\) Fund A: 50% of savings at 6% interest Fund B: 30% of savings at 5% interest Fund C: 20% of savings at 4% interest Time = 2 years Tax = 10% Step 1: Calculate amount in each fund Fund A = 60000 × 0.50 = \\(\\$30000\\) Fund B = 60000 × 0.30 = \\(\\$18000\\) Fund C = 60000 × 0.20 = \\(\\$12000\\) Step 2: Calculate interest from each fund Fund A interest = 30000 × 0.06 × 2 = \\(\\$3600\\) Fund B interest = 18000 × 0.05 × 2 = \\(\\$1800\\) Fund C interest = 12000 × 0.04 × 2 = \\(\\$960\\) Step 3: Calculate total interest = 3600 + 1800 + 960 = \\(\\$6360\\) Step 4: Calculate tax = \\(\\$6360\\) × 0.10 = \\(\\$636\\) Step 5: Calculate net interest = 6360 − 636 = \\(\\$5724\\) Answer: \\(\\$5724\\)", "all_sols": [ { "id": 3530, "source": "human", "user_id": 41, "status_id": 1 } ], "hint_users": [] }, "10039": { "sol_id": 3575, "source": "human", "user_id": 41, "sol_status": 1, "q_status": 3, "type": 2, "q": "A toy costs 50 dollars before any discounts. The toy store gives a 10% discount and then adds 8% tax to the price after the discount. What is the final price the customer pays?", "a": [ "$48.60", null, null, null ], "correct": 0, "sol": "Given: Original price = \\(\\$50\\) Discount = 10% Tax = 8% Step 1: Calculate discounted price = \\(\\$50\\) × 0.90 = \\(\\$45\\) Step 2: Calculate tax = \\(\\$45\\) × 0.08 = \\(\\$3.60\\) Step 3: Calculate final price = 45 + 3.60 = \\(\\$48.60\\) Answer: \\(\\$48.60\\)", "all_sols": [ { "id": 3575, "source": "human", "user_id": 41, "status_id": 1 } ], "hint_users": [ { "user_id": 41, "c": 2 } ] }, "10040": { "sol_id": 3577, "source": "human", "user_id": 41, "sol_status": 1, "q_status": 3, "type": 2, "q": "A video game costs 80 dollars before any discounts. The electronics store offers a 15% discount and then adds 6% sales tax to the price after the discount. What is the final price the customer pays? Answer : $", "a": [ "72.08", null, null, null ], "correct": 0, "sol": "Given: Original price = \\(\\$80\\) Discount = 15% Sales tax = 6% Step 1: Calculate discounted price = \\(\\$80\\) × 0.85 = \\(\\$68\\) Step 2: Calculate sales tax = \\(\\$68\\) × 0.06 = \\(\\$4.08\\) Step 3: Calculate final price = 68 + 4.08 = \\(\\$72.08\\) Answer: \\(\\$72.08\\)", "all_sols": [ { "id": 3577, "source": "human", "user_id": 41, "status_id": 1 } ], "hint_users": [ { "user_id": 41, "c": 2 } ] }, "10042": { "sol_id": 3579, "source": "human", "user_id": 41, "sol_status": 1, "q_status": 3, "type": 1, "q": "Two stores sell the same tablet for \\(\\$1200\\). Store X gives a 20% discount. Store Y gives a 10% discount first, then another 15% off the new price. Which store has the better deal and how much money do you save?", "a": [ "Store X saves $42 more", "Store Y saves $42 more", "Store X saves $18 more", "Store Y saves $18 more" ], "correct": 1, "sol": "Given: Original price = \\(\\$1200\\) Store X: 20% discount Store Y: 10% discount then 15% discount Step 1: Calculate Store X price = \\(\\$1200\\) × 0.80 = \\(\\$960\\) Step 2: Calculate Store Y price after first discount = \\(\\$1200\\) × 0.90 = \\(\\$1080\\) Step 3: Calculate Store Y price after second discount = \\(\\$1080\\) × 0.85 = \\(\\$918\\) Step 4: Compare prices Store X = \\(\\$960\\) Store Y = \\(\\$918\\) Difference = 960 − 918 = \\(\\$42\\) Answer: Store Y has the better deal; You save \\(\\$42\\)", "all_sols": [ { "id": 3579, "source": "human", "user_id": 41, "status_id": 1 } ], "hint_users": [ { "user_id": 41, "c": 1 } ] }, "10054": { "sol_id": 3564, "source": "human", "user_id": 41, "sol_status": 3, "q_status": 3, "type": 2, "q": "The price of a toy after tax is 132 dollars. The tax rate is 10 percent. What was the price of the toy before tax? Answer : $", "a": [ "120", null, null, null ], "correct": 2, "sol": "Method: division by tax multiplier Steps: 1. Original price + 10% tax = 110% of original price 2. 132 dollars = 110% of original price 3. Original price = 132 ÷ 1.10 = 120 Final: 120", "all_sols": [ { "id": 3564, "source": "human", "user_id": 41, "status_id": 3 } ], "hint_users": [ { "user_id": 41, "c": 3 } ] }, "10055": { "sol_id": 3565, "source": "human", "user_id": 41, "sol_status": 3, "q_status": 3, "type": 2, "q": "The price of a book after tax is 220 dollars. The tax rate is 10 percent. What was the price of the book before tax? Answer : $", "a": [ "200", null, null, null ], "correct": 1, "sol": "Method: percentage calculation Steps: 1. Price with tax = Original price × 1.10 2. 220 = Original price × 1.10 3. Original price = 220 ÷ 1.10 = 200 Final: 200", "all_sols": [ { "id": 3565, "source": "human", "user_id": 41, "status_id": 3 } ], "hint_users": [ { "user_id": 41, "c": 3 } ] }, "10057": { "sol_id": 3592, "source": "human", "user_id": 41, "sol_status": 1, "q_status": 3, "type": 2, "q": "A bicycle costs 200 dollars before any discounts. The bike shop gives a 20% discount and then adds 5% sales tax to the price after the discount. What is the final price the customer pays? Answer : $", "a": [ null, "168", null, null ], "correct": 1, "sol": "Given: Original price = \\(\\$200\\) Discount = 20% Sales tax = 5% Step 1: Calculate discounted price = \\(\\$200\\) × 0.80 = \\(\\$160\\) Step 2: Calculate sales tax = \\(\\$160\\) × 0.05 = \\(\\$8\\) Step 3: Calculate final price = 160 + 8 = \\(\\$168\\) Answer: \\(\\$168\\)", "all_sols": [ { "id": 3592, "source": "human", "user_id": 41, "status_id": 1 } ], "hint_users": [ { "user_id": 41, "c": 1 } ] }, "10059": { "sol_id": 3595, "source": "human", "user_id": 41, "sol_status": 1, "q_status": 3, "type": 2, "q": "A jacket costs 80 dollars before any discounts. The clothing store gives a 30% discount and then adds 10% sales tax to the price after the discount. What is the final price the customer pays? Answer : $", "a": [ null, "61.60", null, null ], "correct": 1, "sol": "Given: Original price = \\(\\$80\\) Discount = 30% Sales tax = 10% Step 1: Calculate discounted price = \\(\\$80\\) × 0.70 = \\(\\$56\\) Step 2: Calculate sales tax = \\(\\$56\\) × 0.10 = \\(\\$5.60\\) Step 3: Calculate final price = 56 + 5.60 = \\(\\$61.60\\) Answer: \\(\\$61.60\\)", "all_sols": [ { "id": 3595, "source": "human", "user_id": 41, "status_id": 1 } ], "hint_users": [ { "user_id": 41, "c": 1 } ] }, "10070": { "sol_id": 3614, "source": "human", "user_id": 41, "sol_status": 1, "q_status": 3, "type": 2, "q": "The ratio of Kevin's marbles to Leon's marbles is 7 : 3. If Kevin gives 20 marbles to Leon, the ratio becomes 3 : 2. How many marbles did Kevin have at first? Answer :", "a": [ "140", null, null, null ], "correct": null, "sol": "Given: Original ratio of Kevin to Leon = 7 : 3 After Kevin gives 20 to Leon, ratio = 3 : 2 Step 1: Let 1 unit in original ratio = x Kevin = 7x, Leon = 3x Step 2: Set up equation after transfer Kevin = 7x − 20, Leon = 3x + 20 Step 3: Solve using new ratio (7x − 20) : (3x + 20) = 3 : 2 2(7x − 20) = 3(3x + 20) 14x − 40 = 9x + 60 14x − 9x = 60 + 40 5x = 100 x = 20 Step 4: Calculate Kevin's original marbles Kevin = 7 × 20 = 140 Step 5: Verify Leon = 3 × 20 = 60 After transfer: Kevin = 140 − 20 = 120, Leon = 60 + 20 = 80 Ratio = 120 : 80 = 3 : 2 ✓ Answer: 140 marbles", "all_sols": [ { "id": 3614, "source": "human", "user_id": 41, "status_id": 1 } ], "hint_users": [] }, "10074": { "sol_id": 3610, "source": "human", "user_id": 41, "sol_status": 1, "q_status": 3, "type": 2, "q": "The ratio of Peter's stamps to Quinn's stamps is 8 : 5. Peter gives 1\/4 of his stamps to Quinn. What is the new ratio of Peter's stamps to Quinn's stamps? New Peter : Quinn = :", "a": [ "6", "7", null, null ], "correct": null, "sol": "Given: Ratio of Peter to Quinn = 8 : 5 Peter gives 1\/4 of his stamps to Quinn Step 1: Let Peter = 8 units, Quinn = 5 units Step 2: Calculate stamps Peter gives away Peter gives = 1\/4 × 8 = 2 units Step 3: Calculate new quantities Peter (after) = 8 − 2 = 6 units Quinn (after) = 5 + 2 = 7 units Step 4: Find new ratio Peter : Quinn = 6 : 7 Answer: 6 : 7", "all_sols": [ { "id": 3610, "source": "human", "user_id": 41, "status_id": 1 } ], "hint_users": [] }, "10077": { "sol_id": 3608, "source": "human", "user_id": 41, "sol_status": 1, "q_status": 3, "type": 2, "q": "Marcus and Nathan had money in the ratio 7 : 9. After Marcus spent 25 dollars and Nathan spent 65 dollars, they had the same amount of money left. How much money did they have altogether at first? Answer : $", "a": [ "320", null, null, null ], "correct": null, "sol": "Given: Original ratio of Marcus to Nathan = 7 : 9 Marcus spent = \\(\\$25\\) Nathan spent = \\(\\$65\\) After spending, they have equal amounts Step 1: Let 1 unit = x Marcus = 7x, Nathan = 9x Step 2: Set up equation (equal amounts after spending) 7x − 25 = 9x − 65 65 − 25 = 9x − 7x 40 = 2x x = 20 Step 3: Calculate original amounts Marcus = 7 × 20 = \\(\\$140\\) Nathan = 9 × 20 = \\(\\$180\\) Step 4: Calculate total Total = 140 + 180 = \\(\\$320\\) Step 5: Verify Marcus left = 140 − 25 = \\(\\$115\\) Nathan left = 180 − 65 = \\(\\$115\\) ✓ Answer: \\(\\$320\\)", "all_sols": [ { "id": 3608, "source": "human", "user_id": 41, "status_id": 1 } ], "hint_users": [] }, "10081": { "sol_id": 3605, "source": "human", "user_id": 41, "sol_status": 1, "q_status": 3, "type": 2, "q": "The ratio of the number of 2-dollar notes to 5-dollar notes to 10-dollar notes in a box is 5 : 4 : 3. The total value of all the notes is \\(\\$720\\). How many notes are there altogether?", "a": [ "144", null, null, null ], "correct": null, "sol": "Given: Ratio of 2-dollar notes to 5-dollar notes to 10-dollar notes = 5 : 4 : 3 Total value = \\(\\$720\\) Step 1: Let the ratio units = 5x, 4x, 3x Step 2: Calculate total value in terms of x Value of 2-dollar notes = 5x × 2 = \\(\\$1\\)0x Value of 5-dollar notes = 4x × 5 = \\(\\$2\\)0x Value of 10-dollar notes = 3x × 10 = \\(\\$3\\)0x Step 3: Set up equation Total value = 10x + 20x + 30x = \\(\\$720\\) 60x = 720 x = 12 Step 4: Calculate number of each note \\(\\$2\\) notes = 5 × 12 = 60 \\(\\$5\\) notes = 4 × 12 = 48 \\(\\$10\\) notes = 3 × 12 = 36 Step 5: Calculate total notes Total = 60 + 48 + 36 = 144 Step 6: Verify Value = (60 × 2) + (48 × 5) + (36 × 10) = 120 + 240 + 360 = \\(\\$720\\) ✓ Answer: 144 notes", "all_sols": [ { "id": 3605, "source": "human", "user_id": 41, "status_id": 1 } ], "hint_users": [] }, "10082": { "sol_id": 3615, "source": "human", "user_id": 41, "sol_status": 1, "q_status": 3, "type": 2, "q": "The ratio of the length to breadth of a rectangle is 7 : 4. If the length is increased by 20% and the breadth is decreased by 10%, what is the new ratio of length to breadth? New ratio = :", "a": [ "7", "3", null, null ], "correct": null, "sol": "Given: Original ratio of length to breadth = 7 : 4 Length increased by 20% Breadth decreased by 10% Step 1: Let original length = 7 units, breadth = 4 units Step 2: Calculate new length New length = 7 × 1.20 = 8.4 units Step 3: Calculate new breadth New breadth = 4 × 0.90 = 3.6 units Step 4: Find new ratio Length : Breadth = 8.4 : 3.6 = 84 : 36 (multiply by 10) = 7 : 3 (divide by 12) Answer: 7 : 3", "all_sols": [ { "id": 3615, "source": "human", "user_id": 41, "status_id": 1 } ], "hint_users": [] }, "10086": { "sol_id": 3618, "source": "human", "user_id": 41, "sol_status": 1, "q_status": 3, "type": 2, "q": "The ratio of Ryan's age to his sister's age is 4 : 3. In 6 years, the ratio will be 5 : 4. How old is Ryan now? Answer : years old", "a": [ "24", null, null, null ], "correct": null, "sol": "Given: Current ratio of Ryan to Sister = 4 : 3 In 6 years, ratio = 5 : 4 Step 1: Let 1 unit in current ratio = x Ryan = 4x, Sister = 3x Step 2: Set up equation for future ages In 6 years: Ryan = 4x + 6, Sister = 3x + 6 Step 3: Solve using future ratio (4x + 6) : (3x + 6) = 5 : 4 4(4x + 6) = 5(3x + 6) 16x + 24 = 15x + 30 16x − 15x = 30 − 24 x = 6 Step 4: Calculate Ryan's current age Ryan = 4 × 6 = 24 years Step 5: Verify Sister = 3 × 6 = 18 years Current ratio = 24 : 18 = 4 : 3 ✓ In 6 years: Ryan = 30, Sister = 24 Future ratio = 30 : 24 = 5 : 4 ✓ Answer: 24 years", "all_sols": [ { "id": 3618, "source": "human", "user_id": 41, "status_id": 1 } ], "hint_users": [] }, "10088": { "sol_id": 3620, "source": "human", "user_id": 41, "sol_status": 1, "q_status": 3, "type": 2, "q": "The ratio of Tom's hourly wage to Jerry's hourly wage is 5 : 4. Tom works 6 hours and Jerry works 8 hours. If Jerry earns \\(\\$32\\) more than Tom, what is Tom's hourly wage? Answer : $", "a": [ "80", null, null, null ], "correct": null, "sol": "Given: Ratio of Tom's wage to Jerry's wage = 5 : 4 Tom works 6 hours Jerry works 8 hours Jerry earns \\(\\$32\\) more than Tom Step 1: Let Tom's hourly wage = 5x, Jerry's hourly wage = 4x Step 2: Calculate earnings Tom's earnings = 5x × 6 = 30x Jerry's earnings = 4x × 8 = 32x Step 3: Set up equation Jerry − Tom = \\(\\$32\\) 32x − 30x = 32 2x = 32 x = 16 Step 4: Calculate Tom's hourly wage Tom's wage = 5 × 16 = \\(\\$80\\) Step 5: Verify Tom earns = 80 × 6 = \\(\\$480\\) Jerry earns = 64 × 8 = \\(\\$512\\) Difference = 512 − 480 = 32 ✓ Answer: \\(\\$80\\)", "all_sols": [ { "id": 3620, "source": "human", "user_id": 41, "status_id": 1 } ], "hint_users": [] }, "10089": { "sol_id": 3621, "source": "human", "user_id": 41, "sol_status": 1, "q_status": 3, "type": 2, "q": "Andy and Barry have money in the ratio 7 : 4. If Andy gives \\(\\$30\\) to Barry, they will have equal amounts. How much money do they have altogether? Answer : $", "a": [ "220", null, null, null ], "correct": null, "sol": "Given: Ratio of Andy to Barry = 7 : 4 Andy gives \\(\\$30\\) to Barry They become equal Step 1: Let 1 unit = x Andy = 7x, Barry = 4x Total = 11x Step 2: After transfer, both have equal amounts Each has 11x ÷ 2 = 5.5x Step 3: Andy gives away to reach equal 7x − 30 = 5.5x 1.5x = 30 x = 20 Step 4: Calculate total Total = 11 × 20 = \\(\\$220\\) Step 5: Verify Andy = 7 × 20 = \\(\\$140\\) Barry = 4 × 20 = \\(\\$80\\) After: Andy = 140 − 30 = \\(\\$110\\) Barry = 80 + 30 = \\(\\$110\\) ✓ Answer: \\(\\$220\\)", "all_sols": [ { "id": 3621, "source": "human", "user_id": 41, "status_id": 1 } ], "hint_users": [] }, "10091": { "sol_id": 3622, "source": "human", "user_id": 41, "sol_status": 1, "q_status": 3, "type": 2, "q": "The ratio of boys to girls in a class is 5 : 7. If 20% of the boys and 25% of the girls wear glasses, and 22 students wear glasses, how many students are there in the class? Answer :", "a": [ "96", null, null, null ], "correct": null, "sol": "Given: Ratio of boys to girls = 5 : 7 20% of boys wear glasses 25% of girls wear glasses Total wearing glasses = 22 Step 1: Let 1 unit = x Boys = 5x, Girls = 7x Step 2: Calculate students wearing glasses Boys with glasses = 20% × 5x = 0.20 × 5x = x Girls with glasses = 25% × 7x = 0.25 × 7x = 1.75x Step 3: Set up equation x + 1.75x = 22 2.75x = 22 x = 22 ÷ 2.75 = 8 Step 4: Calculate total students Boys = 5 × 8 = 40 Girls = 7 × 8 = 56 Total = 40 + 56 = 96 Step 5: Verify Boys with glasses = 20% × 40 = 8 Girls with glasses = 25% × 56 = 14 Total with glasses = 8 + 14 = 22 ✓ Answer: 96 students", "all_sols": [ { "id": 3622, "source": "human", "user_id": 41, "status_id": 1 } ], "hint_users": [] }, "10093": { "sol_id": 3624, "source": "human", "user_id": 41, "sol_status": 1, "q_status": 3, "type": 2, "q": "The ratio of Alan's money to Bob's money was 5 : 3. Alan gave 30 dollars to Bob. Then Bob gave 10 dollars back to Alan. The ratio is now 7 : 5. How much money did Alan have at first? Answer :", "a": [ "300", null, null, null ], "correct": null, "sol": "Given: Original ratio of Alan to Bob = 5 : 3 Alan gives \\(\\$30\\) to Bob Bob gives \\(\\$10\\) back to Alan New ratio = 7 : 5 Step 1: Calculate net transfer Net transfer from Alan to Bob = \\(\\$30\\) − \\(\\$10\\) = \\(\\$20\\) Step 2: Let 1 unit in original ratio = x Alan = 5x, Bob = 3x Step 3: Set up equation after net transfer Alan (new) = 5x − 20 Bob (new) = 3x + 20 Step 4: Solve using new ratio (5x − 20) : (3x + 20) = 7 : 5 5(5x − 20) = 7(3x + 20) 25x − 100 = 21x + 140 25x − 21x = 140 + 100 4x = 240 x = 60 Step 5: Calculate Alan's original money Alan = 5 × 60 = \\(\\$300\\) Step 6: Verify Bob (original) = 3 × 60 = \\(\\$180\\) Alan (new) = 300 − 20 = \\(\\$280\\) Bob (new) = 180 + 20 = \\(\\$200\\) Ratio = 280 : 200 = 7 : 5 ✓ Answer: \\(\\$300\\)", "all_sols": [ { "id": 3624, "source": "human", "user_id": 41, "status_id": 1 } ], "hint_users": [] }, "10095": { "sol_id": 3626, "source": "human", "user_id": 41, "sol_status": 1, "q_status": 3, "type": 2, "q": "The ratio of Emily's stickers to Fiona's stickers is 3 : 7. After Emily receives 40 more stickers, the ratio becomes 1 : 1. How many stickers does Fiona have? Answer :", "a": [ "70", null, null, null ], "correct": null, "sol": "Given: Original ratio of Emily to Fiona = 3 : 7 Emily receives 40 more stickers New ratio = 1 : 1 Step 1: Let 1 unit in original ratio = x Emily = 3x, Fiona = 7x Step 2: Fiona's stickers remain unchanged After Emily receives 40, they are equal 3x + 40 = 7x 40 = 7x − 3x 40 = 4x x = 10 Step 3: Calculate Fiona's stickers Fiona = 7 × 10 = 70 Step 4: Verify Emily (original) = 3 × 10 = 30 Emily (new) = 30 + 40 = 70 Ratio = 70 : 70 = 1 : 1 ✓ Answer: 70 stickers", "all_sols": [ { "id": 3626, "source": "human", "user_id": 41, "status_id": 1 } ], "hint_users": [] }, "10098": { "sol_id": 3634, "source": "human", "user_id": 41, "sol_status": 1, "q_status": 3, "type": 2, "q": "In a basketball team tryout, the ratio of successful players to unsuccessful players was 3 : 7. If 12 more players had passed, the ratio would have been 1 : 1. How many players attended the tryout? Answer :", "a": [ "60", null, null, null ], "correct": null, "sol": "Given: Original ratio of successful to unsuccessful = 3 : 7 If 12 more passed, ratio = 1 : 1 Step 1: Let 1 unit = x Successful = 3x, Unsuccessful = 7x Total = 10x Step 2: For ratio to be 1 : 1, both groups must be equal If 12 more pass, successful = 3x + 12, unsuccessful = 7x − 12 Step 3: Set up equation 3x + 12 = 7x − 12 12 + 12 = 7x − 3x 24 = 4x x = 6 Step 4: Calculate total players Total = 10 × 6 = 60 Step 5: Verify Successful = 3 × 6 = 18 Unsuccessful = 7 × 6 = 42 After 12 more pass: 30 and 30 = 1 : 1 ✓ Answer: 60 players", "all_sols": [ { "id": 3634, "source": "human", "user_id": 41, "status_id": 1 } ], "hint_users": [] }, "10101": { "sol_id": 3631, "source": "human", "user_id": 41, "sol_status": 1, "q_status": 3, "type": 2, "q": "Factory X and Factory Y produce toys in the ratio 9 : 7. Factory X produces 450 toys per day. Due to increased demand, Factory Y increases production by 40%. What is the new ratio of production between Factory X and Factory Y? Answer = :", "a": [ "45", "49", null, null ], "correct": null, "sol": "Given: Original ratio of X to Y = 9 : 7 Factory X produces 450 toys per day Factory Y increases production by 40% Step 1: Find value of 1 unit 9 units = 450 1 unit = 450 ÷ 9 = 50 Step 2: Calculate Factory Y original production Y = 7 × 50 = 350 toys Step 3: Calculate Factory Y new production Y (new) = 350 × 1.40 = 490 toys Step 4: Find new ratio X : Y = 450 : 490 = 45 : 49 (dividing by 10) Answer: 45 : 49", "all_sols": [ { "id": 3631, "source": "human", "user_id": 41, "status_id": 1 } ], "hint_users": [] } }