1594 lines
80 KiB
JSON
1594 lines
80 KiB
JSON
[
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||
{
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"question": "Ken created a care package to send to his brother, who was away at boarding school. Ken placed a box on a scale, and then he poured into the box enough jelly beans to bring the weight to 2 pounds. Then, he added enough brownies to cause the weight to triple. Next, he added another 2 pounds of jelly beans. And finally, he added enough gummy worms to double the weight once again. What was the final weight of the box of goodies, in pounds?",
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||
"explanation": "To the initial 2 pounds of jelly beans, he added enough brownies to cause the weight to triple, bringing the weight to 2*3=<<2*3=6>>6 pounds.\nNext, he added another 2 pounds of jelly beans, bringing the weight to 6+2=<<6+2=8>>8 pounds.\nAnd finally, he added enough gummy worms to double the weight once again, to a final weight of 8*2=<<8*2=16>>16 pounds.",
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||
"answer": 16.0,
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||
"validation": {
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||
"input": {},
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||
"process": [
|
||
{
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||
"id": "",
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||
"expr": "2*3"
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||
},
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||
{
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||
"id": "",
|
||
"expr": "6+2"
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||
},
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||
{
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||
"id": "",
|
||
"expr": "8*2"
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||
}
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||
],
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||
"output": ""
|
||
}
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||
},
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||
{
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"question": "Mrs. Snyder used to spend 40% of her monthly income on rent and utilities. Her salary was recently increased by $600 so now her rent and utilities only amount to 25% of her monthly income. How much was her previous monthly income?",
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"explanation": "Let her previous monthly income be p\nThe cost of her rent and utilities was 40% of p which is (40/100)*p = 2p/5\nHer income was increased by $600 so it is now p+$600\nThe cost of her rent and utilities now amount to 25% of (p+$600) which is (25/100)*(p+$600) = (p+$600)/4\nEquating both expressions for cost of rent and utilities: 2p/5 = (p+$600)/4\nMultiplying both sides of the equation by 20 gives 8p = 5p+$3000\nSubtracting 5p from both sides gives: 3p = $3000\nDividing both sides by 3 gives p = $1000",
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"answer": 1000.0,
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||
"validation": {
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||
"input": {},
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||
"process": [],
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||
"output": ""
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||
}
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||
},
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{
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"question": "Alyssa, Keely, and Kendall ordered 100 chicken nuggets from a fast-food restaurant. Keely and Kendall each ate twice as many as Alyssa. How many did Alyssa eat?",
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"explanation": "To figure out this problem we need to turn it into an equation. Let’s make A the number of nuggets Alyssa ate. We know all three girls ate 100 nuggets total, so 100 nuggets = A (how many Alyssa ate) + 2A (how many Keely ate) + 3A (how many Kendall ate) or 100 = A + 2A + 3A which is 100 = 5A\nThen we will divide each side by 5 to figure out how many nuggets Alyssa ate, 100/5 = 5A/5 or 20 = A.",
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"answer": 20.0,
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"validation": {
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||
"input": {},
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||
"process": [],
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||
"output": ""
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||
}
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||
},
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{
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"question": "Janet filmed a new movie that is 60% longer than her previous 2-hour long movie. Her previous movie cost $50 per minute to film, and the newest movie cost twice as much per minute to film as the previous movie. What was the total amount of money required to film Janet's entire newest film?",
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"explanation": "The first movie was 2*60=<<2*60=120>>120 minutes\nSo this movie is 120*.6=<<120*.6=72>>72 minutes longer\nSo this movie is 192 minutes\nIt also cost 50*2=$<<50*2=100>>100 per minute to film\nSo it cost 192*100=$1920",
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"answer": 1920.0,
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"validation": {
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||
"input": {},
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"process": [
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{
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||
"id": "",
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"expr": "2*60"
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},
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{
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"id": "",
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"expr": "120*.6"
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},
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||
{
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"id": "",
|
||
"expr": "50*2"
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}
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||
],
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||
"output": ""
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||
}
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||
},
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{
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"question": "A farmer has twice as many pigs as cows, and 4 more cows than goats. If the farmer has 56 animals total, how many goats does he have?",
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"explanation": "Let x be the number of goats\nCows:4+x\nPigs:2(4+x)=8+2x\nTotal:x+4+x+8+2x=56\n4x+12=56\n4x=44\nx=<<11=11>>11 goats",
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"answer": 11.0,
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"validation": {
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||
"input": {},
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"process": [
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||
{
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||
"id": "",
|
||
"expr": "11"
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||
}
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||
],
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"output": ""
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||
}
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||
},
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{
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"question": "Students at Highridge High earn 2 points for each correct answer during a quiz bowl If a student correctly answers all the questions in a round, the student is awarded an additional 4 point bonus. They played a total of five rounds each consisting of five questions. If James only missed one question, how many points did he get?",
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"explanation": "If James only missed one question in all five rounds of five questions, he correctly answered 5 * 5 - 1 = <<5*5-1=24>>24 questions\nBefore the bonus, James earned 24 correct answers * 2 points/answer = <<24*2=48>>48 points.\nSince missing one question would only disqualify him from receiving a bonus in one round, he would earn a bonus for 5-1=<<5-1=4>>4 rounds.\nHe should expect a bonus of 4 rounds* 4 points/round= <<4*4=16>>16 points.\nIncluding his bonus, James scored a total of 48 + 16 = <<48+16=64>>64 points.",
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"answer": 66.0,
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"validation": {
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"input": {},
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"process": [
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{
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||
"id": "",
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||
"expr": "5*5-1"
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},
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||
{
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"id": "",
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||
"expr": "24*2"
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},
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||
{
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||
"id": "",
|
||
"expr": "5-1"
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||
},
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||
{
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||
"id": "",
|
||
"expr": "4*4"
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||
},
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||
{
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||
"id": "",
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||
"expr": "48+16"
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}
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||
],
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||
"output": ""
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||
}
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||
},
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||
{
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||
"question": "An amoeba reproduces by fission, splitting itself into two separate amoebae. An amoeba reproduces every two days. How many days will it take one amoeba to divide into 16 amoebae?",
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"explanation": "The amoeba will divide into 1 * 2 = <<1*2=2>>2 amoebae after 2 days.\nThe amoeba will divide into 2 * 2 = <<2*2=4>>4 amoebae after 4 days.\nThe amoeba will divide into 4 * 2 = <<4*2=8>>8 amoebae after 6 days.\nThe amoeba will divide into 8 * 2 = <<8*2=16>>16 amoebae after 8 days.",
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"answer": 8.0,
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"validation": {
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"input": {},
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||
"process": [
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||
{
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||
"id": "",
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||
"expr": "1*2"
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||
},
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||
{
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||
"id": "",
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||
"expr": "2*2"
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},
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||
{
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||
"id": "",
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||
"expr": "4*2"
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||
},
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||
{
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||
"id": "",
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"expr": "8*2"
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}
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],
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"output": ""
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}
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},
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{
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"question": "Pete has to take a 10-minute walk down to the train station and then board a 1hr 20-minute train to LA. When should he leave if he cannot get to LA later than 0900 hours? (24-hr time)",
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"explanation": "There are 60 minutes in an hour so 1 hour 20 minutes = (60+20) minutes = 80 minutes\nHe will spend a total of 80+10 = <<80+10=90>>90 minutes\n90 minutes is = (60/60) hours and 30 minutes = 1 hour 30 minutes = 0130 in 24-hr time\nHe has to leave 0130 hours earlier than 0900 i.e. 0900-0130 = 0730 hours",
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"answer": 730.0,
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"validation": {
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"input": {},
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"process": [
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{
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"id": "",
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"expr": "80+10"
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}
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],
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"output": ""
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}
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},
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{
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"question": "Every morning, Carla puts 79 apples in her backpack to eat for lunch. Unfortunately, Buffy stole some of Carla's apples on the school bus, and 26 apples fell out of a hole on the bottom. So at lunchtime, Carla only had 8 apples remaining. How many apples did Buffy steal from Carla?",
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"explanation": "Let B be the number of apples that Buffy stole. Then 79 - B - 26 = 8.\nCombining constants produces 53 - B = 8.\nAdding B to both sides produces 52 = B + 8\nThus the number of apples stolen by Buffy is B = 53 - 8 = <<53-8=45>>45.",
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"answer": 45.0,
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"validation": {
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"input": {},
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"process": [
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{
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"id": "",
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"expr": "53-8"
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}
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],
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"output": ""
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}
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},
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{
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"question": "Yolanda leaves home for work at 7:00 AM, riding her bike at 20 miles per hour. 15 minutes after she leaves, her husband realizes that she forgot her lunch, and jumps in the car to bring it to her. If he drives at 40 miles per hour and follows the exact same route as Yolanda, how many minutes will it take him to catch her?",
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"explanation": "Let x be the number of minutes it takes Yolanda's husband to catch her.\nWe know that Yolanda will spend a total of x + 15 minutes riding her bike since she left 15 minutes before her husband.\nThe distance each person travels is equal to their travel speed times the number of minutes they spend traveling. That means Yolanda's distance is equal to 20 mph * (x + 15) and her husband's distance is equal to 40 mph * x\nYolanda's husband catches up to her when they've both traveled the same distance, which is when 20(x + 15) = 40x\nWe can simplify this equation by multiplying 20 through the parentheses to get 20x + 300 = 40x\nThen we can subtract 20x from each side to get 300 = 20x\nFinally, we divide both sides by 20 to find that x = 15.",
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"answer": 15.0,
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"validation": {
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"input": {},
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"process": [],
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"output": ""
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}
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},
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{
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"question": "John writes 3 stories every week. Each short story is 50 pages. He also writes a novel that is 1200 pages each year. Each sheet of paper can hold 2 pages. Over 12 weeks, how many reams of paper does he need to buy if a ream contains 500 sheets?",
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"explanation": "He writes 3*50=<<3*50=150>>150 pages a week\nThat means he writes 150*52=<<150*52=7800>>7800 pages of short stories a year\nSo he writes 7800+1200=<<7800+1200=9000>>9000 pages a year\nSo he needs 9000/2=<<9000/2=4500>>4500 sheets of paper\nThat means he needs 4500/500=<<4500/500=9>>9 reams of paper",
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"answer": 3.0,
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"validation": {
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"input": {},
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||
"process": [
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||
{
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||
"id": "",
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"expr": "3*50"
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},
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{
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"id": "",
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"expr": "150*52"
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},
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{
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"id": "",
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"expr": "7800+1200"
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},
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||
{
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"id": "",
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"expr": "9000/2"
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||
},
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||
{
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"id": "",
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"expr": "4500/500"
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}
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],
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"output": ""
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||
}
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},
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{
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"question": "Matt needs to buy new plates for his home. He only wants to do dishes once a week. Three days a week it is only him and his son eating and they use 1 plate each. On the remainder of the days, his parents join them and everyone uses 2 plates that day. How many plates does he need to buy?",
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"explanation": "So for 3 of the days, there are 1+1=2 people eating\nSo for those days they use 3*2=<<3*2=6>>6 plates\nOn 7-3=4 days the parents join them\nOn those days there are 2+2=<<2+2=4>>4 people eating\nThey use 4*2=<<4*2=8>>8 plates\nSo they use 8*4=<<8*4=32>>32 plates\nThat means they use a total of 32+6=<<32+6=38>>38 plates",
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"answer": 38.0,
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||
"validation": {
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||
"input": {},
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||
"process": [
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||
{
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||
"id": "",
|
||
"expr": "3*2"
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},
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||
{
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"id": "",
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"expr": "2+2"
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},
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||
{
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||
"id": "",
|
||
"expr": "4*2"
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},
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{
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||
"id": "",
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||
"expr": "8*4"
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},
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{
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"id": "",
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||
"expr": "32+6"
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}
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||
],
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"output": ""
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||
}
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||
},
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||
{
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"question": "Erin works in the school cafeteria serving soup. Each bowl of soup has 10 ounces, and Erin can serve 5 bowls per minute. If the pot of soup has 6 gallons of soup, how long will it take Erin to serve all the soup, rounded to the nearest minute? (There are 128 ounces to a gallon.)",
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"explanation": "First find the number of ounces Erin serves per minute: 10 ounces/bowl * 5 bowls/minute = <<10*5=50>>50 ounces/minute\nThen find the number of ounces in the pot: 6 gallons * 128 ounces/gallon = <<6*128=768>>768 ounces\nThen divide the total amount of soup by the amount of soup Erin serves per minute: 768 minutes / 50 ounces/minute = <<768/50=15.36>>15.36 minutes, which rounds down to 15 minutes",
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||
"answer": 15.0,
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||
"validation": {
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||
"input": {},
|
||
"process": [
|
||
{
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||
"id": "",
|
||
"expr": "10*5"
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||
},
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||
{
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||
"id": "",
|
||
"expr": "6*128"
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||
},
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||
{
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||
"id": "",
|
||
"expr": "768/50"
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}
|
||
],
|
||
"output": ""
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||
}
|
||
},
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||
{
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"question": "Hadley loves to do volunteer work at the local library. On a certain day, she neatly arranges 100 books on the shelf. By lunchtime, a certain number of books had been borrowed. She added 40 more books to the same shelf. By evening, 30 more books had been borrowed. If the shelf had 60 books remaining by the evening, how many books had been borrowed by lunchtime?",
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"explanation": "Let x be the number of books borrowed by lunchtime.\nSo by lunchtime, the remaining number of books will be 100-x\nAfter adding 40 more books, the total number of books increased to 100-x+40.\nBy evening, after 30 more books have been borrowed, the total number of books remaining is 100-x+40-30 = 60\nThus 110 - x = 60.\nThus x = <<50=50>>50 books",
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||
"answer": 50.0,
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||
"validation": {
|
||
"input": {},
|
||
"process": [
|
||
{
|
||
"id": "",
|
||
"expr": "50"
|
||
}
|
||
],
|
||
"output": ""
|
||
}
|
||
},
|
||
{
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||
"question": "Pearl wants to order 5 monogrammed Christmas stockings for each of her 5 grandchildren and her own 4 children. The stockings are $20.00 each and currently 10% off. The monogramming will costs $5.00 per stocking. How much will the stockings costs?",
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"explanation": "She has 5 grandchildren 4 children so she needs 5+4 = <<5+4=9>>9 stockings\nThe stockings are $20.00 each and currently 10% off so that's 20*.10 = $<<20*.10=2.00>>2.00 off\nThe stockings are $20.00 with a $2.00 discount so they are each 20-2 = $<<20-2=18.00>>18.00\nThe stockings are now $18.00 and she needs 9 so that's $<<18*9=162>>162.00\nShe also wants to monogram each stocking at $5.00 per stocking so that's 9*5 = $<<9*5=45.00>>45.00\nThe stockings are $162.00 and the monogramming will cost $45.00 so the stockings will cost 162+45 = $<<162+45=207.00>>207.00",
|
||
"answer": 1035.0,
|
||
"validation": {
|
||
"input": {},
|
||
"process": [
|
||
{
|
||
"id": "",
|
||
"expr": "5+4"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "20*.10"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "20-2"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "18*9"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "9*5"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "162+45"
|
||
}
|
||
],
|
||
"output": ""
|
||
}
|
||
},
|
||
{
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||
"question": "Laura is hosting a carwash. She will charge $5 for a car, $6 for a truck, and $7 for an SUV. They raised $100 in total. If they washed 5 SUVs and 5 trucks, how many cars did they wash?",
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"explanation": "They earned $30 from trucks because 5 x 6 = <<5*6=30>>30\nThey earned $35 from SUVs because 5 x 7 = <<5*7=35>>35\nThey earned $35 from cars because 100 - 35 - 30 = <<100-35-30=35>>35\nThey washed 7 cars because 35 / 5 = <<35/5=7>>7",
|
||
"answer": 7.0,
|
||
"validation": {
|
||
"input": {},
|
||
"process": [
|
||
{
|
||
"id": "",
|
||
"expr": "5*6"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "5*7"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "100-35-30"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "35/5"
|
||
}
|
||
],
|
||
"output": ""
|
||
}
|
||
},
|
||
{
|
||
"question": "Tony has a piece of quilt that is 6 feet by 24 feet. If he wants to turn it into a square and use all the fabric, how long is each side of the square?",
|
||
"explanation": "The quilt is 144 square feet because 6 x 24 = <<6*24=144>>144\nA square quilt would be 12 feet per side because √(144) = 12",
|
||
"answer": 12.0,
|
||
"validation": {
|
||
"input": {},
|
||
"process": [
|
||
{
|
||
"id": "",
|
||
"expr": "6*24"
|
||
}
|
||
],
|
||
"output": ""
|
||
}
|
||
},
|
||
{
|
||
"question": "Brad’s zip code consists of five numbers that add up to 10. The first and second numbers are the same. The third number is zero. The fourth number is double the first number. The fourth and fifth numbers add up to 8. What is Brad’s zip code?",
|
||
"explanation": "The five numbers add up to 10, so the first three numbers add up to 10 - 8 = <<10-8=2>>2.\nThe third number is 0, so the first two numbers add up to 2 - 0 = <<2-0=2>>2.\nThe first and second numbers are equal, so they are both 2 / 2 = <<2/2=1>>1.\nThe fourth number is double the first number, so it is 2 * 1 = <<1*2=2>>2.\nThe fifth number is 8 - 2 = <<8-2=6>>6.\nThus, Brad’s zip code is 11026.",
|
||
"answer": 11026.0,
|
||
"validation": {
|
||
"input": {},
|
||
"process": [
|
||
{
|
||
"id": "",
|
||
"expr": "10-8"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "2-0"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "2/2"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "1*2"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "8-2"
|
||
}
|
||
],
|
||
"output": ""
|
||
}
|
||
},
|
||
{
|
||
"question": "Compared to the amount of water she drank, Carla drank three times as much soda minus 6 ounces. If she drank 54 ounces of liquid total, how much water did she drink?",
|
||
"explanation": "Let s be the amount of soda Carla drank and w be the amount of water she drank. We know that s + w = 54 and s = 3w - 6. Substituting the second equation into the first, we get 3w - 6 + w = 54.\nCombining like terms, we get 4w - 6 = 54\nAdding 6 to both sides, we get 4w = 60\nDividing both sides by 4, we get w = 15",
|
||
"answer": 15.0,
|
||
"validation": {
|
||
"input": {},
|
||
"process": [],
|
||
"output": ""
|
||
}
|
||
},
|
||
{
|
||
"question": "Madeline needs $1200 to pay rent, $400 for groceries, $200 for medical expenses, and $60 for utilities. She also wants to save $200 in case of an emergency. She makes $15 per hour at her job. How many hours will Madeline need to work this month?",
|
||
"explanation": "Madeline needs 1200+400+200+60+200 = $<<1200+400+200+60+200=2060>>2060 to pay all of her bills.\nShe will need to work $2060/$15 per hour = 137.33 hours.\nShe will need to work 138 hours to pay all of her bills",
|
||
"answer": 138.0,
|
||
"validation": {
|
||
"input": {},
|
||
"process": [
|
||
{
|
||
"id": "",
|
||
"expr": "1200+400+200+60+200"
|
||
}
|
||
],
|
||
"output": ""
|
||
}
|
||
},
|
||
{
|
||
"question": "The teacher told the class that if they averaged at least 75% on their final exam, they could have a pizza party. Everyone took the exam on Monday, except for William, who was allowed to take it on Tuesday. If there are 30 people in the class, and the average before he took the test was a 74%, what score does he have to get to make sure they get to have a pizza party?",
|
||
"explanation": "Let x be the score that William needs to achieve.\nSince there are 30 people in the class, there are 30 - 1 = <<30-1=29>>29 people without him.\nSince their average was a 74%, this means that (29 * 74 + x) / 30 >= 75.\nThus, 29 * 74 + x >= 30 * 75\nThus, 29 * 74 + x >= 2250\nThus, 2146 + x >= 2250\nThus, x >= 2250 - 2146\nThus, x >= 94",
|
||
"answer": 94.0,
|
||
"validation": {
|
||
"input": {},
|
||
"process": [
|
||
{
|
||
"id": "",
|
||
"expr": "30-1"
|
||
}
|
||
],
|
||
"output": ""
|
||
}
|
||
},
|
||
{
|
||
"question": "Carmen is counting the cars that pass by her window. All the cars are either white, black, or red. She sees 50 trucks and 40 cars. Half the trucks are red, and another 20% are black. If she picks one car at random, what is the percentage chance it's a white truck, rounded to the nearest integer?",
|
||
"explanation": "First find the total number of vehicles Carmen counted: 50 trucks + 40 cars = <<50+40=90>>90 vehicles\nThen find the number of trucks that were red: 50 trucks / 2 = <<50/2=25>>25 trucks\nThen find the number of trucks that were black: 50 trucks * .2 = <<50*.2=10>>10 trucks\nThen subtract the red and black trucks from the total number of trucks to find the number of white trucks: 50 trucks - 25 trucks - 10 trucks = <<50-25-10=15>>15 trucks\nThen divide the number of white trucks by the number of vehicles and multiply by 100% to find the percentage of vehicles that are white trucks: 15 trucks / 90 vehicles * 100% = 16.66...%, which rounds up to 17%.",
|
||
"answer": 17.0,
|
||
"validation": {
|
||
"input": {},
|
||
"process": [
|
||
{
|
||
"id": "",
|
||
"expr": "50+40"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "50/2"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "50*.2"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "50-25-10"
|
||
}
|
||
],
|
||
"output": ""
|
||
}
|
||
},
|
||
{
|
||
"question": "Janet buys 3 pounds of broccoli for $4 a pound, 3 oranges for $0.75 each, a cabbage for $3.75, a pound of bacon for $3, and two pounds of chicken for $3 a pound. What percentage of her grocery budget did she spend on meat, rounded to the nearest percent?",
|
||
"explanation": "First find the total cost of the broccoli: 3 pounds * $4/pound = $<<3*4=12>>12\nThen find the total cost of the oranges: 3 oranges * $0.75/orange = $<<3*0.75=2.25>>2.25\nThen find the total cost of the vegetables: $12 + $2.25 + $3.75 = $<<12+2.25+3.75=18>>18\nThen find the total cost of the chicken: $3/pound * 2 pounds = $<<3*2=6>>6\nThen add the cost of the bacon to find the total cost of the meat: $6 + $3 = $<<6+3=9>>9\nThen add the cost of the meat and vegetables to find the total cost of the groceries: $9 + $18 = $<<9+18=27>>27\nThen divide the cost of the meat by the total grocery bill and multiply by 100% to express the answer as a percentage: $9 / $27 * 100% = 33.333%, which rounds down to 33%",
|
||
"answer": 33.0,
|
||
"validation": {
|
||
"input": {},
|
||
"process": [
|
||
{
|
||
"id": "",
|
||
"expr": "3*4"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "3*0.75"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "12+2.25+3.75"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "3*2"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "6+3"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "9+18"
|
||
}
|
||
],
|
||
"output": ""
|
||
}
|
||
},
|
||
{
|
||
"question": "Darrel is an experienced tracker. He can tell a lot about an animal by the footprints it leaves behind. One day he saw a set of coyote footprints. Based on the impressions, he could tell the animal was traveling east at 15 miles per hour, and that the animal left the prints 1 hour ago. If the coyote continues to travel east at 15 miles per hour, and Darrell hops on his motorbike and travels east at 30 miles per hour, how long, in hours, will it take for Darrel to catch up to the coyote?",
|
||
"explanation": "If we let x be the amount of time, in hours, it will take for Darrel to catch up to the coyote, then we can figure this out.\nBecause the distance Darrel travels is defined as the length of time Darrel travels (x) and Darrel's speed (20mph), or the expression 2*x.\nAnd the distance the coyote travels is defined as the length of time the coyote travels (x+1 hour) and the coyote's speed (15 mph), or the expression (x+1)*1.\nAnd since the distance Darrel and the coyote travel is the same, then 2*x=(x+1)*1\nSimplifying the expression, we get 2*x=x+1.\nIf we subtract 1 x from each side, we get x=1, the amount of time in hours.",
|
||
"answer": 1.0,
|
||
"validation": {
|
||
"input": {},
|
||
"process": [],
|
||
"output": ""
|
||
}
|
||
},
|
||
{
|
||
"question": "The lifespan of a hamster is 6 years less than that of a bat. The lifespan of a frog is 4 times that of a hamster. Altogether, the lifespan of the animals is 30 years. What is the lifespan of the bat?",
|
||
"explanation": "Let’s set up an equation by calling the lifespan of a bat x, and therefore the lifespan of the hamster x – 6, and the lifespan of the frog 4 (x – 6) which add together to equal 30, like this: x + x – 6 + 4 (x – 6) = 30.\nThat gives us 6x – 30 = 30 and we should add 30 to each side to try to isolate the x.\nNow we have 6x = 60, which we will divide by 6, 6x / 6 = 60 / 6.\nThis gives us x = <<10=10>>10. The bat has a lifespan of 10 years.",
|
||
"answer": 10.0,
|
||
"validation": {
|
||
"input": {},
|
||
"process": [
|
||
{
|
||
"id": "",
|
||
"expr": "10"
|
||
}
|
||
],
|
||
"output": ""
|
||
}
|
||
},
|
||
{
|
||
"question": "Jason is counting the number of cars that drive by his window. He counted four times as many green cars as red cars, and 6 more red cars than purple cars. If he counted 312 cars total, how many of them were purple?",
|
||
"explanation": "Let g be the number of green cars, r be the number of red cars, and p be the number of purple cars. We know that g + r + p = 315, r = p + 6, and g = 4r\nSubstitute the second equation into the third equation to get: g = 4r = 4(p + 6) = 4p + 24\nNow substitute the equations that express g and r in terms of p in the equation for the total number of cars: 4p + 24 + p + 6 + p = 315\nNow combine like terms to get 6p + 30 = 312\nNow subtract 30 from both sides to get 6p = 282\nNow divide both sides by 6 to get p = 47",
|
||
"answer": 47.0,
|
||
"validation": {
|
||
"input": {},
|
||
"process": [],
|
||
"output": ""
|
||
}
|
||
},
|
||
{
|
||
"question": "Annie has 6 barrettes, twice as many scrunchies as barrettes, and three fewer bobby pins than barrettes. What percentage of her hair decorations are bobby pins, rounded to the nearest percent?",
|
||
"explanation": "First find the total number of scrunchies: 6 barrettes * 2 = <<6*2=12>>12 scrunchies\nThen subtract three fewer bobby pins than barrettes 6-3 =<<6-3=3>>3 bobby pins\nThen add the number of each type of hair decorations to find the total number: 6 decorations + 12 decorations + 3 decorations = <<6+12+3=21>>21 decorations\nThen divide the number of bobby pins by the total number of decorations and multiply by 100% to express the answer as a percentage: 3 bobby pins / 21 decorations * 100% = 14.28 which rounds down to 14%",
|
||
"answer": 14.0,
|
||
"validation": {
|
||
"input": {},
|
||
"process": [
|
||
{
|
||
"id": "",
|
||
"expr": "6*2"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "6-3"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "6+12+3"
|
||
}
|
||
],
|
||
"output": ""
|
||
}
|
||
},
|
||
{
|
||
"question": "Robert and Teddy are planning to buy snacks for their friends. Robert orders five boxes of pizza at $10 each box and ten cans of soft drinks at $2 each. Teddy buys six hamburgers at $3 each and an additional ten cans of soft drinks. How much do they spend in all?",
|
||
"explanation": "Five boxes of pizza cost 5 x $10 = $<<5*10=50>>50.\nTen cans of soft drinks cost 10 x $2 = $<<10*2=20>>20.\nSo, Robert spends $50 + $20 = $<<50+20=70>>70.\nSix hamburgers cost 6 x $3 = $<<6*3=18>>18.\nThus, Teddy spends $18 + $20 = $<<18+20=38>>38.\nTherefore, they spend $70 + $38 = $<<70+38=108>>108 in all.",
|
||
"answer": 106.0,
|
||
"validation": {
|
||
"input": {},
|
||
"process": [
|
||
{
|
||
"id": "",
|
||
"expr": "5*10"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "10*2"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "50+20"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "6*3"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "18+20"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "70+38"
|
||
}
|
||
],
|
||
"output": ""
|
||
}
|
||
},
|
||
{
|
||
"question": "Mr. Zubir bought a pair of pants, a shirt, and a coat. The pair of pants and shirt costs $100. The pants and coat cost $244. The coat costs 5 times as much as the shirt. How much did Mr. Zubir pay for his coat?",
|
||
"explanation": "Let X be the coat's price. The shirt's price is X/5. The pants and the shirt cost $100, so the pants price is $100 - X/5.\nThe pants and coat costs ($100 - X/5) + X = $244.\nCombining like terms and subtracting $100 from both sides, we get 4/5*X = $144.\nDividing both sides by 4/5, we get X = $180.",
|
||
"answer": 180.0,
|
||
"validation": {
|
||
"input": {},
|
||
"process": [],
|
||
"output": ""
|
||
}
|
||
},
|
||
{
|
||
"question": "Jason spent 1/4 of his money and an additional $10 on some books. He then spent 2/5 of the remaining money and an additional $8 on some DVDs. If he was left with $130, how much money did he have at first?",
|
||
"explanation": "Let X be the money Jason had at first.\nJason spent 1/4*X + 10 on books.\nJason spent 2/5*[X - (1/4*X + 10)] + 8 on some DVDs.\nJason has X - (1/4*X + 10) - {2/5*[X - (1/4*X + 10)] + 8} = $130 left.\nX - 1/4*X - 10 - 2/5*X + 1/10*X + 4 - 8 = $130.\n9/20*X - 14 = $130.\nX = $<<320=320>>320.",
|
||
"answer": 320.0,
|
||
"validation": {
|
||
"input": {},
|
||
"process": [
|
||
{
|
||
"id": "",
|
||
"expr": "320"
|
||
}
|
||
],
|
||
"output": ""
|
||
}
|
||
},
|
||
{
|
||
"question": "Andy gets a cavity for every 4 candy canes he eats. He gets 2 candy canes from his parents and 3 candy canes each from 4 teachers. Then he uses his allowance to buy 1/7 as many candy canes as he was given. How many cavities does he get from eating all his candy canes?",
|
||
"explanation": "First find how many candy canes Andy gets from his teachers: 3 canes/teacher * 4 teachers = <<3*4=12>>12 canes\nThen add the number of candy canes he gets from his parents: 12 canes + 2 canes = <<12+2=14>>14 canes\nThen divide that number by 7 to find the number of canes he buys: 14 canes / 7 = <<14/7=2>>2 canes\nThen add the number of candy canes he gets from each source to find the total number: 2 canes + 14 canes = <<2+14=16>>16 canes\nThen divide the total number of candy canes by the number of candy canes it takes to get one cavity to find the number of cavities Andy gets: 16 canes / 4 canes/cavity = <<16/4=4>>4 cavities",
|
||
"answer": 16.0,
|
||
"validation": {
|
||
"input": {},
|
||
"process": [
|
||
{
|
||
"id": "",
|
||
"expr": "3*4"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "12+2"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "14/7"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "2+14"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "16/4"
|
||
}
|
||
],
|
||
"output": ""
|
||
}
|
||
},
|
||
{
|
||
"question": "On his farm, Mr. Mathews has goats and sheep in the ratio of 5:7. He decides to sell half of the goats at $40 each and 2/3 of the sheep at $30 each. How much money does he make from the sale of the animals if the total number of sheep and goats on the farm is 360?",
|
||
"explanation": "The total ratio of goats and sheep on the farm is 5+7 = <<5+7=12>>12\nThe fraction that represents goats from the total ratio is 5/12, and since there are 360 goats and sheep on the farm, the number of goats is 5/12*360= <<5/12*360=150>>150\nThe number of sheep on Mr. Mathews's farm is 360-150 = <<360-150=210>>210.\nMr. Mathews sold 1/2*150 = <<1/2*150=75>>75 goats.\nIf each goat went for $40, the total amount of money Mr. Mathews made from the sale of his goats is 75*$40 = $<<75*40=3000>>3000\nHe also sold 2/3*210 = <<2/3*210=140>>140 of the total sheep on his farm.\nThe income from the sale of the sheep is 140*$30=$<<140*30=4200>>4200\nFrom the sale of goats and sheep, Mr. Mathews made $4200+$3000 = $8600",
|
||
"answer": 7200.0,
|
||
"validation": {
|
||
"input": {},
|
||
"process": [
|
||
{
|
||
"id": "",
|
||
"expr": "5+7"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "5/12*360"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "360-150"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "1/2*150"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "75*40"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "2/3*210"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "140*30"
|
||
}
|
||
],
|
||
"output": ""
|
||
}
|
||
},
|
||
{
|
||
"question": "Jerry is trying to cut down on the amount of soda he drinks. Right now, he drinks 48 sodas a week. If he cuts the number of sodas he drinks in half each week, how many weeks will it take him to only drink 6 sodas per week?",
|
||
"explanation": "Figure out how many sodas Jerry drinks after 1 week by dividing the starting number of sodas by 2: 48 sodas / 2 = <<48/2=24>>24 sodas\nNow repeat the process to figure out how many soda he drinks after 2 weeks: 24 sodas / 2 = <<24/2=12>>12 sodas\nRepeat the process one more time to find the number of sodas after 3 weeks: 12 sodas / 2 = <<12/2=6>>6 sodas. It takes Jerry 3 weeks to get down to 6 sodas.",
|
||
"answer": 3.0,
|
||
"validation": {
|
||
"input": {},
|
||
"process": [
|
||
{
|
||
"id": "",
|
||
"expr": "48/2"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "24/2"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "12/2"
|
||
}
|
||
],
|
||
"output": ""
|
||
}
|
||
},
|
||
{
|
||
"question": "Agnes is 25 years old and her daughter, Jane is 6 years old. In how many years will Agnes be twice as old as Jane?",
|
||
"explanation": "Let the number of years after which Agnes will be twice as old as Jane be x\nAfter x years, 25+x = 2(6+x)\nSolving the equation by expanding and collecting like terms gives: x-2x = 12-25\nFurther solving gives: -x = -13\nMultiplying both sides by -1 gives x = 13",
|
||
"answer": 13.0,
|
||
"validation": {
|
||
"input": {},
|
||
"process": [],
|
||
"output": ""
|
||
}
|
||
},
|
||
{
|
||
"question": "Lyla, a grocery store owner, bought rice weighing 30 kg less than green beans, which weigh 10 kg more than sugar. While carrying the goods to the store, the bags fell down and 1/3 weight of the rice and 1/5 weight of sugar was lost. If the green beans weighed 60 kgs, then how much did the remaining stock weigh?",
|
||
"explanation": "If rice weighed 30 kg less than the green beans, then the total rice weight is 60 kg - 30 kg = 30 kg\nIf the green beans weighed 10 kg more than sugar, then the total sugar weight is 60 kg - 10 kg = <<60-10=50>>50 kg\nWhen 1/3 weight of rice was lost, the weight loss became 1/3*30 = <<1/3*30=10>>10kg\nThe weight of rice after the loss is 30 kg - 10 kg = <<30-10=20>>20 kg.\nWhen 1/5 weight of sugar was lost, the lost weight was 1/5 * 50 kg = <<1/5*50=10>>10 kg\nThe weight of sugar after the loss is 50 kg - 10 kg = <<50-10=40>>40 kg.\nThe total weight for all the items is 40 kg + 20 kg + 60 kg = <<40+20+60=120>>120 kg",
|
||
"answer": 120.0,
|
||
"validation": {
|
||
"input": {},
|
||
"process": [
|
||
{
|
||
"id": "",
|
||
"expr": "60-10"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "1/3*30"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "30-10"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "1/5*50"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "50-10"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "40+20+60"
|
||
}
|
||
],
|
||
"output": ""
|
||
}
|
||
},
|
||
{
|
||
"question": "Haley is getting ready to watch a comet fly over her house. She spends two hours shopping for a telescope, half an hour getting everything set up in the backyard, three times the setup time making snacks, and 20 minutes watching the comet. What percentage of the total time she spent on all those activities was spent watching the comet, rounded to the nearest percent?",
|
||
"explanation": "First convert Haley's shopping time to minutes: 2 hours * 60 minutes/hour = <<2*60=120>>120 minutes\nThen convert Haley's setup time to minutes: .5 hours * 60 minutes/hour = <<.5*60=30>>30 minutes\nThen find the total time she spends making a snack: 3 * 30 minutes = <<3*30=90>>90 minutes\nThen add the time she spends on each activity to find the total time: 120 minutes + 30 minutes + 90 minutes = <<120+30+90=240>>240 minutes\nThen divide the time she spends watching the comet by the total time and multiply by 100% to express the answer as a percentage: 20 minutes / 240 minutes = 8.333...%, which rounds down to 8%",
|
||
"answer": 8.0,
|
||
"validation": {
|
||
"input": {},
|
||
"process": [
|
||
{
|
||
"id": "",
|
||
"expr": "2*60"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": ".5*60"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "3*30"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "120+30+90"
|
||
}
|
||
],
|
||
"output": ""
|
||
}
|
||
},
|
||
{
|
||
"question": "Andrew eats 14 donuts on Monday, and half as many on Tuesday. On Wednesday Andrew eats 4 times as many as he did on Monday. How many donuts did Andrew eat total in the three days?",
|
||
"explanation": "Monday:14\nTuesday:14/2=7\nWednesday:4(7)=28\nTotal:14+7+28=<<14+7+28=49>>49 donuts",
|
||
"answer": 49.0,
|
||
"validation": {
|
||
"input": {},
|
||
"process": [
|
||
{
|
||
"id": "",
|
||
"expr": "14+7+28"
|
||
}
|
||
],
|
||
"output": ""
|
||
}
|
||
},
|
||
{
|
||
"question": "Ben spends 20% of his after-tax income on his car. If his car payment is $400 and he pays 1/3 of his gross income in taxes, how much does he make per month before taxes?",
|
||
"explanation": "First divide that amount of the car payment by 20% to find Ben's after-tax salary: $400 / .2 = $<<400/.2=2000>>2000\nThen find the proportion of his salary Ben keeps after taxes by subtracting the tax rate from 1: 1 - 1/3 = 2/3\nThen divide Ben's after-tax salary by the proportion of his salary he keeps to find his before-tax salary: $2000 / 2/3 = $3000",
|
||
"answer": 3000.0,
|
||
"validation": {
|
||
"input": {},
|
||
"process": [
|
||
{
|
||
"id": "",
|
||
"expr": "400/.2"
|
||
}
|
||
],
|
||
"output": ""
|
||
}
|
||
},
|
||
{
|
||
"question": "Marcia wants to buy some fruit. Apples cost $2, bananas cost $1, and oranges cost $3. If Marcia buys 12 apples, 4 bananas and 4 oranges, what is the average cost of each piece of fruit in dollars?",
|
||
"explanation": "Find the price of each group of fruit\n12 apples * $2 per apple = $<<12*2=24>>24\n4 bananas * $1 per banana = $<<4*1=4>>4\n3 oranges * $4 per orange = $<<3*4=12>>12\n$24 + $4 + $12 = $<<24+4+12=40>>40 in total that was spent\n12 + 4 + 4 = <<12+4+4=20>>20 total fruits bought\n$40 / 20 fruits = $<<40/20=2>>2 per fruit",
|
||
"answer": 2.0,
|
||
"validation": {
|
||
"input": {},
|
||
"process": [
|
||
{
|
||
"id": "",
|
||
"expr": "12*2"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "4*1"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "3*4"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "24+4+12"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "12+4+4"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "40/20"
|
||
}
|
||
],
|
||
"output": ""
|
||
}
|
||
},
|
||
{
|
||
"question": "Brinley's teacher took the grade six students to the San Diego Zoo to watch and learn about animals. While at the zoo, Brinley counted 100 snakes, 80 arctic foxes, and 20 leopards. She also saw ten times more bee-eaters than leopards, half as many cheetahs as snakes, and twice as many alligators as the total number of Arctic foxes and leopards. What's the total number of animals Brinley counted at the zoo?",
|
||
"explanation": "There were 10*20 = <<10*20=200>>200 more bee-eaters at the zoo.\nThere were 1/2*100 = <<1/2*100=50>>50 cheetahs.\nThe total number of foxes and leopards is 80+20 = <<80+20=100>>100.\nThere were 2*100 = <<2*100=200>>200 alligators.\nThe total number of animals is 200 alligators+220 bee-eaters+100 snakes+80 tactic foxes+20 leopards+50 cheetahs = <<200+220+100+80+20+50=670>>670 animals.",
|
||
"answer": 670.0,
|
||
"validation": {
|
||
"input": {},
|
||
"process": [
|
||
{
|
||
"id": "",
|
||
"expr": "10*20"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "1/2*100"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "80+20"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "2*100"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "200+220+100+80+20+50"
|
||
}
|
||
],
|
||
"output": ""
|
||
}
|
||
},
|
||
{
|
||
"question": "This evening in the nighttime sky over Texas, Mars can be seen until 12:10 AM. Jupiter does not appear until 2 hours and 41 minutes later, and Uranus does not appear until 3 hours and 16 minutes after Jupiter makes its first appearance. How many minutes after 6:00 AM does Uranus first appear in the evening sky over Texas this evening?",
|
||
"explanation": "Jupiter appears 2 hours and 41 minutes after 12:10 AM, which can be calculated in two parts;\n2 hours after 12:10 AM is 12:10+2:00 = 2:10 AM.\nAnd an additional 41 minutes after 2:10 AM is 2:10+0:41 = 2:51 AM.\nUranus appears 3 hours and 16 minutes after 2:51 AM, which can be calculated in two parts:\n3 hours after 2:51 AM is 2:51+3:00 = 5:51 AM.\nAnd 16 minutes after 5:51 AM is 5:51+0:16 = 5:67 AM = 6:07 AM.\nThus, 6:07 AM is 7 minutes after 6:00 AM.",
|
||
"answer": 7.0,
|
||
"validation": {
|
||
"input": {},
|
||
"process": [],
|
||
"output": ""
|
||
}
|
||
},
|
||
{
|
||
"question": "Mark goes into the store to buy some groceries. He buys 6 2$ cans of soup, 2 $5 loaves of bread, 2 3$ boxes of cereal, and 2 $4 gallons of milk. When he gets to the register, he opens his wallet to pay and realizes he only has $10 bills in there. How many $10 bills does he need to use to pay?",
|
||
"explanation": "Mark buys 6 $2 cans of soup, meaning he spends 6*2= <<6*2=12>>12 dollars on soup.\nMark buys 2 $5 loaves of bread, meaning he spends 2*5= <<2*5=10>>10 dollars on bread.\nMark buys 2 $3 boxes of cereal, meaning he spends 2*3= <<2*3=6>>6 dollars on cereal.\nMark buys 2 $4 gallons of milk, meaning he spends 2*4= <<2*4=8>>8 dollars on milk.\nAll added together, this means Mark spends 12+10+6+8= <<12+10+6+8=36>>36 dollars\nSince Mark only has $10 bills, he spends 36/10= <<36/10=3.6>>3.6 tens on it, which rounds up to 4 as you cannot spend .6 of an undividable item.",
|
||
"answer": 4.0,
|
||
"validation": {
|
||
"input": {},
|
||
"process": [
|
||
{
|
||
"id": "",
|
||
"expr": "6*2"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "2*5"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "2*3"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "2*4"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "12+10+6+8"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "36/10"
|
||
}
|
||
],
|
||
"output": ""
|
||
}
|
||
},
|
||
{
|
||
"question": "Brittany uses 1/4 ounce of shampoo to wash her hair every other day. She buys shampoo in 14-ounce bottles. How many bottles does she need to get her through a leap year?",
|
||
"explanation": "A leap year is one day shorter than a regular year, so it is 365 – 1 = <<365-1=364>>364 days.\nBrittany washes her hair every other day, so she will wash it 364 / 2 = <<364/2=182>>182 times in a leap year.\nA bottle of shampoo lasts her 14 / 1 / 4 = 14 * 4 = 56 washes.\nIf she buys 3 bottles, she will only have enough for 56 * 3 = <<3*56=168>>168 washes.\nIf she buys 4 bottles, she will have enough for 56 * 4 = <<4*56=224>>224 washes.\nSince 168 < 182 and 224 > 182, Brittany needs 4 bottles of shampoo to get her through a leap year.",
|
||
"answer": 4.0,
|
||
"validation": {
|
||
"input": {},
|
||
"process": [
|
||
{
|
||
"id": "",
|
||
"expr": "365-1"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "364/2"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "3*56"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "4*56"
|
||
}
|
||
],
|
||
"output": ""
|
||
}
|
||
},
|
||
{
|
||
"question": "Matt has six cats and half of them are female. If each female cat has 7 kittens, and Matt sells 9 of them, what percentage of his remaining cats are kittens (rounded to the nearest percent)?",
|
||
"explanation": "First find the number of cats that are females: 6 cats / 2 = <<6/2=3>>3 cats\nThen find the total number of kittens born: 7 kittens/cat * 3 cats = <<7*3=21>>21 kittens\nThen subtract the 9 kittens that were sold: 21 kittens - 9 kittens = <<21-9=12>>12 kittens\nThen add the number of kittens to the number of adult cats to find the total number of cats: 12 kittens + 6 cats = <<12+6=18>>18 cats\nThen divide the number of kittens by the total number of cats and multiply by 100% to find the percentage of cats that are kittens: 12 kittens / 18 cats * 100% = 66.666...%, which rounds up to 67%",
|
||
"answer": 67.0,
|
||
"validation": {
|
||
"input": {},
|
||
"process": [
|
||
{
|
||
"id": "",
|
||
"expr": "6/2"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "7*3"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "21-9"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "12+6"
|
||
}
|
||
],
|
||
"output": ""
|
||
}
|
||
},
|
||
{
|
||
"question": "Delaney has to catch a bus that leaves at 8:00. a.m to school every day. He always takes 30 minutes to reach the pick-up point from his home. One day he woke up late and left his home at 7:50. How much time did he miss the bus by when he reached the pick-up point?",
|
||
"explanation": "If he left his home at 7:50 a.m. and the distance to the pick-up point is 30 minutes away, he arrived at the pick-up point at 7:50 + 30 minutes = 8:20 a.m.\nIf the bus leaves at 8:00 a.m. every day, then Delaney was 8:20 a.m. - 8:00 a.m. = <<820-800=20>>20 minutes late when the bus had already left.",
|
||
"answer": 20.0,
|
||
"validation": {
|
||
"input": {},
|
||
"process": [
|
||
{
|
||
"id": "",
|
||
"expr": "820-800"
|
||
}
|
||
],
|
||
"output": ""
|
||
}
|
||
},
|
||
{
|
||
"question": "Jerry was contracted to work on a house by his neighbor Miss Stevie. The time it took him to fix the broken kitchen counter was three times longer than the time he took painting the house. He took 8 hours painting the house and then helped mow Miss Stevie's lawn, taking 6 hours. If he charged Miss Stevie $15 per hour of work, calculate the amount of money that Miss Stevie paid him.",
|
||
"explanation": "Jerry took 2*8 = 24 hours fixing the broken kitchen counter\nTogether, painting the house and fixing the broken kitchen counter took him 24+8 = <<24+8=32>>32 hours.\nIf he also took 6 hours mowing the lawn, the total time he spent working for Miss Stevie is 32+6 = <<32+6=38>>38\nSince he charged $15 per hour of work, he was paid 38*$15 = $<<38*15=570>>570",
|
||
"answer": 570.0,
|
||
"validation": {
|
||
"input": {},
|
||
"process": [
|
||
{
|
||
"id": "",
|
||
"expr": "24+8"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "32+6"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "38*15"
|
||
}
|
||
],
|
||
"output": ""
|
||
}
|
||
},
|
||
{
|
||
"question": "Francine wants to know if a local chemical plant is releasing toxic waste that makes the frogs mutate. In one local pond, she catches 5 frogs with extra legs, 2 frogs with 2 heads, two frogs that are bright red, and 18 normal frogs. What percentage of the frogs have mutated, rounded to the nearest integer?",
|
||
"explanation": "First add up the numbers of the three kinds of mutant frog: 5 frogs + 2 frogs + 2 frogs = <<5+2+2=9>>9 frogs\nThen add that number to the number of normal frogs to find the total number of frogs: 9 frogs + 18 frogs = <<9+18=27>>27 frogs\nFinally, divide the number of mutant frogs by the total number of frogs and multiply by 100% to find the percentage of frogs that are mutants: 9 frogs / 27 frogs * 100% = 33.333...%, which rounds to 33%",
|
||
"answer": 33.0,
|
||
"validation": {
|
||
"input": {},
|
||
"process": [
|
||
{
|
||
"id": "",
|
||
"expr": "5+2+2"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "9+18"
|
||
}
|
||
],
|
||
"output": ""
|
||
}
|
||
},
|
||
{
|
||
"question": "In a yard, the number of tanks is five times the number of trucks. If there are 20 trucks in the yard, calculate the total number of tanks and trucks in the yard.",
|
||
"explanation": "There are 5*20 = <<5*20=100>>100 tanks in the yard.\nAltogether, there are 100+20 = <<100+20=120>>120 trucks and tanks in the yard.",
|
||
"answer": 140.0,
|
||
"validation": {
|
||
"input": {},
|
||
"process": [
|
||
{
|
||
"id": "",
|
||
"expr": "5*20"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "100+20"
|
||
}
|
||
],
|
||
"output": ""
|
||
}
|
||
},
|
||
{
|
||
"question": "A school is buying virus protection software to cover 50 devices. One software package costs $40 and covers up to 5 devices. The other software package costs $60 and covers up to 10 devices. How much money, in dollars, can the school save by buying the $60 software package instead of the $40 software package?",
|
||
"explanation": "There are 50/5 = <<50/5=10>>10 sets of 5 devices in the school.\nSo the school will pay a total of $40 x 10 = $<<40*10=400>>400 for the $40 software package.\nThere are 50/10 = <<50/10=5>>5 sets of 10 devices in the school.\nSo the school will pay a total of $60 x 5 = $<<60*5=300>>300 for the $60 software package.\nThus, the school can save $400 - $100 = $<<400-100=300>>300 from buying the $60 software instead of the $40 software package.",
|
||
"answer": 100.0,
|
||
"validation": {
|
||
"input": {},
|
||
"process": [
|
||
{
|
||
"id": "",
|
||
"expr": "50/5"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "40*10"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "50/10"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "60*5"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "400-100"
|
||
}
|
||
],
|
||
"output": ""
|
||
}
|
||
},
|
||
{
|
||
"question": "A shop is offering a discount on pens. If you buy 10 pens at the regular price, you can get the next 10 for half off. A customer came in and bought 20 pens for $30. What's the regular price of one pen in dollars?",
|
||
"explanation": "Let p be the cost of a full-priced pen.\nWe know that the first 10 pens are sold at the regular price, so they cost 10*p.\nWe also know the any pens purchased after the first 10 are half-price, so they cost (20 pens - 10 pens) * p/2 on those.\nIf we add the cost of the first 10 pens and the pens sold at half-price it equals the total purchase of price of $30=10*p + (20-10)*p/2.\nThus, $30 = 10*p + 10 * p/2.\nAnd, $30 = 10 *p + 5*p.\nSo, $30 = 15* p.\nFinally, p=$<<2=2>>2.",
|
||
"answer": 2.0,
|
||
"validation": {
|
||
"input": {},
|
||
"process": [
|
||
{
|
||
"id": "",
|
||
"expr": "2"
|
||
}
|
||
],
|
||
"output": ""
|
||
}
|
||
},
|
||
{
|
||
"question": "Bill and Joan both work for a library. 5 years ago, Joan had 3 times as much experience as Bill. Now she has twice as much experience as Bill. How many years of experience does Bill have now?",
|
||
"explanation": "Let b be Bill's years of experience and j be Joan's years of experience. We know that j - 5 = 3(b - 5) and j = 2b.\nSubstituting the second equation into the first equation, we get 2b - 5 = 3(b - 5)\nMultiplying through the parentheses, we get 2b - 5 = 3b - 15\nAdding 15 to both sides, we get 2b + 10 = 3b\nSubtracting 2b from both sides, we get 10 = b",
|
||
"answer": 10.0,
|
||
"validation": {
|
||
"input": {},
|
||
"process": [],
|
||
"output": ""
|
||
}
|
||
},
|
||
{
|
||
"question": "There are 325 students in a local high school. 40 percent of the students have glasses, how many students do not have glasses?",
|
||
"explanation": "People that do not have glasses 100%-40%=60%\n325(.10)=32.5\n32.5*6=<<32.5*6=195>>195 students",
|
||
"answer": 195.0,
|
||
"validation": {
|
||
"input": {},
|
||
"process": [
|
||
{
|
||
"id": "",
|
||
"expr": "32.5*6"
|
||
}
|
||
],
|
||
"output": ""
|
||
}
|
||
},
|
||
{
|
||
"question": "I caught 4 fewer fish than the number in my tank and added them to my fish tank. If the tank has 20 fish right now, how many did I add?",
|
||
"explanation": "Let's say the number of fish that was in the tank before was x\nIf you caught 4 fewer fish than the number that was there, then you caught x-4\nAfter adding x-4 fish into the tank, the tank now had 20 fish, meaning the total number of fish in the tank is x+x-4=20\n2x=20+4\nThe total number of fish that was initially in the tank is 2x=24\nInitially, there were x=24/2 fish in the tank\nx=<<12=12>>12\nIf you caught 4 fewer fish than the number in my tank initially, you caught 12-4=<<12-4=8>>8 fish.",
|
||
"answer": 8.0,
|
||
"validation": {
|
||
"input": {},
|
||
"process": [
|
||
{
|
||
"id": "",
|
||
"expr": "12"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "12-4"
|
||
}
|
||
],
|
||
"output": ""
|
||
}
|
||
},
|
||
{
|
||
"question": "Mr. and Mrs. Boyden take their 3 children to a leisure park. They buy tickets for the whole family. The cost of an adult ticket is $6 more than the cost of a child ticket. The total cost of the 5 tickets is $77. What is the cost of an adult ticket?",
|
||
"explanation": "Let X be the cost of an adult ticket.\nSo the cost of a child ticket is X-6.\nThe total cost of the 5 tickets is X*2 + 3*(X-6) = 77.\nX*2 + 3*X - 3*6 = 77.\n5*X - 18 = 77.\n5*X = 77 + 18 = 95\nX = <<19=19>>19",
|
||
"answer": 19.0,
|
||
"validation": {
|
||
"input": {},
|
||
"process": [
|
||
{
|
||
"id": "",
|
||
"expr": "19"
|
||
}
|
||
],
|
||
"output": ""
|
||
}
|
||
},
|
||
{
|
||
"question": "There are 480 zombies in the shopping mall. If the number of zombies doubled every day, how many days ago were there less than 50 zombies in the mall?",
|
||
"explanation": "First find how many zombies there were one day ago: 480 zombies / 2 = <<480/2=240>>240 zombies\nThen find how many zombies there were two days ago: 240 zombies / 2 = <<240/2=120>>120 zombies\nThen find the number of zombies there were three days ago: 120 zombies / 2 = <<120/2=60>>60 zombies\nThen find the number of zombies there were four days ago: 60 zombies / 2 = <<60/2=30>>30 zombies, which is less than 50, so there were less than 50 zombies 4 days ago.",
|
||
"answer": 4.0,
|
||
"validation": {
|
||
"input": {},
|
||
"process": [
|
||
{
|
||
"id": "",
|
||
"expr": "480/2"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "240/2"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "120/2"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "60/2"
|
||
}
|
||
],
|
||
"output": ""
|
||
}
|
||
},
|
||
{
|
||
"question": "Christina's age will be half of 80 years in five years to come. If Oscar will be 3/5 times as old as Christina is now in 15 years, calculate Oscar's age now.",
|
||
"explanation": "Christina's age will be half of 80 in five years to come, meaning in five years, Christina's age will be 1/2*80=40 years.\nIf in five years Christina will be 40, currently she is 40-5=<<40-5=35>>35 years old.\nOscar will be 3/5 times as old as Christina is now in 15 years, meaning he will be 3/5*35=<<3/5*35=21>>21 years old in 15 years.\nCurrently, Oscar is 21-15=<<21-15=6>>6 years old.",
|
||
"answer": 6.0,
|
||
"validation": {
|
||
"input": {},
|
||
"process": [
|
||
{
|
||
"id": "",
|
||
"expr": "40-5"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "3/5*35"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "21-15"
|
||
}
|
||
],
|
||
"output": ""
|
||
}
|
||
},
|
||
{
|
||
"question": "Mitch is a freelancer, she works 5 hours every day from Monday to Friday and 3 hours every Saturday and Sunday. If she earns $3 per hour and earns double on weekends, how much does she earn every week?",
|
||
"explanation": "Mitch earns 5 x $3 = $<<5*3=15>>15 every weekday.\nSo, she earns $15 x 5 = $<<15*5=75>>75 from Monday to Friday.\nAnd she earns $3 x 2 = $<<3*2=6>>6 per hour every weekend.\nHence, the total amount she earns every weekend is $6 x 3= $<<6*3=18>>18.\nSo, she earns $18 x 2 = $<<18*2=36>>36 every Saturday and Sunday.\nTherefore, the total amount she earns every week is $75 + $36= $<<75+36=111>>111.",
|
||
"answer": 111.0,
|
||
"validation": {
|
||
"input": {},
|
||
"process": [
|
||
{
|
||
"id": "",
|
||
"expr": "5*3"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "15*5"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "3*2"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "6*3"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "18*2"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "75+36"
|
||
}
|
||
],
|
||
"output": ""
|
||
}
|
||
},
|
||
{
|
||
"question": "Josue planted a tree in his backyard that grows at the rate of 2 feet per week. If the tree is currently 10 feet tall, what would be the tree's total height after 4 months (assuming each month is 4 weeks long)?",
|
||
"explanation": "Since a month has four weeks, the tree will increase its height by 2 feet for 4*4=16 weeks after four months of growing.\nSince the tree grows at 2 feet per week, after 16 weeks, the tree would have increased its height by 2*16=<<2*16=32>>32 feet.\nIf the tree is currently 10 feet tall, its height after four months will be 10+32=<<10+32=42>>42 feet.",
|
||
"answer": 42.0,
|
||
"validation": {
|
||
"input": {},
|
||
"process": [
|
||
{
|
||
"id": "",
|
||
"expr": "2*16"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "10+32"
|
||
}
|
||
],
|
||
"output": ""
|
||
}
|
||
},
|
||
{
|
||
"question": "Tomas is hoping to run a marathon next year, which is 26.3 miles. He knows that each month he trains, he can run twice as far as the month before. If he can run 3 miles during the first month of training, how many total months before the marathon should he start training to ensure he can run far enough?",
|
||
"explanation": "In the first month he can run 3 miles.\nIn the second month he can run 6 miles because 3 x 2 = <<3*2=6>>6\nIn the third month he can run 12 miles because 6 x 2 = <<6*2=12>>12\nIn fourth month he can run 24 miles because 12 x 2 = <<12*2=24>>24\nIn fifth month he can run 48 miles because 24 x 2 = <<24*2=48>>48\nHe needs to start training 5 months ahead of time because 24 < 26.3 and 48>26.3.",
|
||
"answer": 5.0,
|
||
"validation": {
|
||
"input": {},
|
||
"process": [
|
||
{
|
||
"id": "",
|
||
"expr": "3*2"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "6*2"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "12*2"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "24*2"
|
||
}
|
||
],
|
||
"output": ""
|
||
}
|
||
},
|
||
{
|
||
"question": "Ms. Warren ran at 6 mph for 20 minutes. After the run, she walked at 2 mph for 30 minutes. How many miles did she run and walk in total?",
|
||
"explanation": "20 minutes is 20/60=1/3 of an hour.\nMs. Warren ran 6/3=<<6/3=2>>2 miles.\n30 minutes is 30/60=1/2 of an hour.\nMs. Warren walked 2/2=<<2/2=1>>1 mile.\nMs Warren ran and walked 2+1=<<2+1=3>>3 miles in total.",
|
||
"answer": 3.0,
|
||
"validation": {
|
||
"input": {},
|
||
"process": [
|
||
{
|
||
"id": "",
|
||
"expr": "6/3"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "2/2"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "2+1"
|
||
}
|
||
],
|
||
"output": ""
|
||
}
|
||
},
|
||
{
|
||
"question": "Tanesha needs to buy rope so cut into 10 pieces that are each six inches long. She sees a 6-foot length of rope that cost $5 and also sees 1-foot lengths of rope that cost $1.25 each. What is the least she has to spend to get the rope she needs?",
|
||
"explanation": "She needs 60 inches of rope because 10 x 6 equals <<10*6=60>>60\nThe six-foot length of rope is 72 inches long because 6 x 12 = <<6*12=72>>72\nThe six-foot length of rope would give her 12 pieces because 72 / 6 = <<72/6=12>>12\nThe six-foot length is long enough because 12 > 10\nEach 1-foot rope equals 12 inches\nShe would need 5 of the 1-foot ropes because 60 / 12 = <<60/12=5>>5\nIf she bought one-foot ropes it would cost $6.25 because 5 x 1.25 = 6.25\nThe cheapest rope to buy is the 6-foot rope because 5 < 6.25",
|
||
"answer": 5.0,
|
||
"validation": {
|
||
"input": {},
|
||
"process": [
|
||
{
|
||
"id": "",
|
||
"expr": "10*6"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "6*12"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "72/6"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "60/12"
|
||
}
|
||
],
|
||
"output": ""
|
||
}
|
||
},
|
||
{
|
||
"question": "Tim has some cans of soda. Jeff comes by, and takes 6 cans of soda from Tim. Tim then goes and buys another half the amount of soda cans he had left. If Tim has 24 cans of soda in the end, how many cans of soda did Tim have at first?",
|
||
"explanation": "Let x be the number of cans Tim has at first.\nAfter Jeff comes by, Tim has x-6 cans left.\nTim buys another (x-6)/2 cans.\nx-6+(x-6)/2=24\n2*x-12+x-6=48\n3*x-18=48\n3*x=66\nx=<<22=22>>22",
|
||
"answer": 22.0,
|
||
"validation": {
|
||
"input": {},
|
||
"process": [
|
||
{
|
||
"id": "",
|
||
"expr": "22"
|
||
}
|
||
],
|
||
"output": ""
|
||
}
|
||
},
|
||
{
|
||
"question": "Two-fifths of the seats in an auditorium that holds 500 people are currently taken. It was found that 1/10 of the seats are broken. How many seats are still available?",
|
||
"explanation": "500/ 2/5 = 200 seats are already taken.\n500/ 1/10 = <<500/1/10=50>>50 seats are broken.\nSo 200 + 50 = <<200+50=250>>250 seats are either taken or broken.\nTherefore, 500 - 250 = <<500-250=250>>250 seats are still available.",
|
||
"answer": 250.0,
|
||
"validation": {
|
||
"input": {},
|
||
"process": [
|
||
{
|
||
"id": "",
|
||
"expr": "500/1/10"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "200+50"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "500-250"
|
||
}
|
||
],
|
||
"output": ""
|
||
}
|
||
},
|
||
{
|
||
"question": "Bridgette has 2 dogs, 3 cats, and 4 birds. She gives the dogs a bath twice a month. She gives the cats a bath once a month. She gives the birds a bath once every 4 months. In a year, how many baths does she give?",
|
||
"explanation": "Each dog gets 24 baths a year because 2 x 12 = <<2*12=24>>24\nEach cat gets 12 baths a year because 1 x 12 = <<1*12=12>>12\nEach bird averages .25 baths per month because 1 / 4 = <<1/4=.25>>.25\nEach bird gets 3 baths a year because .25 x 12 = <<.25*12=3>>3\nShe gives 48 dog baths because 2 x 24 = <<2*24=48>>48\nShe gives 72 cat baths because 3 x 12 = 36\nShe gives 12 bird baths a year because 4 x 3 = <<4*3=12>>12\nShe gives 132 baths a year because 48 + 36+ 12 = <<48+36+12=96>>96",
|
||
"answer": 96.0,
|
||
"validation": {
|
||
"input": {},
|
||
"process": [
|
||
{
|
||
"id": "",
|
||
"expr": "2*12"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "1*12"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "1/4"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": ".25*12"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "2*24"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "4*3"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "48+36+12"
|
||
}
|
||
],
|
||
"output": ""
|
||
}
|
||
},
|
||
{
|
||
"question": "Together, Alan and Marcy handed out 150 parking tickets. If Marcy handed out 6 fewer than 5 times as many tickets as Alan, how many tickets did Alan hand out?",
|
||
"explanation": "Let a be the number of tickets Alan hands out and m be the number Marcy hands out. We know that a + m = 150 and m = 5a - 6\nSubstituting the second equation into the first, we get a + 5a - 6 = 150\nAdding 2 to both sides, we get a + 5a = 156\nCombining like terms, we get 6a = 156\nDividing both sides by 6, we get a = 26",
|
||
"answer": 26.0,
|
||
"validation": {
|
||
"input": {},
|
||
"process": [],
|
||
"output": ""
|
||
}
|
||
},
|
||
{
|
||
"question": "Rick likes to separate his collection of books into various groups by genre. He has 400 books in total and proceeds to divide them into two separate equally-sized categories repeatedly until he has each book in a category with 24 other books. How many times must he break these groups into smaller groups to accomplish this?",
|
||
"explanation": "Rick starts with 400 books and divides them into two categories of equal size, meaning there are two categories of 400/2= <<400/2=200>>200 books.\nRick repeats this process again, dividing the 200 book categories into equal halves, leaving him with 200/2=<<200/2=100>>100 books in each.\nRick repeats this process again, dividing the 100 book categories into equal halves, leaving him with 100/2=<<100/2=50>>50 books in each.\nRick repeats this process again, dividing the 50 book categories into equal halves, leaving him with 50/2=<<50/2=25>>25 books in each.\nSince Rick is looking for categories with 25 books in each, he accomplishes this by the 4th step.",
|
||
"answer": 4.0,
|
||
"validation": {
|
||
"input": {},
|
||
"process": [
|
||
{
|
||
"id": "",
|
||
"expr": "400/2"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "200/2"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "100/2"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "50/2"
|
||
}
|
||
],
|
||
"output": ""
|
||
}
|
||
},
|
||
{
|
||
"question": "Martha is grinding a spice paste. She adds 3 tablespoons of ginger, 1 teaspoon of cardamom, 1 teaspoon of mustard, 2 tablespoons of garlic, and four times as much chile powder as mustard. What percentage of the spice paste is ginger, rounded to the nearest integer? (Remember there are three teaspoons per tablespoon.)",
|
||
"explanation": "First convert the ginger to teaspoons: 3 tablespoons * 3 teaspoons/tablespoon = <<3*3=9>>9 teaspoons\nThen convert the garlic to teaspoons: 2 tablespoons * 3 teaspoons/tablespoon = <<2*3=6>>6 teaspoons\nThen find how much chile powder there is: 1 teaspoon * 4 = <<1*4=4>>4 teaspoons\nThen add up the amount of each spice to find the total amount: 9 teaspoons + 6 teaspoons + 4 teaspoons + 1 teaspoons + 1 teaspoon = <<9+6+4+1+1=21>>21 teaspoons\nThen divide the amount of ginger by the total amount of spice paste and multiply by 100% to find the percentage of the spice paste that's ginger: 9 teaspoons / 21 teaspoons * 100% = 42.857, which rounds down to 43%",
|
||
"answer": 43.0,
|
||
"validation": {
|
||
"input": {},
|
||
"process": [
|
||
{
|
||
"id": "",
|
||
"expr": "3*3"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "2*3"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "1*4"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "9+6+4+1+1"
|
||
}
|
||
],
|
||
"output": ""
|
||
}
|
||
},
|
||
{
|
||
"question": "Jed collects stamp cards. Every week, he gets 6 cards. But every two weeks, he gives 2 cards to his friends. If Jed started with 20 cards, after how many weeks will he have a total of 40 cards?",
|
||
"explanation": "In the first week, Jed has 20 + 6 = <<20+6=26>>26 cards.\nIn the second week, he has 26 + 6 = <<26+6=32>>32 cards.\nBut he is left with 32 - 2 = <<32-2=30>>30 cards on the 2nd week after giving 2 cards to his friend.\nThen Jed has 30 + 6 = <<30+6=36>>36 cards on the 3rd week.\nHe has 36 + 6 = <<36+6=42>>42 cards on the 4th week.\nAfter giving his friend 2 cards, he is then left with 42 - 2 = <<42-2=40>>40 cards on the 4th week.\nHence, Jed will have a total of 40 cards in 4 weeks.",
|
||
"answer": 4.0,
|
||
"validation": {
|
||
"input": {},
|
||
"process": [
|
||
{
|
||
"id": "",
|
||
"expr": "20+6"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "26+6"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "32-2"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "30+6"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "36+6"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "42-2"
|
||
}
|
||
],
|
||
"output": ""
|
||
}
|
||
},
|
||
{
|
||
"question": "If you double a number and add 5 to the result, then that's 20 more than half of the original number. What's the original number?",
|
||
"explanation": "Let x be the original number.\n2*x+5=20+x/2\n2*x-x/2=15\n4*x-x=30\n3*x=30\nx=<<10=10>>10",
|
||
"answer": 4.0,
|
||
"validation": {
|
||
"input": {},
|
||
"process": [
|
||
{
|
||
"id": "",
|
||
"expr": "10"
|
||
}
|
||
],
|
||
"output": ""
|
||
}
|
||
},
|
||
{
|
||
"question": "John and Yasmin's dad is named Gabriel. If John has twice the number of children that her sister has and Gabriel has six grandkids, how many children does Yasmin have?",
|
||
"explanation": "We don't know Yasmin's number of children yet, but let's represent it as Y.\nIf John has twice the number of children Yasmin has, then John has 2*Y = 2Y kids\nIf Gabriel has 6 grandkids between John's and Yasmin's children, then we can represent this as 6 = 2Y + Y\nIf we solve the latest equation then we learn that 6=3Y\nGiven that Y represents how many kids Yasmin has, then solving for Y we know that Y=6/3 or Y=2 kids",
|
||
"answer": 2.0,
|
||
"validation": {
|
||
"input": {},
|
||
"process": [],
|
||
"output": ""
|
||
}
|
||
},
|
||
{
|
||
"question": "Angelo and Melanie want to plan how many hours over the next week they should study together for their test next week. They have 2 chapters of their textbook to study and 4 worksheets to memorize. They figure out that they should dedicate 3 hours to each chapter of their textbook and 1.5 hours for each worksheet. If they plan to study no more than 4 hours each day, how many days should they plan to study total over the next week if they take a 10-minute break every hour, include 3 10-minute snack breaks each day, and 30 minutes for lunch each day?",
|
||
"explanation": "Angelo and Melanie think they should dedicate 3 hours to each of the 2 chapters, 3 hours x 2 chapters = <<3*2=6>>6 hours total.\nFor the worksheets they plan to dedicate 1.5 hours for each worksheet, 1.5 hours x 4 worksheets = <<1.5*4=6>>6 hours total.\nAngelo and Melanie need to start with planning 12 hours to study, at 4 hours a day, 12 / 4 = <<12/4=3>>3 days.\nHowever, they need to include time for breaks and lunch. Every hour they want to include a 10-minute break, so 12 total hours x 10 minutes = <<12*10=120>>120 extra minutes for breaks.\nThey also want to include 3 10-minute snack breaks, 3 x 10 minutes = <<3*10=30>>30 minutes.\nAnd they want to include 30 minutes for lunch each day, so 120 minutes for breaks + 30 minutes for snack breaks + 30 minutes for lunch = 180 minutes, or 180 / 60 minutes per hour = 3 extra hours.\nSo Angelo and Melanie want to plan 12 hours to study + 3 hours of breaks = <<12+3=15>>15 hours total.\nThey want to study no more than 4 hours each day, 15 hours / 4 hours each day = <<15/4=3.75>>3.75\nThey will need to plan to study 4 days to allow for all the time they need.",
|
||
"answer": 4.0,
|
||
"validation": {
|
||
"input": {},
|
||
"process": [
|
||
{
|
||
"id": "",
|
||
"expr": "3*2"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "1.5*4"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "12/4"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "12*10"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "3*10"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "12+3"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "15/4"
|
||
}
|
||
],
|
||
"output": ""
|
||
}
|
||
},
|
||
{
|
||
"question": "Mark does a gig every other day for 2 weeks. For each gig, he plays 3 songs. 2 of the songs are 5 minutes long and the last song is twice that long. How many minutes did he play?",
|
||
"explanation": "He played 7*2 = <<7*2=14>>14 gigs\nThe long song was 5*2=<<5*2=10>>10 minutes\nSo all the gigs were 5+5+10=<<5+5+10=20>>20 minutes\nSo he played 14*20=140 minutes",
|
||
"answer": 280.0,
|
||
"validation": {
|
||
"input": {},
|
||
"process": [
|
||
{
|
||
"id": "",
|
||
"expr": "7*2"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "5*2"
|
||
},
|
||
{
|
||
"id": "",
|
||
"expr": "5+5+10"
|
||
}
|
||
],
|
||
"output": ""
|
||
}
|
||
}
|
||
] |