gemma-4-12B-it-TT-BFP8-P150 / evidence /p3d-pc-gate-s1 /sampling /runs /spec-gsm /gsm-recommended-s2.jsonl
| {"idx": 0, "text": "To find out how much Janet makes at the farmers' market every day, we can follow these steps:\n\n1. **Determine the total number of eggs laid daily:**\n Janet's ducks lay 16 eggs per day.\n\n2. **Calculate how many eggs are used for breakfast:**\n She eats 3 eggs for breakfast.\n $16 - 3 = 13$ eggs remaining.\n\n3. **Calculate how many eggs are used for muffins:**\n She uses 4 eggs for muffins.\n $13 - 4 = 9$ eggs remaining.\n\n4. **Identify the number of eggs available to sell:**\n The remainder of the eggs is 9.\n\n5. **Calculate the total earnings from selling the eggs:**\n She sells each egg for $2.\n $9 \\text{ eggs} \\times \\$2 \\text{ per egg} = \\$18$.\n\n#### 18", "pred": "18", "gold": "18", "correct": true, "n_new": 207, "stop": "stop", "seconds": 2.372112512588501} | |
| {"idx": 1, "text": "To solve the problem, we can break it down into steps:\n\n1. **Identify the amount of blue fiber:**\n The problem states the robe takes 2 bolts of blue fiber.\n\n2. **Calculate the amount of white fiber:**\n The problem states it takes half as much white fiber as blue fiber.\n Half of 2 is $2 \\div 2 = 1$.\n So, the robe takes 1 bolt of white fiber.\n\n3. **Calculate the total amount of fiber:**\n Add the blue fiber and the white fiber together.\n $2 \\text{ (blue)} + 1 \\text{ (white)} = 3$.\n\nThe total number of bolts is 3.\n\n#### 3", "pred": "3", "gold": "3", "correct": true, "n_new": 161, "stop": "stop", "seconds": 2.8910655975341797} | |
| {"idx": 2, "text": "To find the profit Josh made, we need to calculate his total investment, the final value of the house, and then subtract the total investment from the final value.\n\n**Step 1: Calculate the total investment (Cost).**\nJosh spent money on both the purchase of the house and the repairs.\nCost = Purchase Price + Repair Costs\nCost = $80,000 + $50,000\nCost = $130,000\n\n**Step 2: Determine the value of the house after repairs.**\nThe problem states that the repairs increased the value of the house by 150%. This increase is based on the original value of the house ($80,000).\nValue Increase = 150% of $80,000\nValue Increase = 1.50 \u00d7 $80,000\nValue Increase = $120,000\n\n**Step 3: Calculate the final value of the house.**\nThe final value is the original price plus the value added by the repairs.\nFinal Value = Original Price + Value Increase\nFinal Value = $80,000 + $120,000\nFinal Value = $200,000\n\n**Step 4: Calculate the profit.**\nProfit is the final value minus the total cost invested.\nProfit = Final Value - Total Investment\nProfit = $200,000 - $130,000\nProfit = $70,000\n\n#### 70000", "pred": "70000", "gold": "70000", "correct": true, "n_new": 338, "stop": "stop", "seconds": 3.889765977859497} | |
| {"idx": 3, "text": "To find the total number of meters James runs in a week, we can break the problem down into steps:\n\n1. **Calculate the distance run in one session:**\n James runs 3 sprints per session, and each sprint is 60 meters.\n $3 \\text{ sprints} \\times 60 \\text{ meters/sprint} = 180 \\text{ meters per session}$\n\n2. **Calculate the total distance run per week:**\n James runs these sessions 3 times a week.\n $180 \\text{ meters/session} \\times 3 \\text{ sessions/week} = 540 \\text{ meters per week}$\n\nAlternatively, you can multiply all numbers together:\n$3 \\text{ sprints} \\times 3 \\text{ times a week} \\times 60 \\text{ meters} = 9 \\times 60 = 540 \\text{ meters}$\n\n#### 540", "pred": "540", "gold": "540", "correct": true, "n_new": 213, "stop": "stop", "seconds": 2.2925913333892822} | |
| {"idx": 4, "text": "To find the number of cups of feed Wendi needs to give her chickens in the final meal, we can follow these steps:\n\n1. **Determine the total number of cups each chicken eats per day:**\n Wendi feeds each chicken 3 cups of feed per day.\n\n2. **Calculate the total amount of feed needed for the entire flock per day:**\n There are 20 chickens in the flock.\n Total feed per day = (Number of chickens) \u00d7 (Cups per chicken)\n Total feed per day = 20 \u00d7 3 = 60 cups.\n\n3. **Calculate the total amount of feed already given in the first two meals:**\n Morning meal = 15 cups.\n Afternoon meal = 25 cups.\n Total feed already given = 15 + 25 = 40 cups.\n\n4. **Calculate the amount of feed needed for the final meal:**\n Final meal = (Total feed per day) - (Total feed already given)\n Final meal = 60 - 40 = 20 cups.\n\n#### 20", "pred": "20", "gold": "20", "correct": true, "n_new": 244, "stop": "stop", "seconds": 4.050663471221924} | |
| {"idx": 5, "text": "To find the total cost of the glasses, we can break the problem down into steps:\n\n1. **Determine the price of each type of glass:**\n - The first glass in a pair costs $5.\n - The second glass in a pair costs 60% of the first glass's price.\n - Calculation: $5 \\times 0.60 = \\$3$.\n\n2. **Identify the number of pairs:**\n - Kylar wants to buy 16 glasses in total.\n - Since the pricing logic applies to \"every second glass,\" we can think of these as 8 pairs of glasses.\n\n3. **Calculate the cost per pair:**\n - Each pair consists of one glass at $5 and one glass at $3.\n - Calculation: $5 + 3 = \\$8$ per pair.\n\n4. **Calculate the total cost for 16 glasses:**\n - There are 8 pairs of glasses.\n - Calculation: $8 \\text{ pairs} \\times \\$8 \\text{ per pair} = \\$64$.\n\nAlternatively, you can calculate it by the quantity of each price point:\n- Number of \"first\" glasses (odd-numbered): 8\n- Number of \"second\" glasses (even-numbered): 8\n- Total cost = $(8 \\times \\$5) + (8 \\times \\$3) = \\$40 + \\$24 = \\$64$.\n\n#### 64", "pred": "64", "gold": "64", "correct": true, "n_new": 317, "stop": "stop", "seconds": 4.2976508140563965} | |
| {"idx": 6, "text": "To find the total number of sheep in Toulouse, Charleston, and Seattle, we can solve the problem step by step:\n\n1. **Determine the number of sheep in Seattle:**\n The problem states that Seattle has 20 sheep.\n Seattle = 20\n\n2. **Determine the number of sheep in Charleston:**\n The problem states that Charleston has 4 times as many sheep as Seattle.\n Charleston = 4 \u00d7 20 = 80\n\n3. **Determine the number of sheep in Toulouse:**\n The problem states that Toulouse has twice as many sheep as Charleston.\n Toulouse = 2 \u00d7 80 = 160\n\n4. **Calculate the total number of sheep:**\n To find the total, add the sheep from all three cities together:\n Total = Toulouse + Charleston + Seattle\n Total = 160 + 80 + 20\n Total = 240 + 20\n Total = 260\n\n#### 260", "pred": "260", "gold": "260", "correct": true, "n_new": 227, "stop": "stop", "seconds": 2.3986997604370117} | |
| {"idx": 7, "text": "To find the total time it takes Carla to download the file, we break the process into three distinct stages:\n\n**Stage 1: The first attempt before the restart**\n1. Carla downloads 40% of the 200 GB file.\n $200\\text{ GB} \\times 0.40 = 80\\text{ GB}$.\n2. Her download speed is 2 GB/minute.\n $\\text{Time} = \\frac{80\\text{ GB}}{2\\text{ GB/min}} = 40\\text{ minutes}$.\n\n**Stage 2: The Windows update interruption**\n1. The system forces a restart for updates.\n $\\text{Time} = 20\\text{ minutes}$.\n\n**Stage 3: The second attempt (the full download)**\n1. Carla must restart the download from the beginning.\n2. She needs to download the entire 200 GB file.\n $\\text{Time} = \\frac{200\\text{ GB}}{2\\text{ GB/min}} = 100\\text{ minutes}$.\n\n**Total Time Calculation:**\nTo find the total time, we sum the duration of all three stages:\n$\\text{Total Time} = 40\\text{ minutes (Stage 1)} + 20\\text{ minutes (Stage 2)} + 100\\text{ minutes (Stage 3)}$\n$\\text{Total Time} = 160\\text{ minutes}$.\n\n#### 160", "pred": "160", "gold": "160", "correct": true, "n_new": 345, "stop": "stop", "seconds": 4.247485399246216} | |
| {"idx": 8, "text": "To find out how far John is from home at the end of the 4 hours, we need to calculate the total distance he traveled away from home and then subtract the distance he traveled back toward home.\n\n**Step 1: Calculate the initial distance from home.**\nJohn drives for 3 hours at a speed of 60 mph.\n$\\text{Distance} = \\text{Speed} \\times \\text{Time}$\n$60 \\text{ mph} \\times 3 \\text{ hours} = 180 \\text{ miles}$\nSo, John is initially 180 miles away from home.\n\n**Step 2: Calculate the distance traveled back towards home.**\nJohn spends a total of 4 hours trying to get back. We break this down into three segments:\n1. **First 2 hours:** He is in standstill traffic.\n $\\text{Distance} = 0 \\text{ mph} \\times 2 \\text{ hours} = 0 \\text{ miles}$\n2. **Next half-hour (0.5 hours):** He drives at 30 mph.\n $\\text{Distance} = 30 \\text{ mph} \\times 0.5 \\text{ hours} = 15 \\text{ miles}$\n3. **Remaining time:** The total time spent was 4 hours. He has used $2 + 0.5 = 2.5$ hours. The remaining time is $4 - 2.5 = 1.5$ hours. He drives this time at 80 mph.\n $\\text{Distance} = 80 \\text{ mph} \\times 1.5 \\text{ hours} = 120 \\text{ miles}$\n\n**Step 3: Calculate the total distance traveled back.**\n$\\text{Total distance back} = 0 \\text{ miles} + 15 \\text{ miles} + 120 \\text{ miles} = 135 \\text{ miles}$\n\n**Step 4: Calculate the final distance from home.**\nJohn started 180 miles away and traveled 135 miles back toward home.\n$\\text{Final distance} = 180 \\text{ miles} - 135 \\text{ miles} = 45 \\text{ miles}$\n\n#### 45", "pred": "45", "gold": "45", "correct": true, "n_new": 510, "stop": "stop", "seconds": 6.000898838043213} | |
| {"idx": 9, "text": "To find Eliza's total earnings for the week, we need to calculate her regular pay and her overtime pay separately and then sum them up.\n\n**Step 1: Calculate regular earnings.**\nEliza works 40 hours at a regular rate of $10 per hour.\nRegular Earnings = 40 hours \u00d7 $10/hour\nRegular Earnings = $400\n\n**Step 2: Calculate the overtime rate.**\nOvertime is paid at 1.2 times her regular hourly rate.\nOvertime Rate = $10 \u00d7 1.2\nOvertime Rate = $12 per hour\n\n**Step 3: Calculate the overtime hours worked.**\nEliza worked a total of 45 hours. The first 40 hours are regular hours.\nOvertime Hours = Total Hours - Regular Hours\nOvertime Hours = 45 - 40\nOvertime Hours = 5 hours\n\n**Step 4: Calculate overtime earnings.**\nOvertime Earnings = 5 hours \u00d7 $12/hour\nOvertime Earnings = $60\n\n**Step 5: Calculate total earnings.**\nTotal Earnings = Regular Earnings + Overtime Earnings\nTotal Earnings = $400 + $60\nTotal Earnings = $460\n\n#### 460", "pred": "460", "gold": "460", "correct": true, "n_new": 273, "stop": "stop", "seconds": 3.2584359645843506} | |
| {"idx": 10, "text": "To find the total number of downloads over the three months, we calculate the downloads for each month step by step:\n\n1. **Month 1:**\n The problem states the program had 60 downloads in the first month.\n *Month 1 Total = 60*\n\n2. **Month 2:**\n The downloads in the second month were three times as many as the downloads in the first month.\n $60 \\times 3 = 180$\n *Month 2 Total = 180*\n\n3. **Month 3:**\n The downloads in the third month were reduced by 30% from the second month's count.\n First, calculate 30% of the second month's downloads:\n $180 \\times 0.30 = 54$\n Next, subtract that amount from the second month's count:\n $180 - 54 = 126$\n *Month 3 Total = 126*\n\n4. **Total Downloads:**\n Add the downloads from all three months together:\n $60 + 180 + 126 = 366$\n\n#### 366", "pred": "366", "gold": "366", "correct": true, "n_new": 277, "stop": "stop", "seconds": 2.8992817401885986} | |
| {"idx": 11, "text": "To find the total cost of the pastries Toula bought, we will calculate the cost of each type of pastry separately and then sum them up.\n\n**Step 1: Calculate the cost of the donuts.**\nToula bought 3 dozen donuts at $68 per dozen.\n$3 \\times 68 = 204$\nThe cost for the donuts is $204.\n\n**Step 2: Calculate the cost of the mini cupcakes.**\nToula bought 2 dozen mini cupcakes at $80 per dozen.\n$2 \\times 80 = 160$\nThe cost for the mini cupcakes is $160.\n\n**Step 3: Calculate the cost of the mini cheesecakes.**\nToula bought 6 dozen mini cheesecakes at $55 per dozen.\n$6 \\times 55 = 330$\nThe cost for the mini cheesecakes is $330.\n\n**Step 4: Calculate the total cost.**\nAdd the costs of all three types of pastries together:\n$204 + 160 + 330$\n$204 + 160 = 364$\n$364 + 330 = 694$\n\nThe total cost of the pastries is $694.\n\n#### 694", "pred": "694", "gold": "694", "correct": true, "n_new": 294, "stop": "stop", "seconds": 3.0543718338012695} | |
| {"idx": 12, "text": "To find out how many years it will take for Carlos to start earning money, we need to calculate the annual profit from the tree and determine how long it takes to cover the initial cost.\n\n**Step 1: Calculate the annual revenue.**\nThe tree produces 7 lemons each year, and each lemon sells for $1.50.\nAnnual Revenue = $7 \\times \\$1.50 = \\$10.50$\n\n**Step 2: Calculate the annual profit.**\nIt costs $3 each year to water and feed the tree. We subtract this cost from the annual revenue.\nAnnual Profit = $\\$10.50 - \\$3.00 = \\$7.50$\n\n**Step 3: Calculate the time to cover the initial cost.**\nThe initial cost to plant the tree is $90. We divide the initial cost by the annual profit to find out how many years it takes to break even.\nYears = $\\$90 / \\$7.50$\n\nLet's perform the division:\n$90 \\div 7.5 = 900 \\div 75$\n$900 / 75 = 12$\n\n**Step 4: Determine when he starts earning money.**\nAfter 12 years, Carlos will have recovered his initial investment of $90 (12 years $\\times$ $7.50/year = $90). Therefore, in the 13th year, he will begin to have a net profit. \n\nHowever, the question asks how many years it will take *before* he starts earning money (reaching the break-even point). After 12 years, the cost is covered.\n\n#### 12", "pred": "12", "gold": "13", "correct": false, "n_new": 367, "stop": "stop", "seconds": 4.855315446853638} | |
| {"idx": 13, "text": "To find out how many vacuum cleaners Melanie started with, we can work backward from the final number of vacuum cleaners she had left.\n\n**Step 1: Analyze the situation at the orange house.**\nMelanie sold half of what she had left at the orange house and was left with 5. \nIf 5 is half of what she had before visiting the orange house, we multiply by 2:\n$5 \\times 2 = 10$.\nSo, she had 10 vacuum cleaners before arriving at the orange house.\n\n**Step 2: Analyze the situation at the red house.**\nBefore the orange house, she had 10 vacuum cleaners. She had sold 2 vacuum cleaners at the red house to get to that number. \nTo find how many she had before the red house, we add those 2 back:\n$10 + 2 = 12$.\nSo, she had 12 vacuum cleaners before arriving at the red house.\n\n**Step 3: Analyze the situation at the green house.**\nBefore the red house, she had 12 vacuum cleaners. These 12 represent what was left after she sold a third of her initial stock at the green house.\nIf she sold $\\frac{1}{3}$, then $\\frac{2}{3}$ of her original stock remains.\nLet $x$ be the total number she started with.\n$\\frac{2}{3}x = 12$\nTo solve for $x$, multiply both sides by $\\frac{3}{2}$:\n$x = 12 \\times \\frac{3}{2}$\n$x = 6 \\times 3$\n$x = 18$.\n\n**Verification:**\n1. Start with 18.\n2. Green house: Sells $\\frac{1}{3}$ of 18 (6). Left: $18 - 6 = 12$.\n3. Red house: Sells 2. Left: $12 - 2 = 10$.\n4. Orange house: Sells half of 10 (5). Left: 5.\nThe numbers match the problem description.\n\n#### 18", "pred": "18", "gold": "18", "correct": true, "n_new": 469, "stop": "stop", "seconds": 6.163822650909424} | |
| {"idx": 14, "text": "To find the percentage of the entire class enrolled in hip-hop dance, we can follow these steps:\n\n**Step 1: Find the number of students in contemporary dance.**\nThe total number of students is 20.\n20% of 20 = $0.20 \\times 20 = 4$ students.\n\n**Step 2: Find the remaining number of students.**\nRemaining students = Total students - Contemporary students\nRemaining students = $20 - 4 = 16$ students.\n\n**Step 3: Find the number of students in jazz dance.**\n25% of the remaining 16 students enrolled in jazz dance.\n25% of 16 = $0.25 \\times 16 = 4$ students.\n\n**Step 4: Find the number of students in hip-hop dance.**\nThe rest of the students enrolled in hip-hop.\nHip-hop students = Remaining students - Jazz students\nHip-hop students = $16 - 4 = 12$ students.\n\n**Step 5: Calculate the percentage of the entire class in hip-hop dance.**\nTo find the percentage, divide the number of hip-hop students by the total number of students and multiply by 100.\nPercentage = $(\\frac{12}{20}) \\times 100$\nPercentage = $0.6 \\times 100 = 60\\%$.\n\n#### 60", "pred": "60", "gold": "60", "correct": true, "n_new": 317, "stop": "stop", "seconds": 3.330814838409424} | |
| {"idx": 15, "text": "To find the maximum profit the merchant can make, we need to calculate the expected profit for both purchase plans and compare them.\n\n**Step 1: Calculate the profit for the jewelry plan.**\n- Initial value of jewelry: $5,000\n- Expected growth rate: 2.5%\n- Profit calculation: $5,000 \\times 0.025$\n- $5,000 \\times 0.02 = 100$\n- $5,000 \\times 0.005 = 25$\n- Total profit for jewelry: $100 + 25 = \\$125$\n\n**Step 2: Calculate the profit for the electronic gadgets plan.**\n- Initial value of electronics: $8,000\n- Expected growth rate: 1.2%\n- Profit calculation: $8,000 \\times 0.012$\n- $8,000 \\times 0.01 = 80$\n- $8,000 \\times 0.002 = 16$\n- Total profit for electronics: $80 + 16 = \\$96$\n\n**Step 3: Compare the profits to find the maximum.**\n- Jewelry profit: $125\n- Electronics profit: $96\n- The merchant wants to maximize profit, so he will choose the jewelry.\n\nThe maximum profit is $125.\n\n#### 125", "pred": "125", "gold": "125", "correct": true, "n_new": 329, "stop": "stop", "seconds": 3.977235794067383} | |
| {"idx": 16, "text": "To find the total distance covered by each train, we can break the problem down into steps:\n\n1. **Identify the distance traveled on the first day:**\n Both trains travel westward for 80 miles.\n Distance for Day 1 = 80 miles.\n\n2. **Identify the distance traveled on the second day:**\n Both trains travel northwards for 150 miles.\n Distance for Day 2 = 150 miles.\n\n3. **Calculate the total distance for each train:**\n Since both trains followed the same path and covered the same distances on both days, we add the distances from Day 1 and Day 2 together.\n Total Distance = Distance Day 1 + Distance Day 2\n Total Distance = 80 miles + 150 miles\n Total Distance = 230 miles.\n\nEach train covered a total of 230 miles over the two days.\n\n#### 230", "pred": "230", "gold": "230", "correct": true, "n_new": 209, "stop": "stop", "seconds": 2.359416961669922} | |
| {"idx": 17, "text": "To find Jill's annual salary, we can calculate her weekly earnings from each job and then multiply by the number of weeks worked per year.\n\n**Step 1: Calculate weekly earnings as a teacher.**\nJill works 35 hours a week as a teacher at a rate of $20 per hour.\n$35 \\text{ hours} \\times \\$20/\\text{hour} = \\$700$\n\n**Step 2: Calculate weekly earnings as a cheerleading coach.**\nJill works 15 hours a week as a coach at a rate of $30 per hour.\n$15 \\text{ hours} \\times \\$30/\\text{hour} = \\$450$\n\n**Step 3: Calculate total weekly earnings.**\nAdd her earnings from both jobs together.\n$\\$700 + \\$450 = \\$1,150$\n\n**Step 4: Calculate annual salary.**\nMultiply the total weekly earnings by the number of weeks she works per year (50 weeks).\n$\\$1,150 \\times 50 \\text{ weeks} = \\$57,500$\n\n#### 57500", "pred": "57500", "gold": "57500", "correct": true, "n_new": 254, "stop": "stop", "seconds": 2.8261337280273438} | |
| {"idx": 18, "text": "To find the number of dozens of eggs Claire will eat in 4 weeks, we can follow these steps:\n\n1. **Calculate the number of eggs eaten per day:**\n Claire eats 3 eggs every morning.\n Daily eggs = 3\n\n2. **Calculate the number of eggs eaten per week:**\n There are 7 days in a week.\n Eggs per week = $3 \\text{ eggs/day} \\times 7 \\text{ days/week} = 21 \\text{ eggs/week}$\n\n3. **Calculate the total number of eggs eaten in 4 weeks:**\n Total eggs = $21 \\text{ eggs/week} \\times 4 \\text{ weeks} = 84 \\text{ eggs}$\n\n4. **Convert the total number of eggs into dozens:**\n There are 12 eggs in one dozen.\n Dozens = $84 \\text{ eggs} \\div 12 \\text{ eggs/dozen}$\n $84 \\div 12 = 7$\n\nClaire will eat 7 dozens of eggs in 4 weeks.\n\n#### 7", "pred": "7", "gold": "7", "correct": true, "n_new": 250, "stop": "stop", "seconds": 2.594709634780884} | |
| {"idx": 19, "text": "To find the required speed for the remaining distance, we can follow these steps:\n\n**1. Determine the total distance and the target average speed:**\n* Total distance = 12 miles.\n* Target average speed = 4 miles per hour (mph).\n\n**2. Calculate the total time allowed to reach the target average speed:**\n* $\\text{Total Time} = \\frac{\\text{Total Distance}}{\\text{Average Speed}}$\n* $\\text{Total Time} = \\frac{12 \\text{ miles}}{4 \\text{ mph}} = 3 \\text{ hours}$.\n\n**3. Calculate the distance and time already covered:**\n* First leg: 4 miles in 1 hour.\n* Second leg: 2 miles in 1 hour.\n* Total distance covered = $4 + 2 = 6$ miles.\n* Total time spent = $1 + 1 = 2$ hours.\n\n**4. Calculate the remaining distance and remaining time:**\n* Remaining distance = $\\text{Total distance} - \\text{Distance covered}$\n* Remaining distance = $12 - 6 = 6$ miles.\n* Remaining time = $\\text{Total time allowed} - \\text{Time spent}$\n* Remaining time = $3 - 2 = 1$ hour.\n\n**5. Calculate the required speed for the remaining distance:**\n* $\\text{Required Speed} = \\frac{\\text{Remaining distance}}{\\text{Remaining time}}$\n* $\\text{Required Speed} = \\frac{6 \\text{ miles}}{1 \\text{ hour}} = 6 \\text{ mph}$.\n\n#### 6", "pred": "6", "gold": "6", "correct": true, "n_new": 365, "stop": "stop", "seconds": 3.8512990474700928} | |
| {"idx": 20, "text": "To solve the problem, we will calculate the amount of water in each drink step by step.\n\n**Step 1: Analyze the orange drink.**\n* Initial volume of orange drink = 10 liters.\n* Fraction of water in the orange drink = $\\frac{2}{3}$.\n* Amount of water in the initial 10 liters = $10 \\times \\frac{2}{3} = \\frac{20}{3}$ liters.\n\n**Step 2: Account for the spill.**\n* One liter of the orange drink is spilled. Since the mixture is uniform, the spilled liter contains the same proportion of water as the rest of the drink ($\\frac{2}{3}$).\n* Volume of orange drink remaining = $10 - 1 = 9$ liters.\n* Amount of water in the remaining 9 liters of orange drink = $9 \\times \\frac{2}{3} = 6$ liters.\n\n**Step 3: Analyze the pineapple drink.**\n* Volume of pineapple drink = 15 liters.\n* Fraction of water in the pineapple drink = $\\frac{3}{5}$.\n* Amount of water in the pineapple drink = $15 \\times \\frac{3}{5} = 9$ liters.\n\n**Step 4: Calculate the total volume and total water.**\n* Remaining orange drink volume = 9 liters.\n* Pineapple drink volume = 15 liters.\n* Total volume = $9 + 15 = 24$ liters (this matches the total mentioned in the problem).\n* Total water = Water in orange drink + Water in pineapple drink.\n* Total water = $6 \\text{ liters} + 9 \\text{ liters} = 15$ liters.\n\n#### 15", "pred": "15", "gold": "15", "correct": true, "n_new": 392, "stop": "stop", "seconds": 4.8762288093566895} | |
| {"idx": 21, "text": "To find out how many years ago Raymond's son was born, we need to determine Raymond's current age and then subtract the age he was when his son was born.\n\n1. **Find Raymond's current age:**\n Samantha is currently 31 years old. Raymond was born 6 years before Samantha, which means he is 6 years older than her.\n $31 + 6 = 37$\n Raymond is currently 37 years old.\n\n2. **Find the age of Raymond's son:**\n Raymond had his son when he was 23 years old. To find out how many years ago that was, we subtract his age at the time of the birth from his current age.\n $37 - 23 = 14$\n\nAlternatively, we can calculate it this way:\nSamantha's age is 31.\nRaymond's age is 31 + 6 = 37.\nRaymond's son was born when Raymond was 23.\nThe years elapsed since the son's birth is $37 - 23 = 14$.\n\n#### 14", "pred": "14", "gold": "14", "correct": true, "n_new": 251, "stop": "stop", "seconds": 3.419123411178589} | |
| {"idx": 22, "text": "To find the total number of DVDs Billy sold, we can break the problem down step by step based on the groups of customers:\n\n1. **First group of customers:**\n There are 3 customers who each buy 1 DVD.\n Calculation: $3 \\times 1 = 3$ DVDs.\n\n2. **Second group of customers:**\n There are 2 customers who each buy 2 DVDs.\n Calculation: $2 \\times 2 = 4$ DVDs.\n\n3. **Third group of customers:**\n There are 3 customers who buy 0 DVDs.\n Calculation: $3 \\times 0 = 0$ DVDs.\n\n4. **Total DVDs sold:**\n Add the DVDs from all groups together.\n Calculation: $3 + 4 + 0 = 7$ DVDs.\n\n(Verification of customer count: $3 + 2 + 3 = 8$ customers, which matches the problem description.)\n\n#### 7", "pred": "7", "gold": "7", "correct": true, "n_new": 214, "stop": "stop", "seconds": 2.5179924964904785} | |
| {"idx": 23, "text": "To find out how many centimeters shorter the candle will be, we can follow these steps:\n\n1. **Determine the total time elapsed:**\n The candle burns from 1:00 PM to 5:00 PM.\n $5 - 1 = 4$ hours.\n\n2. **Identify the rate of melting:**\n The candle melts at a rate of 2 centimeters per hour.\n\n3. **Calculate the total reduction in length:**\n Multiply the total time by the melting rate:\n $4 \\text{ hours} \\times 2 \\text{ cm/hour} = 8 \\text{ cm}$.\n\nThe candle will be 8 centimeters shorter.\n\n#### 8", "pred": "8", "gold": "8", "correct": true, "n_new": 154, "stop": "stop", "seconds": 1.7122976779937744} | |
| {"idx": 24, "text": "To find the original price of the book, we can follow these steps:\n\n1. **Identify the known information:**\n * Sale Price = $19.50\n * Discount Percentage = 25%\n\n2. **Understand the relationship between the prices:**\n * If the discount is 25%, then Kyle paid 75% of the original price (since 100% - 25% = 75%).\n\n3. **Set up the equation:**\n Let $x$ be the original price of the book.\n The equation is: $0.75 \\times x = 19.50$\n\n4. **Solve for $x$:**\n To find $x$, divide the sale price by the percentage paid (expressed as a decimal):\n $x = 19.50 / 0.75$\n\n5. **Perform the calculation:**\n $19.50 \\div 0.75$\n $1950 \\div 75$\n $75 \\times 2 = 150$\n $195 - 150 = 45$\n Bring down the 0 to make 450.\n $75 \\times 6 = 450$\n So, $x = 26$\n\n6. **Verify the answer:**\n 25% of $26.00 is $6.50.\n $26.00 - $6.50 = $19.50.\n The calculation is correct.\n\n#### 26.00", "pred": "26", "gold": "26", "correct": true, "n_new": 372, "stop": "stop", "seconds": 4.449349641799927} | |
| {"idx": 25, "text": "To find out how many boxes of pizza Marie ordered, we need to calculate the total cost of the items we know and subtract that from the total amount paid.\n\n**Step 1: Calculate the cost of the chicken meal.**\nCost = $12.00\n\n**Step 2: Calculate the cost of the milk.**\nMarie bought 5 packs of milk at $3 each.\n$5 \\times 3 = \\$15.00$\n\n**Step 3: Calculate the cost of the apples.**\nMarie bought 4 apples at $1.50 each.\n$4 \\times 1.50 = \\$6.00$\n\n**Step 4: Calculate the subtotal of the items identified so far.**\nSubtotal = Cost of chicken + Cost of milk + Cost of apples\nSubtotal = $\\$12.00 + \\$15.00 + \\$6.00 = \\$33.00$\n\n**Step 5: Calculate the total amount spent on pizza.**\nMarie paid a total of $50. We subtract the subtotal from the total.\nPizza Total = Total Paid - Subtotal\nPizza Total = $\\$50.00 - \\$33.00 = \\$17.00$\n\n**Step 6: Calculate the number of pizza boxes.**\nEach box of pizza costs $8.50. We divide the pizza total by the cost per box.\nNumber of boxes = $\\$17.00 \\div \\$8.50$\n$17 \\div 8.5 = 2$\n\nMarie ordered 2 boxes of pizza.\n\n#### 2", "pred": "2", "gold": "2", "correct": true, "n_new": 353, "stop": "stop", "seconds": 4.257699966430664} | |
| {"idx": 26, "text": "To find the total amount Mishka spent, we need to calculate the cost of each type of clothing item and then sum them up.\n\n**Step 1: Calculate the cost of the shorts.**\nMishka bought 3 pairs of shorts, and each pair costs $16.50.\n$3 \\times \\$16.50 = \\$49.50$\n\n**Step 2: Calculate the cost of the pants.**\nMishka bought 3 pairs of pants, and each pair costs $22.50.\n$3 \\times \\$22.50 = \\$67.50$\n\n**Step 3: Calculate the cost of the shoes.**\nMishka bought 3 pairs of shoes, and each pair costs $42.00.\n$3 \\times \\$42.00 = \\$126.00$\n\n**Step 4: Calculate the total cost.**\nAdd the costs of the shorts, pants, and shoes together:\n$\\$49.50 + \\$67.50 + \\$126.00$\n\nFirst, add the shorts and pants:\n$\\$49.50 + \\$67.50 = \\$117.00$\n\nThen, add the shoes to that sum:\n$\\$117.00 + \\$126.00 = \\$243.00$\n\nMishka spent a total of $243 on all the clothing items.\n\n#### 243", "pred": "243", "gold": "243", "correct": true, "n_new": 330, "stop": "stop", "seconds": 3.627285957336426} | |
| {"idx": 27, "text": "To find the total amount Cynthia spends on ice cream after 60 days, we can follow these steps:\n\n1. **Determine the total number of servings needed:**\n Cynthia eats 1 serving every night. Over 60 days, she needs:\n $60 \\text{ days} \\times 1 \\text{ serving/day} = 60 \\text{ servings}$.\n\n2. **Determine how many cartons she needs to buy:**\n Each carton contains 15 servings. To find the number of cartons, divide the total servings by the servings per carton:\n $60 \\text{ servings} \\div 15 \\text{ servings/carton} = 4 \\text{ cartons}$.\n\n3. **Calculate the total cost:**\n Each carton costs $4.00. Multiply the number of cartons by the price per carton:\n $4 \\text{ cartons} \\times \\$4.00/\\text{carton} = \\$16.00$.\n\n#### 16", "pred": "16", "gold": "16", "correct": true, "n_new": 225, "stop": "stop", "seconds": 2.458240032196045} | |
| {"idx": 28, "text": "To find the number of miles Henry traveled between his first and second stops, we can follow these steps:\n\n1. **Identify the total distance:** The total trip distance is 60 miles.\n2. **Determine the location of the first stop:** Henry made his first stop after 20 miles.\n3. **Determine the location of the second stop:** The second stop was 15 miles before the end of the trip. To find the distance from the start to this stop, subtract 15 from the total distance:\n $60 - 15 = 45$ miles.\n4. **Calculate the distance between the two stops:** Subtract the distance of the first stop from the distance of the second stop:\n $45 - 20 = 25$ miles.\n\nAlternatively, you can calculate it this way:\nThe distance remaining after the first stop is $60 - 20 = 40$ miles. \nSince the second stop is 15 miles from the end, the distance traveled between the first stop and the second stop is $40 - 15 = 25$ miles.\n\n#### 25", "pred": "25", "gold": "25", "correct": true, "n_new": 253, "stop": "stop", "seconds": 2.760258674621582} | |
| {"idx": 29, "text": "To find the cost of the boots, we need to determine the cost of the two pairs of high heels and then use the relationship provided in the problem.\n\n**Step 1: Find the cost of the first pair of high heels.**\nThe problem states that one pair of heels costs $33.\n\n**Step 2: Find the cost of the second pair of high heels.**\nThe problem states that the other pair costs twice as much as the first pair.\n$33 \\times 2 = 66$\nSo, the second pair costs $66.\n\n**Step 3: Find the total cost of both pairs of high heels.**\nAdd the costs of the two pairs together:\n$33 + 66 = 99$\nThe total cost for the two pairs of heels is $99.\n\n**Step 4: Determine the cost of the boots.**\nThe problem states that the two pairs of high heels together cost five dollars less than the boots. This means the boots cost five dollars more than the total cost of the heels.\n$99 + 5 = 104$\n\nThus, the boots cost $104.\n\n#### 104", "pred": "104", "gold": "104", "correct": true, "n_new": 255, "stop": "stop", "seconds": 3.0017333030700684} | |
| {"idx": 30, "text": "To find Allen's age 10 years from now, we can follow these steps:\n\n**Step 1: Determine the total parts in the ratio.**\nThe ratio of Darrell's age to Allen's age is 7:11.\nTotal parts = $7 + 11 = 18$.\n\n**Step 2: Calculate the value of one part.**\nThe total sum of their ages is 162. To find the value of one \"part,\" we divide the total age by the total number of parts:\nValue of one part = $162 \\div 18$.\n$162 \\div 18 = 9$.\n\n**Step 3: Calculate Allen's current age.**\nSince Allen's portion of the ratio is 11, we multiply the value of one part by 11:\nAllen's current age = $11 \\times 9 = 99$.\n\n**Step 4: Calculate Allen's age 10 years from now.**\nAdd 10 years to Allen's current age:\nAllen's age in 10 years = $99 + 10 = 109$.\n\n(Verification: Darrell's current age is $7 \\times 9 = 63$. Sum: $63 + 99 = 162$. Correct.)\n\n#### 109", "pred": "109", "gold": "109", "correct": true, "n_new": 303, "stop": "stop", "seconds": 3.351494312286377} | |
| {"idx": 31, "text": "To find the average guess, we need to determine the value of each friend's guess and then calculate the mean.\n\n**Step 1: Identify the first guess.**\nThe first friend says there are 80 jelly beans.\n* Guess 1 = 80\n\n**Step 2: Calculate the second guess.**\nThe second friend says there are \"20 more than half the first one.\"\n* Half of the first guess = 80 / 2 = 40\n* 20 more than that = 40 + 20 = 60\n* Guess 2 = 60\n\n**Step 3: Calculate the third guess.**\nThe third friend says there are \"25% more than the first one.\"\n* 25% of the first guess = 0.25 * 80 = 20\n* The first guess plus 25% = 80 + 20 = 100\n* Guess 3 = 100\n\n**Step 4: Calculate the total of all guesses.**\n* Total = 80 + 60 + 100 = 240\n\n**Step 5: Calculate the average.**\nThere are 3 friends making guesses.\n* Average = Total / Number of guesses\n* Average = 240 / 3 = 80\n\n#### 80", "pred": "80", "gold": "80", "correct": true, "n_new": 308, "stop": "stop", "seconds": 3.6836180686950684} | |
| {"idx": 32, "text": "To find the total number of hours John spends taking care of dogs each week, follow these steps:\n\n1. **Calculate the total time spent per day:**\n John has 10 dogs, and each dog requires 0.5 hours of care per day.\n $10 \\text{ dogs} \\times 0.5 \\text{ hours/dog} = 5 \\text{ hours per day}$\n\n2. **Calculate the total time spent per week:**\n There are 7 days in a week. Multiply the daily hours by the number of days in a week.\n $5 \\text{ hours/day} \\times 7 \\text{ days/week} = 35 \\text{ hours per week}$\n\n#### 35", "pred": "35", "gold": "35", "correct": true, "n_new": 165, "stop": "stop", "seconds": 1.8778290748596191} | |
| {"idx": 33, "text": "To find out how many gold coins Gretchen has, we can follow these steps:\n\n1. **Define the variables:**\n Let $G$ be the number of gold coins.\n Let $S$ be the number of silver coins.\n\n2. **Set up the equations based on the problem description:**\n * The total number of coins is 110:\n $G + S = 110$\n * There are 30 more gold coins than silver coins:\n $G = S + 30$\n\n3. **Substitute the second equation into the first:**\n Replace $G$ in the first equation with $(S + 30)$:\n $(S + 30) + S = 110$\n\n4. **Solve for $S$ (silver coins):**\n Combine like terms:\n $2S + 30 = 110$\n Subtract 30 from both sides:\n $2S = 80$\n Divide by 2:\n $S = 40$\n\n5. **Solve for $G$ (gold coins):**\n Use the relationship $G = S + 30$:\n $G = 40 + 30$\n $G = 70$\n\n6. **Verification:**\n Total coins: $70 + 40 = 110$ (Correct)\n Difference: $70 - 40 = 30$ (Correct)\n\nGretchen has 70 gold coins.\n\n#### 70", "pred": "70", "gold": "70", "correct": true, "n_new": 355, "stop": "stop", "seconds": 3.472564935684204} | |
| {"idx": 34, "text": "To find out how many jewels Siobhan has, we can solve the problem step by step based on the information provided:\n\n1. **Find the number of jewels Raymond has:**\n Raymond has 40 jewels.\n\n2. **Find the number of jewels Aaron has:**\n The problem states that Aaron has 5 more jewels than half of Raymond's jewels.\n * Half of Raymond's jewels: $40 / 2 = 20$\n * Aaron's jewels: $20 + 5 = 25$\n\n3. **Find the number of jewels Siobhan has:**\n The problem states that Siobhan has 2 fewer jewels than Aaron.\n * Siobhan's jewels: $25 - 2 = 23$\n\n#### 23", "pred": "23", "gold": "23", "correct": true, "n_new": 182, "stop": "stop", "seconds": 1.9796233177185059} | |
| {"idx": 35, "text": "To find the total number of points Mike scored, we can follow these steps:\n\n1. **Find the points scored in the first 20 minutes:**\n Mike scored 4 points in the first 20 minutes.\n\n2. **Calculate the points scored in the second 20 minutes:**\n He scored 25% more points than he did in the first 20 minutes.\n First, find 25% of 4:\n $0.25 \\times 4 = 1$\n Now, add that to the initial 4 points:\n $4 + 1 = 5$ points.\n (Alternatively, $4 \\times 1.25 = 5$).\n\n3. **Calculate the total points:**\n Add the points from the first period to the points from the second period:\n $4 + 5 = 9$ points.\n\n#### 9", "pred": "9", "gold": "9", "correct": true, "n_new": 203, "stop": "stop", "seconds": 2.3492209911346436} | |
| {"idx": 36, "text": "To find out how much Terry spends on yogurt over 30 days, we can follow these steps:\n\n1. **Calculate the total number of yogurts Terry eats in 30 days:**\n Terry eats 2 yogurts a day.\n $2 \\text{ yogurts/day} \\times 30 \\text{ days} = 60 \\text{ yogurts}$\n\n2. **Determine the price per yogurt:**\n The store sells 4 yogurts for $5.00.\n $\\$5.00 \\div 4 \\text{ yogurts} = \\$1.25 \\text{ per yogurt}$\n\n3. **Calculate the total cost for 60 yogurts:**\n Multiply the total number of yogurts by the price per yogurt.\n $60 \\text{ yogurts} \\times \\$1.25 = \\$75.00$\n\n *Alternative calculation method:*\n Since Terry needs 60 yogurts and they are sold in packs of 4:\n $60 \\div 4 = 15 \\text{ packs}$\n $15 \\text{ packs} \\times \\$5.00 \\text{ per pack} = \\$75.00$\n\n#### 75.00", "pred": "75", "gold": "75", "correct": true, "n_new": 282, "stop": "stop", "seconds": 3.30517315864563} | |
| {"idx": 37, "text": "To find out how many lego sets John still has, let's follow the steps of the problem:\n\n1. **Calculate the total money John made from selling the lego sets:**\n John sold some lego sets for $15 each. We don't know how many he sold yet, but let's look at the spending.\n\n2. **Calculate the total amount John spent on video games:**\n He bought 8 video games for $20 each.\n $8 \\times \\$20 = \\$160$\n\n3. **Calculate the total amount of money John had before buying the games:**\n He spent $160 and had $5 left over.\n $\\$160 + \\$5 = \\$165$\n\n4. **Calculate how many lego sets he sold:**\n Since he got his money from selling lego sets at $15 each, we divide his total money by the price per set.\n $\\$165 \\div \\$15 = 11$\n John sold 11 lego sets.\n\n5. **Calculate how many lego sets he has left:**\n He started with 13 lego sets and sold 11 of them.\n $13 - 11 = 2$\n\nJohn has 2 lego sets left.\n\n#### 2", "pred": "2", "gold": "2", "correct": true, "n_new": 289, "stop": "stop", "seconds": 3.652055501937866} | |
| {"idx": 38, "text": "To find out how fast John runs, we need to determine his total running time and his total distance.\n\n**Step 1: Determine the running time for each day.**\n* Day 1: John runs for 3 hours.\n* Day 2: He runs half as much as Day 1.\n $3 \\text{ hours} \\div 2 = 1.5 \\text{ hours}$.\n* Day 3: He runs half as much as Day 1.\n $3 \\text{ hours} \\div 2 = 1.5 \\text{ hours}$.\n\n**Step 2: Calculate the total running time for the week.**\n* Total Time = $3 \\text{ hours (Day 1)} + 1.5 \\text{ hours (Day 2)} + 1.5 \\text{ hours (Day 3)}$\n* Total Time = $6 \\text{ hours}$.\n\n**Step 3: Identify the total distance.**\n* John runs 60 miles a week.\n\n**Step 4: Calculate his speed.**\n* Speed is calculated as Distance divided by Time.\n* $\\text{Speed} = \\frac{60 \\text{ miles}}{6 \\text{ hours}}$\n* $\\text{Speed} = 10 \\text{ miles per hour}$.\n\n#### 10", "pred": "10", "gold": "10", "correct": true, "n_new": 297, "stop": "stop", "seconds": 3.3790552616119385} | |
| {"idx": 39, "text": "To solve the problem, we need to determine Dana's speeds for running and walking, and then calculate the total distance based on the time spent on each activity.\n\n**Step 1: Determine the speeds.**\n- Let $S$ be the speed of skipping. We are given $S = 3$ miles per hour.\n- Dana's running speed ($R$) is twice as fast as her skipping speed (since skipping is half as fast as running).\n $R = 2 \\times S = 2 \\times 3 = 6$ miles per hour.\n- Dana's running speed is four times faster than her walking speed ($W$).\n $R = 4 \\times W \\Rightarrow 6 = 4 \\times W$.\n $W = \\frac{6}{4} = 1.5$ miles per hour.\n\n**Step 2: Determine the time spent on each activity.**\n- Total time = 6 hours.\n- Time spent running = $\\frac{1}{3}$ of 6 hours = $\\frac{1}{3} \\times 6 = 2$ hours.\n- Time spent walking = $\\frac{2}{3}$ of 6 hours = $\\frac{2}{3} \\times 6 = 4$ hours.\n\n**Step 3: Calculate the distance traveled.**\n- Distance while running = $\\text{speed} \\times \\text{time} = 6 \\text{ mph} \\times 2 \\text{ hours} = 12$ miles.\n- Distance while walking = $\\text{speed} \\times \\text{time} = 1.5 \\text{ mph} \\times 4 \\text{ hours} = 6$ miles.\n\n**Step 4: Calculate total distance.**\n- Total distance = $12 \\text{ miles} + 6 \\text{ miles} = 18$ miles.\n\n#### 18", "pred": "18", "gold": "18", "correct": true, "n_new": 415, "stop": "stop", "seconds": 5.063766241073608} | |
| {"idx": 40, "text": "To find the age of Brandon's iPhone, we can follow these steps:\n\n1. **Identify the age of Suzy's iPhone:**\n The problem states that Suzy's iPhone is 1 year old.\n\n2. **Calculate the age of Ben's iPhone:**\n The problem states that Ben's iPhone is two times older than Suzy's iPhone.\n Age of Ben's iPhone = 2 $\\times$ Age of Suzy's iPhone\n Age of Ben's iPhone = 2 $\\times$ 1 = 2 years old.\n\n3. **Calculate the age of Brandon's iPhone:**\n The problem states that Brandon's iPhone is four times as old as Ben's iPhone.\n Age of Brandon's iPhone = 4 $\\times$ Age of Ben's iPhone\n Age of Brandon's iPhone = 4 $\\times$ 2 = 8 years old.\n\n#### 8", "pred": "8", "gold": "8", "correct": true, "n_new": 204, "stop": "stop", "seconds": 2.4011998176574707} | |
| {"idx": 41, "text": "To solve this problem, we need to determine the distance Polly can throw the javelin while holding the sapphire gemstone and then calculate the distance she can stand outside the dragon's reach.\n\n1. **Determine Polly's base throwing distance:**\n Without the gemstone, Polly can throw the gold javelin for a distance of 400 feet.\n\n2. **Determine Polly's throwing distance with the gemstone:**\n The problem states that holding the sapphire gemstone allows her to throw the javelin three times farther than when not holding it.\n Distance with gemstone = $400 \\text{ feet} \\times 3 = 1200 \\text{ feet}$.\n\n3. **Identify the dragon's reach:**\n The dragon, Perg, breathes fire upon anything within a distance of 1000 feet.\n\n4. **Calculate the distance outside the reach:**\n To hit the dragon while remaining outside the reach of the flames, Polly needs to be at a distance greater than 1000 feet from the dragon. However, her maximum throwing range is 1200 feet.\n The \"reach\" of the dragon ends at 1000 feet. Polly can stand at any point between 1000 feet and 1200 feet from the dragon to be safe while still being able to hit the dragon.\n\n5. **Determine the specific distance requested:**\n The question asks \"how far outside of the reach of the dragon's flames could Polly stand and still hit the dragon\". This refers to the maximum distance she can be from the dragon while still being able to throw the javelin to hit it.\n Max throwing distance = 1200 feet.\n Dragon's reach = 1000 feet.\n Distance outside the reach = $1200 \\text{ feet} - 1000 \\text{ feet} = 200 \\text{ feet}$.\n\n#### 200", "pred": "200", "gold": "200", "correct": true, "n_new": 426, "stop": "stop", "seconds": 6.697426080703735} | |
| {"idx": 42, "text": "To find out how many pieces of pie were taken by the guests, we can follow these steps:\n\n1. **Calculate the total number of pieces of pie baked:**\n Grandma Jones baked 5 pies, and each pie was cut into 8 pieces.\n Total pieces = Number of pies \u00d7 Pieces per pie\n Total pieces = $5 \\times 8 = 40$\n\n2. **Identify how many pieces were left over:**\n At the end of the evening, there were 14 pieces remaining.\n\n3. **Calculate the number of pieces taken by the guests:**\n To find the number of pieces eaten, subtract the remaining pieces from the total number of pieces.\n Pieces taken = Total pieces - Remaining pieces\n Pieces taken = $40 - 14 = 26$\n\n#### 26", "pred": "26", "gold": "26", "correct": true, "n_new": 182, "stop": "stop", "seconds": 2.037799596786499} | |
| {"idx": 43, "text": "To find the amount of grams you can eat, follow these steps:\n\n1. **Determine the remaining calorie allowance:**\n Your daily target is 2000 calories, and you have already consumed 1800 calories.\n $2000 - 1800 = 200$ calories remaining.\n\n2. **Determine the calories per gram of chips:**\n The bag weighs 300g and contains 5 servings.\n Weight per serving = $300\\text{g} / 5 = 60\\text{g}$ per serving.\n Since one serving is 250 calories, the calories per gram is:\n $250\\text{ calories} / 60\\text{g} \\approx 4.1667\\text{ calories per gram}$.\n\n3. **Calculate how many grams you can eat with the remaining calories:**\n Divide the remaining calories by the calories per gram:\n $200\\text{ calories} / (250\\text{ calories} / 60\\text{g})$\n This is equivalent to:\n $200 \\times (60 / 250)$\n $200 \\times 0.24 = 48\\text{g}$.\n\nAlternatively, by calculating the number of servings first:\nRemaining calories / calories per serving = $200 / 250 = 0.8$ servings.\nGrams per serving $\\times$ number of servings = $60\\text{g} \\times 0.8 = 48\\text{g}$.\n\n#### 48", "pred": "48", "gold": "48", "correct": true, "n_new": 367, "stop": "stop", "seconds": 4.102771520614624} | |
| {"idx": 44, "text": "To find Charlie's net profit, we need to calculate his total revenue and subtract his total costs.\n\n**Step 1: Determine the amount of beeswax needed.**\nCharlie wants to make and sell 20 candles.\nHe can make 10 candles per pound of beeswax.\n$\\text{Beeswax needed} = \\frac{20 \\text{ candles}}{10 \\text{ candles per pound}} = 2 \\text{ pounds of beeswax}$.\n\n**Step 2: Calculate the total cost of supplies.**\nThe cost of supplies (beeswax and wicks) is $10.00 for every 1 pound of beeswax.\nSince he needs 2 pounds:\n$\\text{Total cost} = 2 \\text{ pounds} \\times \\$10.00/\\text{pound} = \\$20.00$.\n\n**Step 3: Calculate the total revenue.**\nCharlie sells each candle for $2.00.\nHe sells 20 candles.\n$\\text{Total revenue} = 20 \\text{ candles} \\times \\$2.00/\\text{candle} = \\$40.00$.\n\n**Step 4: Calculate the net profit.**\nNet profit is Total Revenue minus Total Cost.\n$\\text{Net profit} = \\$40.00 - \\$20.00 = \\$20.00$.\n\n#### 20", "pred": "20", "gold": "20", "correct": true, "n_new": 305, "stop": "stop", "seconds": 3.590946912765503} | |
| {"idx": 45, "text": "To calculate the total number of hours Meredith spent writing articles, we will find the number of articles written each day and then multiply the total by the time spent per article.\n\n**Step 1: Calculate the number of articles written on Monday.**\nMeredith wrote 5 articles on Monday.\n\n**Step 2: Calculate the number of articles written on Tuesday.**\nShe wrote $2/5$ times *more* articles on Tuesday than on Monday.\nFirst, calculate $2/5$ of Monday's articles:\n$5 \\times \\frac{2}{5} = 2$\nThen, add this to Monday's total to find Tuesday's count:\n$5 + 2 = 7$ articles.\n\n**Step 3: Calculate the number of articles written on Wednesday.**\nShe wrote twice the number of articles she wrote on Tuesday:\n$7 \\times 2 = 14$ articles.\n\n**Step 4: Calculate the total number of articles written over the three days.**\nTotal articles = Monday + Tuesday + Wednesday\nTotal articles = $5 + 7 + 14 = 26$ articles.\n\n**Step 5: Calculate the total number of hours spent.**\nEach article takes an average of 4 hours to research and write.\nTotal hours = $26 \\text{ articles} \\times 4 \\text{ hours/article}$\nTotal hours = $104$ hours.\n\n#### 104", "pred": "104", "gold": "104", "correct": true, "n_new": 312, "stop": "stop", "seconds": 3.759032726287842} | |
| {"idx": 46, "text": "To find the number of Post-it notes in the package Candice purchased, we can follow these steps:\n\n1. **Identify the starting amount:**\n Candice started with 80 Post-it notes in her purse.\n\n2. **Identify the amount used:**\n She placed a single Post-it note on each of 220 cups of coffee. Therefore, she used 220 Post-it notes.\n\n3. **Identify the final amount:**\n After using the notes, she had 23 Post-it notes remaining.\n\n4. **Calculate the total number of Post-it notes she had in total:**\n To find the total number of notes she had (initial amount + purchased package), we add the amount used to the amount remaining:\n $220 \\text{ (used)} + 23 \\text{ (remaining)} = 243 \\text{ total notes}$\n\n5. **Calculate the number of notes in the package:**\n We know she started with 80 and ended up with a total of 243. The difference between the total amount and the starting amount is the number of notes in the package:\n $243 \\text{ (total)} - 80 \\text{ (initial)} = 163$\n\n**Verification:**\nStarted with 80.\nAdded 163 from the package: $80 + 163 = 243$.\nUsed 220 at work: $243 - 220 = 23$.\nThe remaining amount matches the problem description.\n\n#### 163", "pred": "163", "gold": "163", "correct": true, "n_new": 358, "stop": "stop", "seconds": 5.012131690979004} | |
| {"idx": 47, "text": "To solve the problem, we will break it down into steps:\n\n**Step 1: Determine the number of blue ties John bought.**\nJohn spent $200 on blue ties, and each blue tie cost $40.\nNumber of blue ties = $200 / $40 = 5.\n\n**Step 2: Determine the number of red ties John bought.**\nJohn buys twice as many red ties as blue ties.\nNumber of red ties = 5 * 2 = 10.\n\n**Step 3: Determine the cost of one red tie.**\nThe red ties cost 50% more than the blue ties. The cost of a blue tie is $40.\nCost of a red tie = $40 + (50% of $40)\nCost of a red tie = $40 + $20 = $60.\n\n**Step 4: Calculate the total amount spent on red ties.**\nJohn bought 10 red ties at $60 each.\nTotal spent on red ties = 10 * $60 = $600.\n\n**Step 5: Calculate the total amount spent on all ties.**\nJohn spent $200 on blue ties and $600 on red ties.\nTotal spent = $200 + $600 = $800.\n\n#### 800", "pred": "800", "gold": "800", "correct": true, "n_new": 297, "stop": "stop", "seconds": 3.2046890258789062} | |
| {"idx": 48, "text": "To find the number of pieces Tracy obtained, follow these steps:\n\n1. **Identify the total length of the wire in feet:**\n The wire is 4 feet long.\n\n2. **Identify the length of each piece in inches:**\n Each piece is 6 inches long.\n\n3. **Convert the total length of the wire into inches:**\n Since there are 12 inches in 1 foot:\n 4 feet \u00d7 12 inches/foot = 48 inches.\n\n4. **Calculate the number of pieces:**\n Divide the total length in inches by the length of each piece in inches:\n 48 inches \u00f7 6 inches/piece = 8 pieces.\n\nTracy obtained 8 pieces of wire.\n\n#### 8", "pred": "8", "gold": "8", "correct": true, "n_new": 166, "stop": "stop", "seconds": 1.8725218772888184} | |
| {"idx": 49, "text": "To find the total number of unoccupied units in the building, follow these steps:\n\n1. **Calculate the total number of units in the building:**\n The building has 15 floors, and each floor has 8 units.\n Total units = $15 \\times 8 = 120$.\n\n2. **Determine the fraction of unoccupied units:**\n The problem states that 3/4 of the building is occupied. Therefore, the fraction of unoccupied units is:\n $1 - 3/4 = 1/4$.\n\n3. **Calculate the number of unoccupied units:**\n Multiply the total number of units by the fraction that is unoccupied:\n Unoccupied units = $120 \\times \\frac{1}{4}$.\n Unoccupied units = $120 \\div 4 = 30$.\n\n#### 30", "pred": "30", "gold": "30", "correct": true, "n_new": 190, "stop": "stop", "seconds": 1.978787899017334} | |
| {"idx": 50, "text": "To find out how much Lloyd makes on eggs per week, we can follow these steps:\n\n1. **Calculate the number of eggs produced per week:**\n Lloyd produces 252 eggs per day. Since there are 7 days in a week:\n $252 \\text{ eggs/day} \\times 7 \\text{ days/week} = 1,764 \\text{ eggs/week}$\n\n2. **Calculate the number of dozens produced per week:**\n There are 12 eggs in a dozen.\n $1,764 \\text{ eggs} \\div 12 \\text{ eggs/dozen} = 147 \\text{ dozens}$\n\n3. **Calculate the total weekly income:**\n Lloyd sells each dozen for $2.\n $147 \\text{ dozens} \\times \\$2/\\text{dozen} = \\$294$\n\nAlternatively, you can calculate the daily income first:\n1. **Daily dozens:** $252 \\div 12 = 21 \\text{ dozens per day}$\n2. **Daily income:** $21 \\times \\$2 = \\$42 \\text{ per day}$\n3. **Weekly income:** $\\$42 \\times 7 = \\$294$\n\n#### 294", "pred": "294", "gold": "294", "correct": true, "n_new": 289, "stop": "stop", "seconds": 2.9921014308929443} | |
| {"idx": 51, "text": "To find out how long it takes Tom to get back, we need to determine the distance he traveled during the first leg of his trip.\n\n**Step 1: Determine the duration of the first trip.**\nTom sails from 1 PM to 4 PM.\nDuration = 4 PM - 1 PM = 3 hours.\n\n**Step 2: Determine the distance traveled.**\nTom travels at a speed of 10 miles per hour (mph) for 3 hours.\nDistance = Speed \u00d7 Time\nDistance = 10 mph \u00d7 3 hours = 30 miles.\n\n**Step 3: Determine the time taken to return.**\nTom travels back the same distance (30 miles) at a rate of 6 mph.\nTime = Distance \u00f7 Speed\nTime = 30 miles \u00f7 6 mph = 5 hours.\n\n#### 5", "pred": "5", "gold": "5", "correct": true, "n_new": 184, "stop": "stop", "seconds": 2.187507390975952} | |
| {"idx": 52, "text": "To find out how many toys Uriah needs to remove, we can follow these steps:\n\n1. **Calculate the total weight of the comic books being removed:**\n Uriah is removing 30 comic books. Each comic book weighs $\\frac{1}{4}$ pound.\n $\\text{Weight of comics} = 30 \\times \\frac{1}{4} = \\frac{30}{4} = 7.5 \\text{ pounds}$\n\n2. **Calculate the remaining weight that needs to be removed:**\n Uriah needs to remove a total of 15 pounds. Since he has already removed 7.5 pounds from the comics, we subtract that from the total.\n $\\text{Remaining weight} = 15 - 7.5 = 7.5 \\text{ pounds}$\n\n3. **Calculate the number of toys needed to make up the remaining weight:**\n Each toy weighs $\\frac{1}{2}$ pound. To find how many toys equal 7.5 pounds, we divide the remaining weight by the weight of one toy.\n $\\text{Number of toys} = 7.5 \\div \\frac{1}{2}$\n Dividing by a fraction is the same as multiplying by its reciprocal:\n $\\text{Number of toys} = 7.5 \\times 2 = 15$\n\nUriah needs to remove 15 toys.\n\n#### 15", "pred": "15", "gold": "15", "correct": true, "n_new": 313, "stop": "stop", "seconds": 3.6216280460357666} | |
| {"idx": 53, "text": "To find the difference in revenue between the two days, we need to calculate the total earnings for Thursday and Friday separately.\n\n**Step 1: Calculate the revenue for Thursday.**\nThe mechanic repaired 6 truck tires and 4 car tires.\n- Revenue from truck tires: $6 \\text{ tires} \\times \\$60/\\text{tire} = \\$360$\n- Revenue from car tires: $4 \\text{ tires} \\times \\$40/\\text{tire} = \\$160$\n- Total revenue for Thursday: $\\$360 + \\$160 = \\$520$\n\n**Step 2: Calculate the revenue for Friday.**\nThe mechanic repaired 12 car tires and 0 truck tires.\n- Revenue from car tires: $12 \\text{ tires} \\times \\$40/\\text{tire} = \\$480$\n- Revenue from truck tires: $0 \\text{ tires} \\times \\$60/\\text{tire} = \\$0$\n- Total revenue for Friday: $\\$480 + \\$0 = \\$480$\n\n**Step 3: Compare the revenues and find the difference.**\n- Thursday revenue: $520\n- Friday revenue: $480\nThe day with higher revenue is Thursday. To find how much more revenue was earned on Thursday than on Friday:\n- Difference: $\\$520 - \\$480 = \\$40$\n\n#### 40", "pred": "40", "gold": "40", "correct": true, "n_new": 317, "stop": "stop", "seconds": 3.729217767715454} | |
| {"idx": 54, "text": "To find the total number of kittens the Doubtfire family now has, we can follow these steps:\n\n1. **Identify the number of adopted kittens:**\n The sisters are driving home with 7 kittens adopted from the shelter.\n\n2. **Determine the number of kittens born to Patchy:**\n The mother states that Patchy had thrice (3 times) the number of adopted kittens.\n $7 \\times 3 = 21$ kittens.\n\n3. **Identify the number of kittens born to Trixie:**\n The mother states that Trixie had 12 kittens.\n\n4. **Calculate the total number of kittens:**\n Add the adopted kittens, Patchy's kittens, and Trixie's kittens together:\n $7 \\text{ (adopted)} + 21 \\text{ (Patchy's)} + 12 \\text{ (Trixie's)} = 40$ kittens.\n\n#### 40", "pred": "40", "gold": "40", "correct": true, "n_new": 213, "stop": "stop", "seconds": 2.6854865550994873} | |
| {"idx": 55, "text": "To solve the problem, we follow these steps:\n\n1. **Determine the starting number of lollipops:**\n Jean starts with 30 lollipops.\n\n2. **Calculate how many lollipops are left after eating some:**\n Jean eats 2 lollipops.\n $30 - 2 = 28$\n Jean has 28 lollipops remaining.\n\n3. **Calculate the number of bags that can be filled:**\n Jean wants to put 2 lollipops in each bag.\n To find the number of bags, divide the remaining lollipops by the number of lollipops per bag:\n $28 \\div 2 = 14$\n\nJean can fill 14 bags.\n\n#### 14", "pred": "14", "gold": "14", "correct": true, "n_new": 172, "stop": "stop", "seconds": 1.9242398738861084} | |
| {"idx": 56, "text": "To find out how many times Peter can go to the movies, we can follow these steps:\n\n1. **Calculate the cost of one movie outing:**\n Peter spends money on a ticket and popcorn each time he goes.\n Cost of ticket = $7\n Cost of popcorn = $7\n Total cost per outing = $7 + $7 = $14\n\n2. **Identify the total amount of money Peter has:**\n Total money = $42\n\n3. **Calculate the number of times he can go to the movies:**\n Divide the total amount of money by the cost per outing.\n Number of outings = Total money \u00f7 Cost per outing\n Number of outings = 42 \u00f7 14\n\n4. **Perform the division:**\n $14 \\times 1 = 14$\n $14 \\times 2 = 28$\n $14 \\times 3 = 42$\n So, $42 \\div 14 = 3$\n\nPeter can go to the movies 3 times.\n\n#### 3", "pred": "3", "gold": "3", "correct": true, "n_new": 240, "stop": "stop", "seconds": 2.7144947052001953} | |
| {"idx": 57, "text": "To find the maximum number of boxes the truck can carry without exceeding the bridge's weight limit, we follow these steps:\n\n1. **Identify the total weight limit:**\n The bridge can carry a maximum of 5000 pounds.\n\n2. **Determine the remaining weight capacity for the boxes:**\n We subtract the weight of the driver and the empty truck from the total weight limit.\n Weight of driver and empty truck = 3755 pounds.\n Weight capacity available for boxes = Total limit - Weight of truck/driver\n $5000 - 3755 = 1245$ pounds.\n\n3. **Calculate the maximum number of boxes:**\n Each box weighs 15 pounds. To find the number of boxes ($n$), we divide the available capacity by the weight per box.\n $n = 1245 / 15$\n\n4. **Perform the division:**\n $1245 \\div 15$:\n - $15 \\times 8 = 120$\n - $124 - 120 = 4$\n - Bring down the 5 to get 45.\n - $15 \\times 3 = 45$\n - $45 - 45 = 0$\n So, $1245 \\div 15 = 83$.\n\n5. **Verify the result:**\n Weight of 83 boxes = $83 \\times 15 = 1245$ pounds.\n Total weight = $3755 + 1245 = 5000$ pounds.\n Since 5000 is the maximum weight the bridge can carry, 83 is the maximum number of boxes.\n\n#### 83", "pred": "83", "gold": "83", "correct": true, "n_new": 405, "stop": "stop", "seconds": 4.649160146713257} | |
| {"idx": 58, "text": "To find the final price of Stephen's groceries, we need to calculate the total cost by adding all the fees and tips to the initial bill.\n\n**Step 1: Identify the initial bill.**\nThe initial bill for the groceries is $40.00.\n\n**Step 2: Calculate the 25% vendor fee.**\nThe vendor adds a 25% fee to the final total of the groceries.\n$40.00 \\times 0.25 = \\$10.00$\n\n**Step 3: Add the delivery fee.**\nThe delivery fee is $3.00.\n\n**Step 4: Add the tip.**\nStephen added a tip of $4.00.\n\n**Step 5: Calculate the final total.**\nWe sum the initial bill, the vendor fee, the delivery fee, and the tip:\n$40.00 (Bill) + $10.00 (Vendor Fee) + $3.00 (Delivery Fee) + $4.00 (Tip) = $57.00\n\n#### 57.00", "pred": "57", "gold": "57", "correct": true, "n_new": 241, "stop": "stop", "seconds": 2.695612907409668} | |
| {"idx": 59, "text": "To find the total number of raspberries, follow these steps:\n\n1. **Calculate the total number of fruit in the clusters:**\n There are 6 clusters, and each cluster contains 20 fruits.\n $6 \\times 20 = 120$ fruits.\n\n2. **Identify the number of individual fruits:**\n There are 67 individual fruits scattered across the bush.\n\n3. **Calculate the total count:**\n Add the fruit from the clusters to the individual fruits.\n $120 + 67 = 187$ fruits.\n\n#### 187", "pred": "187", "gold": "187", "correct": true, "n_new": 135, "stop": "stop", "seconds": 1.5045855045318604} | |
| {"idx": 60, "text": "To find the number of good oranges in the basket, we need to subtract the number of bad, unripe, and sour oranges from the total number of oranges.\n\n**Step 1: Identify the total number of oranges.**\nTotal oranges = 25\n\n**Step 2: Identify the number of bad oranges.**\nBad oranges = 1\n\n**Step 3: Calculate the number of unripe oranges.**\nThe problem states that 20% of the oranges are unripe.\nUnripe oranges = 20% of 25\nUnripe oranges = 0.20 \u00d7 25\nUnripe oranges = 5\n\n**Step 4: Identify the number of sour oranges.**\nSour oranges = 2\n\n**Step 5: Calculate the total number of oranges that are not \"good\".**\nTotal non-good oranges = Bad + Unripe + Sour\nTotal non-good oranges = 1 + 5 + 2\nTotal non-good oranges = 8\n\n**Step 6: Calculate the number of good oranges.**\nGood oranges = Total oranges - Total non-good oranges\nGood oranges = 25 - 8\nGood oranges = 17\n\n#### 17", "pred": "17", "gold": "17", "correct": true, "n_new": 256, "stop": "stop", "seconds": 2.8312759399414062} | |
| {"idx": 61, "text": "To find the total amount Janet paid, we will follow these steps:\n\n1. **Calculate the initial cost of materials and construction:**\n * Cost of materials: $500\n * Cost of jeweler construction: $800\n * Subtotal = $500 + $800 = $1,300\n\n2. **Calculate the cost of insurance:**\n * The insurance is 10% of the subtotal ($1,300).\n * Insurance cost = 0.10 \u00d7 $1,300 = $130\n\n3. **Calculate the total amount paid:**\n * Total = Subtotal + Insurance cost\n * Total = $1,300 + $130 = $1,430\n\n#### 1430", "pred": "1430", "gold": "1430", "correct": true, "n_new": 187, "stop": "stop", "seconds": 2.361452579498291} | |
| {"idx": 62, "text": "To find Marcy's annual pension if she quits after 30 years, we follow these steps:\n\n1. **Identify the final pension amount:**\n The base annual pension amount promised for 40 years of service is $50,000/year.\n\n2. **Identify the entitlement rule:**\n Starting after 20 years of service, she becomes entitled to 5% of the value of the pension per year for every year worked beyond that mark.\n\n3. **Calculate the number of qualifying years:**\n Marcy worked for 30 years total. The entitlement begins after 20 years.\n $30\\text{ years (total)} - 20\\text{ years (threshold)} = 10\\text{ years}$.\n\n4. **Calculate the percentage earned:**\n She earns 5% for each of those 10 years.\n $10\\text{ years} \\times 5\\%/\\text{year} = 50\\%$.\n\n5. **Determine the logic of the pension calculation:**\n The problem implies a proportional calculation based on the total 40-year commitment. Since she worked 30 out of 40 years, her base \"pro-rated\" pension for the time served is:\n $\\frac{30}{40} \\times \\$50,000 = \\$37,500$.\n\n6. **Apply the additional entitlement:**\n The 5% per year is an additional entitlement on top of the pension value. However, in standard pension logic for this specific word problem structure, the \"value of the pension\" refers to the final amount ($50,000). The 5% is an incentive for years worked past the 20-year mark.\n \n Actually, looking at the phrasing \"she becomes entitled to 5% of the value of the pension per year,\" it implies she receives a portion of the $50,000 based on her years worked, plus the bonus for the years over 20.\n \n Let's re-evaluate:\n - Proportion of years worked: $\\frac{30}{40} = 0.75$\n - Base amount based on years: $0.75 \\times \\$50,000 = \\$37,50", "pred": "3750", "gold": "25000", "correct": false, "n_new": 512, "stop": "length", "seconds": 7.5792107582092285} | |
| {"idx": 63, "text": "To find the total amount Aleena paid for the streaming service by the end of the year, we can break the calculation down into two halves of the year (6 months each).\n\n**Step 1: Calculate the cost for the first half of the year.**\nThe monthly charge is $140. For the first 6 months, she pays the initial amount.\nCost for the first 6 months = $140 \\times 6$\n$140 \\times 6 = 840$\n\n**Step 2: Calculate the discounted monthly charge for the second half of the year.**\nThe company charges 10% less on the second half of the year.\nDiscount amount = $140 \\times 0.10 = 14$\nDiscounted monthly charge = $140 - 14 = 126$\n\n**Step 3: Calculate the cost for the second half of the year.**\nFor the next 6 months, she pays the discounted rate.\nCost for the second 6 months = $126 \\times 6$\n$126 \\times 6 = 756$\n\n**Step 4: Calculate the total amount paid for the entire year.**\nTotal amount = (Cost of first 6 months) + (Cost of second 6 months)\nTotal amount = $840 + 756 = 1596$\n\n#### 1596", "pred": "1596", "gold": "1596", "correct": true, "n_new": 314, "stop": "stop", "seconds": 3.461108922958374} | |
| {"idx": 64, "text": "To find out how many miles Sophia can drive on a single tank of gas, we need to determine her car's fuel efficiency (miles per gallon) and then multiply that by the total capacity of her tank.\n\n**Step 1: Determine the car's fuel efficiency (miles per gallon).**\nSophia traveled 100 miles and used 4 gallons of gas to refill the tank.\nFuel Efficiency = Total Miles / Gallons Used\nFuel Efficiency = 100 miles / 4 gallons\nFuel Efficiency = 25 miles per gallon (mpg)\n\n**Step 2: Determine the total distance she can drive on a full tank.**\nThe owner's manual states that her tank holds 12 gallons of gas.\nTotal Distance = Fuel Efficiency \u00d7 Tank Capacity\nTotal Distance = 25 mpg \u00d7 12 gallons\nTotal Distance = 300 miles\n\nSophia can drive 300 miles on a single tank of gas.\n\n#### 300", "pred": "300", "gold": "300", "correct": true, "n_new": 208, "stop": "stop", "seconds": 2.5897693634033203} | |
| {"idx": 65, "text": "To find the total number of hours Jim spends on TV and reading in 4 weeks, we can follow these steps:\n\n1. **Determine the time spent reading in one session:**\n Jim watches TV for 2 hours. He reads for half as long as he watches TV.\n Reading time = $2 \\text{ hours} \\div 2 = 1 \\text{ hour}$.\n\n2. **Calculate the total time spent per session:**\n Total time per session = TV time + Reading time\n Total time per session = $2 \\text{ hours} + 1 \\text{ hour} = 3 \\text{ hours}$.\n\n3. **Calculate the total time spent per week:**\n Jim does this 3 times a week.\n Weekly time = $3 \\text{ hours/session} \\times 3 \\text{ sessions/week} = 9 \\text{ hours}$.\n\n4. **Calculate the total time spent in 4 weeks:**\n Total time = $9 \\text{ hours/week} \\times 4 \\text{ weeks} = 36 \\text{ hours}$.\n\n#### 36", "pred": "36", "gold": "36", "correct": true, "n_new": 248, "stop": "stop", "seconds": 2.820983648300171} | |
| {"idx": 66, "text": "To find the total number of people sent by the four schools, we can break the calculation down step by step:\n\n1. **Identify the number of schools:** There are 4 schools.\n2. **Identify the components per school:**\n * A girls' basketball team.\n * A boys' basketball team.\n * A coach for the girls' team.\n * A coach for the boys' team.\n3. **Calculate the number of players and coaches per school:**\n * Each team has 5 players. Since there are 2 teams (girls and boys), there are $5 + 5 = 10$ players per school.\n * Each team has 1 coach. Since there are 2 teams, there are $1 + 1 = 2$ coaches per school.\n4. **Calculate the total number of people per school:**\n * People per school = (Players) + (Coaches)\n * People per school = $10 + 2 = 12$ people.\n5. **Calculate the total number of people for all four schools:**\n * Total people = (Number of schools) \u00d7 (People per school)\n * Total people = $4 \\times 12 = 48$.\n\nAlternatively, you can calculate it by total categories:\n* Total girls' players: $4 \\text{ schools} \\times 5 \\text{ players} = 20$\n* Total boys' players: $4 \\text{ schools} \\times 5 \\text{ players} = 20$\n* Total girls' coaches: $4 \\text{ schools} \\times 1 \\text{ coach} = 4$\n* Total boys' coaches: $4 \\text{ schools} \\times 1 \\text{ coach} = 4$\n* Sum: $20 + 20 + 4 + 4 = 48$\n\n#### 48", "pred": "48", "gold": "48", "correct": true, "n_new": 439, "stop": "stop", "seconds": 4.760506868362427} | |
| {"idx": 67, "text": "To find the total number of gems in the chest, we need to calculate the number of each type of gem step by step.\n\n**Step 1: Find the number of diamonds.**\nThe problem states there are 175 diamonds.\nDiamonds = 175\n\n**Step 2: Find the number of rubies.**\nThe problem states there are 35 fewer rubies than diamonds.\nRubies = 175 - 35\nRubies = 140\n\n**Step 3: Find the number of emeralds.**\nThe problem states there are twice as many emeralds as rubies.\nEmeralds = 140 \u00d7 2\nEmeralds = 280\n\n**Step 4: Find the total number of gems.**\nTo find the total, add the number of diamonds, rubies, and emeralds together.\nTotal = Diamonds + Rubies + Emeralds\nTotal = 175 + 140 + 280\n\nCalculating the sum:\n175 + 140 = 315\n315 + 280 = 595\n\nThe treasure hunter found a total of 595 gems.\n\n#### 595", "pred": "595", "gold": "595", "correct": true, "n_new": 266, "stop": "stop", "seconds": 3.0557968616485596} | |
| {"idx": 68, "text": "To find the number of teachers at Dr. Wertz's school, we can follow these steps:\n\n1. **Find the number of boys:**\n We are told there are 60 girls and that there are twice as many boys as girls.\n Number of boys = $60 \\times 2 = 120$.\n\n2. **Find the total number of students:**\n The total number of students is the sum of the boys and the girls.\n Total students = $120 \\text{ (boys)} + 60 \\text{ (girls)} = 180$.\n\n3. **Find the number of teachers:**\n We are told there are 5 students for every teacher. To find the number of teachers, we divide the total number of students by 5.\n Number of teachers = $180 \\div 5$.\n\n Calculation:\n $180 \\div 5 = 36$\n\n#### 36", "pred": "36", "gold": "36", "correct": true, "n_new": 216, "stop": "stop", "seconds": 2.3976850509643555} | |
| {"idx": 69, "text": "To find out how much money Bailey started with, we can follow these steps:\n\n1. **Calculate the total amount of allowance received:**\n Bailey receives $5 each week for 8 weeks.\n $5 \\times 8 = \\$40$\n\n2. **Set up an equation to represent the situation:**\n Let $x$ be the amount of money Bailey started with.\n The total amount she has at the end is the starting amount plus the total allowance received.\n $x + 40 = 100$\n\n3. **Solve for $x$:**\n Subtract 40 from both sides of the equation to find the starting amount:\n $x = 100 - 40$\n $x = 60$\n\nBailey started with $60.\n\n#### 60", "pred": "60", "gold": "60", "correct": true, "n_new": 184, "stop": "stop", "seconds": 2.143321990966797} | |
| {"idx": 70, "text": "To find out how much money Judy makes in one week, we need to calculate the total number of classes taught, the total number of students, and then multiply by the price per student.\n\n**Step 1: Calculate the number of classes taught during the weekdays.**\nJudy teaches 5 classes every day for 5 weekdays (Monday through Friday).\n$5 \\text{ classes/day} \\times 5 \\text{ days} = 25 \\text{ classes}$\n\n**Step 2: Calculate the total number of classes in a week.**\nShe also teaches 8 classes on Saturday.\n$25 \\text{ weekday classes} + 8 \\text{ Saturday classes} = 33 \\text{ classes total}$\n\n**Step 3: Calculate the total number of students per week.**\nEach class has 15 students.\n$33 \\text{ classes} \\times 15 \\text{ students/class} = 495 \\text{ students}$\n\n**Step 4: Calculate the total money earned.**\nShe charges $15.00 per student.\n$495 \\text{ students} \\times \\$15.00/\\text{student} = \\$7,425.00$\n\n**Verification:**\nAlternative method:\nMoney per class = $15 \\text{ students} \\times \\$15 = \\$225$\nTotal money = $33 \\text{ classes} \\times \\$225 = \\$7,425$\n\n#### 7425", "pred": "7425", "gold": "7425", "correct": true, "n_new": 333, "stop": "stop", "seconds": 3.7378063201904297} | |
| {"idx": 71, "text": "To find the total number of instructions Kelian has to read, we can follow these steps:\n\n1. **Identify the number of instructions in the first recipe:**\n The problem states that the first recipe has 20 instructions.\n\n2. **Calculate the number of instructions in the second recipe:**\n The second recipe has twice as many instructions as the first one.\n $20 \\times 2 = 40$ instructions.\n\n3. **Calculate the total number of instructions for both dishes:**\n To find the total, add the instructions from the first recipe to the instructions from the second recipe.\n $20 + 40 = 60$ instructions.\n\nKelian has to read 60 instructions in total.\n\n#### 60", "pred": "60", "gold": "60", "correct": true, "n_new": 167, "stop": "stop", "seconds": 1.8736600875854492} | |
| {"idx": 72, "text": "To find the total amount of money Tommy raised, we need to calculate the revenue from each type of dessert and then add them together.\n\n**Step 1: Calculate the money from brownies.**\nTommy sold 43 brownies at $3 each.\n$43 \\times \\$3 = \\$129$\n\n**Step 2: Calculate the money from cheesecakes.**\nTommy sold 23 slices of cheesecake at $4 each.\n$23 \\times \\$4 = \\$92$\n\n**Step 3: Calculate the total money raised.**\nAdd the revenue from the brownies and the cheesecake together.\n$\\$129 + \\$92 = \\$221$\n\n#### 221", "pred": "221", "gold": "221", "correct": true, "n_new": 152, "stop": "stop", "seconds": 1.719409704208374} | |
| {"idx": 73, "text": "To find out how much Shiela will pay each month, we will follow these steps:\n\n**Step 1: Calculate the total principal amount.**\nShiela bought 5 cell phones at $150 each.\nTotal Principal = $5 \\times \\$150 = \\$750$\n\n**Step 2: Calculate the total interest charged.**\nA 2% interest is charged for each unit. Since there are 5 units, we can calculate the interest on the total principal.\nInterest Rate = $2\\% = 0.02$\nTotal Interest = $\\$750 \\times 0.02 = \\$15$\n\n**Step 3: Calculate the total amount to be paid.**\nThis is the sum of the principal and the interest.\nTotal Amount = $\\$750 + \\$15 = \\$765$\n\n**Step 4: Calculate the monthly installment.**\nShiela will pay this total amount over a period of 3 months.\nMonthly Payment = $\\$765 \\div 3 = \\$255$\n\n#### 255", "pred": "255", "gold": "255", "correct": true, "n_new": 234, "stop": "stop", "seconds": 2.8690896034240723} | |
| {"idx": 74, "text": "To find the total amount Artie will make, we need to follow these steps:\n\n**Step 1: Determine the rounded prices for each type of flower.**\nSince Artie is rounding all prices to the nearest dollar:\n* **Marigolds:** The original price is $2.74. Rounding to the nearest dollar gives **$3.00**.\n* **Petunias:** The original price is $1.87. Rounding to the nearest dollar gives **$2.00**.\n* **Begonias:** The original price is $2.12. Rounding to the nearest dollar gives **$2.00**.\n\n**Step 2: Calculate the revenue for each type of flower.**\n* **Marigolds:** Artie sells 12 pots at $3.00 each.\n $12 \\times 3 = 36$\n* **Petunias:** Artie sells 9 pots at $2.00 each.\n $9 \\times 2 = 18$\n* **Begonias:** Artie sells 17 pots at $2.00 each.\n $17 \\times 2 = 34$\n\n**Step 3: Calculate the total revenue.**\nSum the revenue from all three types of flowers:\n$36 + 18 + 34$\n\n* $36 + 18 = 54$\n* $54 + 34 = 88$\n\nArtie will make a total of $88.\n\n#### 88", "pred": "88", "gold": "88", "correct": true, "n_new": 349, "stop": "stop", "seconds": 4.059807538986206} | |
| {"idx": 75, "text": "To find the average square footage of a level in Luke's 4-leveled sandcastle, we need to determine the square footage of each level and then calculate their average.\n\n**Step 1: Identify the square footage of each level.**\nWe know there are 4 levels and the top level (Level 1) has a square footage of 16. Each level has half the square footage of the level below it. This means that as we move from the top down, each level is double the size of the level above it.\n\nLet $L_1$ be the top level, $L_2$ the second level, $L_3$ the third level, and $L_4$ the bottom level.\n* Level 1 (Top): $16$ sq ft\n* Level 2: Since Level 1 is half of Level 2, Level 2 is $16 \\times 2 = 32$ sq ft.\n* Level 3: Since Level 2 is half of Level 3, Level 3 is $32 \\times 2 = 64$ sq ft.\n* Level 4 (Bottom): Since Level 3 is half of Level 4, Level 4 is $64 \\times 2 = 128$ sq ft.\n\n**Step 2: Calculate the total square footage of all levels.**\nTotal = Level 1 + Level 2 + Level 3 + Level 4\nTotal = $16 + 32 + 64 + 128$\nTotal = $48 + 64 + 128$\nTotal = $112 + 128$\nTotal = $240$ sq ft.\n\n**Step 3: Calculate the average square footage.**\nThe average is the total square footage divided by the number of levels (4).\nAverage = $240 / 4$\nAverage = $60$\n\n#### 60", "pred": "60", "gold": "60", "correct": true, "n_new": 428, "stop": "stop", "seconds": 4.790872573852539} | |
| {"idx": 76, "text": "To find out how many bags of dog food Cecilia will use in the first year, we need to calculate the total number of cups of food consumed in 365 days and then divide that by the number of cups per bag.\n\n**Step 1: Calculate the food consumed during the first 180 days.**\nDuring the first 180 days, the puppy eats 1 cup of food every day.\n$180 \\text{ days} \\times 1 \\text{ cup/day} = 180 \\text{ cups}$\n\n**Step 2: Calculate the food consumed during the remaining days of the year.**\nA standard year has 365 days.\nNumber of remaining days = $365 - 180 = 185 \\text{ days}$\nDuring these 185 days, the puppy eats 2 cups of food every day.\n$185 \\text{ days} \\times 2 \\text{ cups/day} = 370 \\text{ cups}$\n\n**Step 3: Calculate the total amount of food consumed in the first year.**\nTotal cups = $180 \\text{ cups} + 370 \\text{ cups} = 550 \\text{ cups}$\n\n**Step 4: Calculate the number of bags needed.**\nEach bag contains 110 cups of food.\nNumber of bags = $\\frac{550 \\text{ cups}}{110 \\text{ cups/bag}}$\n$550 \\div 110 = 5$\n\nCecilia will use 5 bags of dog food in the first year.\n\n#### 5", "pred": "5", "gold": "5", "correct": true, "n_new": 361, "stop": "stop", "seconds": 3.8512516021728516} | |
| {"idx": 77, "text": "To solve the problem, we will follow these steps:\n\n1. **Identify Sarah's laundry amount:**\n Sarah does 400 pounds of laundry.\n\n2. **Calculate Raymond's laundry amount:**\n Raymond does half as much laundry as Sarah.\n Raymond = Sarah / 2\n Raymond = 400 / 2 = 200 pounds.\n\n3. **Calculate David's laundry amount:**\n Sarah does 4 times as much laundry as David. This means David does 1/4 as much laundry as Sarah.\n David = Sarah / 4\n David = 400 / 4 = 100 pounds.\n\n4. **Calculate the difference between Raymond's and David's laundry:**\n Difference = Raymond - David\n Difference = 200 - 100 = 100 pounds.\n\n#### 100", "pred": "100", "gold": "100", "correct": true, "n_new": 201, "stop": "stop", "seconds": 2.2347652912139893} | |
| {"idx": 78, "text": "To find out how much money Vincent saves, we need to calculate the cost of buying 18 flowers using both pricing options and then find the difference.\n\n**Step 1: Calculate the cost of buying 18 flowers in packages of 3.**\n- Each package contains 3 flowers and costs $2.50.\n- Number of packages needed: $18 \\div 3 = 6$ packages.\n- Total cost: $6 \\times \\$2.50 = \\$15.00$.\n\n**Step 2: Calculate the cost of buying 18 flowers in packages of 2.**\n- Each package contains 2 flowers and costs $1.00.\n- Number of packages needed: $18 \\div 2 = 9$ packages.\n- Total cost: $9 \\times \\$1.00 = \\$9.00$.\n\n**Step 3: Determine the better price and calculate the savings.**\n- The cost for packages of 3 is $15.00.\n- The cost for packages of 2 is $9.00.\n- The better price is $9.00.\n- Savings: $\\$15.00 - \\$9.00 = \\$6.00$.\n\nVincent saves $6.00 by choosing the better price.\n\n#### 6.00", "pred": "6", "gold": "6", "correct": true, "n_new": 293, "stop": "stop", "seconds": 3.300241231918335} | |
| {"idx": 79, "text": "To find the final cost of the grooming, follow these steps:\n\n1. **Identify the original price:** The original cost of the grooming is $100.\n2. **Calculate the discount amount:** The groomer offers a 30% discount. To find the amount of the discount, multiply the original price by the discount percentage:\n $100 \\times 0.30 = \\$30$\n3. **Subtract the discount from the original price:** To find the final cost, subtract the discount amount from the original price:\n $100 - 30 = \\$70$\n\n#### 70", "pred": "70", "gold": "70", "correct": true, "n_new": 140, "stop": "stop", "seconds": 1.671424150466919} | |
| {"idx": 80, "text": "To find out how many liters of water were left, we can follow these steps:\n\n1. **Calculate how much water each girl got:**\n Each girl received $\\frac{1}{6}$ of the 24 liters.\n $24 \\times \\frac{1}{6} = 4$ liters.\n\n2. **Calculate the total amount of water taken by the two girls:**\n Since there are two girls and each got 4 liters:\n $2 \\times 4 = 8$ liters.\n\n3. **Calculate the total amount of water taken by the girls and the boy:**\n The boy took 6 liters.\n Total taken = (Water taken by girls) + (Water taken by boy)\n Total taken = $8 + 6 = 14$ liters.\n\n4. **Calculate the remaining water:**\n Subtract the total amount taken from the initial amount.\n Remaining water = $24 - 14 = 10$ liters.\n\n#### 10", "pred": "10", "gold": "10", "correct": true, "n_new": 224, "stop": "stop", "seconds": 2.5004453659057617} | |
| {"idx": 81, "text": "To find out how many stickers Charlie has left, we will follow his actions step by step:\n\n1. **Initial amount:** Charlie starts with 10 stickers.\n2. **Bought stickers:** He buys 21 stickers.\n $10 + 21 = 31$ stickers.\n3. **Birthday stickers:** He gets 23 stickers for his birthday.\n $31 + 23 = 54$ stickers.\n4. **Gave stickers away:** He gives 9 stickers to his sister.\n $54 - 9 = 45$ stickers.\n5. **Used stickers:** He uses 28 stickers to decorate a greeting card.\n $45 - 28 = 17$ stickers.\n\nCharlie has 17 stickers left.\n\n#### 17", "pred": "17", "gold": "17", "correct": true, "n_new": 185, "stop": "stop", "seconds": 1.9290850162506104} | |
| {"idx": 82, "text": "To find the combined weights of Grace and Alex, we follow these steps:\n\n1. **Identify Grace's weight:**\n Grace weighs 125 pounds.\n\n2. **Calculate Alex's weight:**\n Alex weighs 2 pounds less than 4 times what Grace weighs.\n * First, calculate 4 times Grace's weight: $4 \\times 125 = 500$ pounds.\n * Then, subtract 2 pounds: $500 - 2 = 498$ pounds.\n So, Alex weighs 498 pounds.\n\n3. **Calculate their combined weights:**\n Add Grace's weight and Alex's weight together:\n $125 + 498 = 623$ pounds.\n\n#### 623", "pred": "623", "gold": "623", "correct": true, "n_new": 182, "stop": "stop", "seconds": 1.9385108947753906} | |
| {"idx": 83, "text": "To find the total number of thorns, we can solve the problem step by step:\n\n1. **Find the total number of roses:**\n Dan has 3 rose bushes, and each bush has 25 roses.\n $3 \\times 25 = 75$ roses.\n\n2. **Find the total number of thorns:**\n There are 75 roses in total, and each rose has 8 thorns.\n $75 \\times 8 = ?$\n\n To calculate $75 \\times 8$:\n $70 \\times 8 = 560$\n $5 \\times 8 = 40$\n $560 + 40 = 600$\n\nThere are 600 thorns in total.\n\n#### 600", "pred": "600", "gold": "600", "correct": true, "n_new": 179, "stop": "stop", "seconds": 1.8162245750427246} | |
| {"idx": 84, "text": "To find out how many games the team won, we can follow these steps:\n\n1. **Identify the variables:**\n Let $W$ be the number of games won.\n Let $L$ be the number of games lost.\n\n2. **Set up the equations based on the problem:**\n The total number of games played is 22:\n $W + L = 22$\n The team won 8 more than they lost:\n $W = L + 8$\n\n3. **Substitute the second equation into the first:**\n Substitute $(L + 8)$ for $W$ in the equation $W + L = 22$:\n $(L + 8) + L = 22$\n\n4. **Solve for $L$:**\n Combine the $L$ terms:\n $2L + 8 = 22$\n Subtract 8 from both sides:\n $2L = 14$\n Divide by 2:\n $L = 7$\n\n5. **Solve for $W$:**\n Now use the value of $L$ to find $W$:\n $W = L + 8$\n $W = 7 + 8$\n $W = 15$\n\n6. **Verify the answer:**\n Total games: $15 + 7 = 22$ (Correct)\n Difference: $15 - 7 = 8$ (Correct)\n\nThe team won 15 games.\n\n#### 15", "pred": "15", "gold": "15", "correct": true, "n_new": 347, "stop": "stop", "seconds": 4.499624967575073} | |
| {"idx": 85, "text": "To find the total number of quilt blocks, we need to determine how many years Gene has been vacationing and how many shirts he collected each year.\n\n1. **Calculate the number of years of vacations:**\n Gene started vacationing when he was 23 years old and is now 34 years old.\n Number of years = $34 - 23 = 11$ years.\n (Note: Since he has a shirt from *each* vacation and the prompt implies he has been vacationing *since* he was 23, we count the years inclusive of the start. However, standard age subtraction $34 - 23 = 11$ represents the span of time. Let's look at the sequence: 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34. If he is *now* 34 and has been vacationing *since* he was 23, he has completed vacations for the ages 23 through 33, or he has completed vacations for 11 years of growth. Usually, \"since he was 23\" to \"now 34\" implies $34 - 23 = 11$ years of vacationing).\n\n2. **Calculate the number of shirts per year:**\n The problem states he goes on four vacations a year.\n Shirts per year = 4.\n\n3. **Calculate the total number of quilt blocks:**\n Total blocks = (Number of years) \u00d7 (Vacations per year)\n Total blocks = $11 \\times 4 = 44$.\n\n *Alternative interpretation check:* If \"since he was 23\" includes his 34th year (meaning he is currently on his 34th year's vacations), it would be 12 years. However, in standard word problems, the difference in age is used to determine the elapsed period. $34 - 23 = 11$.\n\n Let's verify the logic:\n Year 1: Age 23\n Year 2: Age 24\n Year 3: Age 25\n Year 4: Age 26\n Year 5: Age 27", "pred": "27", "gold": "44", "correct": false, "n_new": 512, "stop": "length", "seconds": 7.485224008560181} | |
| {"idx": 86, "text": "To find the total number of times the alarm rang, we can calculate the number of rings for each instance step by step.\n\n1. **First time:**\n The problem states that the first time the alarm went off, it rang 4 times.\n *Count: 4*\n\n2. **Second time:**\n The alarm rang for three times as long as the first time.\n Calculation: $4 \\text{ rings} \\times 3 = 12 \\text{ rings}$.\n *Count: 12*\n\n3. **Third time:**\n The alarm rang for half as long as the second time.\n Calculation: $12 \\text{ rings} \\div 2 = 6 \\text{ rings}$.\n *Count: 6*\n\n4. **Total number of rings:**\n Add the rings from all three instances together:\n Calculation: $4 + 12 + 6 = 22$\n\nThe alarm rang 22 times in total.\n\n#### 22", "pred": "22", "gold": "22", "correct": true, "n_new": 227, "stop": "stop", "seconds": 2.6249353885650635} | |
| {"idx": 87, "text": "To find Sylvie's annual salary after three more years of service, we follow these steps:\n\n1. **Identify the initial monthly and annual salary:**\n * Monthly salary = $600.\n * Annual salary = $600 \u00d7 12 = $7,200.\n\n2. **Identify the salary increase rule:**\n * The increase is 10% of the *initial* salary ($600) every year, but only starting after the employee has stayed for five years.\n * Annual increase amount = 10% of $600 = $60.\n * Monthly increase amount = $60.\n\n3. **Determine the timeline of the increases:**\n * Sylvie clocked 5 years last December. This means she is now eligible for the annual increase.\n * She will receive an increase for each of the \"three more years\" of service.\n\n4. **Calculate the monthly salary after three more years:**\n * Year 1 (after 5 years): $600 + $60 = $660\n * Year 2 (after 6 years): $660 + $60 = $720\n * Year 3 (after 7 years): $720 + $60 = $780\n\n5. **Calculate the final annual salary:**\n * Monthly salary after three more years = $780.\n * Annual salary = $780 \u00d7 12.\n * $780 \u00d7 10 = $7,800\n * $780 \u00d7 2 = $1,560\n * $7,800 + $1,560 = $9,360.\n\n#### 9360", "pred": "9360", "gold": "9360", "correct": true, "n_new": 411, "stop": "stop", "seconds": 5.034768104553223} | |
| {"idx": 88, "text": "To find the number of copies Harald sold, we can follow these steps:\n\n1. **Define the variables:**\n Let $x$ be the number of copies Harald sold.\n Since Marilyn sold 10 times as many copies as Harald, Marilyn sold $10x$ copies.\n\n2. **Set up the equation:**\n The problem states that they sold 88,000 copies combined. Therefore, the sum of Harald's sales and Marilyn's sales equals 88,000:\n $x + 10x = 88,000$\n\n3. **Simplify the equation:**\n Combine the like terms on the left side:\n $11x = 88,000$\n\n4. **Solve for $x$:**\n Divide both sides of the equation by 11:\n $x = \\frac{88,000}{11}$\n $x = 8,000$\n\n5. **Verify the answer:**\n If Harald sold 8,000 copies, then Marilyn sold $10 \\times 8,000 = 80,000$ copies.\n The total copies sold would be $8,000 + 80,000 = 88,000$, which matches the information given in the problem.\n\nHarald sold 8,000 copies.\n\n#### 8000", "pred": "8000", "gold": "8000", "correct": true, "n_new": 327, "stop": "stop", "seconds": 3.4589760303497314} | |
| {"idx": 89, "text": "To find out how much Christina will spend, we can follow these steps:\n\n1. **Determine the number of guests expected to attend:**\n Christina invited 16 friends. Since 1/4 of the attendees don't show up, we calculate how many are expected to attend:\n $16 \\times \\frac{1}{4} = 4$ (friends who won't show up).\n $16 - 4 = 12$ (friends expected to attend).\n *(Alternatively, if 1/4 don't show up, 3/4 do show up: $16 \\times 0.75 = 12$.)*\n\n2. **Calculate the number of gift bags needed:**\n Christina needs 0.75 gift bags per invited guest. \n Note: The problem states she needs 0.75 bags *per invited guest*, not per attending guest.\n Number of bags = $16 \\text{ (invited guests)} \\times 0.75$.\n $16 \\times 0.75 = 12$ gift bags.\n\n3. **Calculate the total cost:**\n Each gift bag costs $2.\n Total cost = $12 \\text{ bags} \\times \\$2 \\text{ per bag}$.\n $12 \\times 2 = 24$.\n\n(Self-correction/Refinement: Re-reading the phrasing \"0.75 gift bags per invited guest\". This confirms we multiply the total number of invites by 0.75.)\n\nCalculation:\n$16 \\times 0.75 = 12$ bags\n$12 \\times 2 = 24$ dollars\n\n#### 24", "pred": "24", "gold": "24", "correct": true, "n_new": 382, "stop": "stop", "seconds": 4.927706956863403} | |
| {"idx": 90, "text": "To find out how many pounds of potato salad Ted needs to bring, we can follow these steps:\n\n1. **Calculate the amount one adult eats:**\n An adult dinosaur eats 10 lbs of potato salad.\n\n2. **Calculate the amount one child eats:**\n A child eats half as much as an adult.\n $10 \\text{ lbs} \\div 2 = 5 \\text{ lbs}$ per child.\n\n3. **Calculate the total amount for all the adults:**\n There are 20 adults.\n $20 \\text{ adults} \\times 10 \\text{ lbs/adult} = 200 \\text{ lbs}$.\n\n4. **Calculate the total amount for all the children:**\n There are 5 children.\n $5 \\text{ children} \\times 5 \\text{ lbs/child} = 25 \\text{ lbs}$.\n\n5. **Calculate the total amount needed for everyone:**\n Add the total for adults and children together.\n $200 \\text{ lbs} + 25 \\text{ lbs} = 225 \\text{ lbs}$.\n\nTed needs to bring 225 pounds of potato salad.\n\n#### 225", "pred": "225", "gold": "225", "correct": true, "n_new": 276, "stop": "stop", "seconds": 3.047137975692749} | |
| {"idx": 91, "text": "To find the total number of pets owned by Jan, Marcia, and Cindy, we can solve the problem step by step:\n\n1. **Identify Cindy's pets:**\n The problem states that Cindy has 4 pets.\n * Cindy = 4\n\n2. **Determine Marcia's pets:**\n The problem states that Marcia has two more pets than Cindy.\n * Marcia = Cindy + 2\n * Marcia = 4 + 2 = 6\n\n3. **Determine Jan's pets:**\n The problem states that Jan has three times the number of pets as Marcia.\n * Jan = 3 \u00d7 Marcia\n * Jan = 3 \u00d7 6 = 18\n\n4. **Calculate the total number of pets:**\n Add the number of pets owned by Jan, Marcia, and Cindy together.\n * Total = Jan + Marcia + Cindy\n * Total = 18 + 6 + 4\n * Total = 28\n\n#### 28", "pred": "28", "gold": "28", "correct": true, "n_new": 230, "stop": "stop", "seconds": 2.411353826522827} | |
| {"idx": 92, "text": "To find out how old Jackson is, we can use the information provided about each child's age relative to the others.\n\n1. **Identify the known age:**\n We are told that James is 10 years old.\n James = 10\n\n2. **Find Corey's age:**\n The problem states that James is 1 year younger than Corey. This means Corey is 1 year older than James.\n Corey = James + 1\n Corey = 10 + 1 = 11\n\n3. **Find Amy's age:**\n The problem states that Amy is 2 years younger than Corey.\n Amy = Corey - 2\n Amy = 11 - 2 = 9\n\n4. **Find Jackson's age:**\n The problem states that Amy is 5 years older than Jackson. This means Jackson is 5 years younger than Amy.\n Jackson = Amy - 5\n Jackson = 9 - 5 = 4\n\n#### 4", "pred": "4", "gold": "4", "correct": true, "n_new": 226, "stop": "stop", "seconds": 2.5703089237213135} | |
| {"idx": 93, "text": "To find out how fast Gerald can run the 400-meter hurdles with his improved diet, we follow these steps:\n\n1. **Determine Lee's time:**\n The problem states that Lee runs the 400-meter hurdles in 38 seconds.\n\n2. **Determine Gerald's original time:**\n Lee used to be able to run the event 2 seconds faster than Gerald.\n If Lee's time is 38 seconds, Gerald's original time was:\n $38 \\text{ seconds} + 2 \\text{ seconds} = 40 \\text{ seconds}$.\n\n3. **Calculate the improvement in Gerald's speed:**\n Gerald's speed improved by 10% due to his diet change. In the context of racing times, an improvement in speed corresponds to a reduction in the time taken.\n The time reduction is 10% of his original time:\n $10\\% \\text{ of } 40 \\text{ seconds} = 0.10 \\times 40 = 4 \\text{ seconds}$.\n\n4. **Calculate Gerald's new time:**\n To find Gerald's new time, we subtract the time saved from his original time:\n $40 \\text{ seconds} - 4 \\text{ seconds} = 36 \\text{ seconds}$.\n\n(Note: In physics/kinematics, \"improving speed by 10%\" mathematically means the new speed $v' = 1.10v$. Since $time = distance / speed$, the new time $t' = \\frac{d}{1.10v} = \\frac{t}{1.10}$. \n$40 / 1.1 = 36.36$ seconds. However, in standard word problems of this type, \"improving speed by X%\" is almost always interpreted as a reduction in the time value by that percentage of the original time. Using the standard interpretation for such problems: $40 - (0.10 \\times 40) = 36$.)\n\nRe-evaluating the wording \"improved his speed by 10%\": \nIf we treat \"speed\" as the numerical value of \"seconds per meter\" (which is technically pace), the calculation is $40 \\times 0.9 = ", "pred": "0.9", "gold": "36", "correct": false, "n_new": 512, "stop": "length", "seconds": 6.813149929046631} | |
| {"idx": 94, "text": "To find the total number of pets in the neighborhood, we can solve the problem step by step:\n\n1. **Find the number of dogs:**\n The problem states there are 60 dogs.\n $\\text{Dogs} = 60$\n\n2. **Find the number of cats:**\n The problem states there are two cats for every dog.\n $\\text{Cats} = 60 \\times 2 = 120$\n\n3. **Find the combined number of dogs and cats:**\n $\\text{Dogs + Cats} = 60 + 120 = 180$\n\n4. **Find the number of rabbits:**\n The number of rabbits is twelve less than the combined number of dogs and cats.\n $\\text{Rabbits} = 180 - 12 = 168$\n\n5. **Find the total number of pets:**\n The total number of pets is the sum of dogs, cats, and rabbits.\n $\\text{Total} = \\text{Dogs} + \\text{Cats} + \\text{Rabbits}$\n $\\text{Total} = 60 + 120 + 168$\n $60 + 120 = 180$\n $180 + 168 = 348$\n\n#### 348", "pred": "348", "gold": "348", "correct": true, "n_new": 310, "stop": "stop", "seconds": 3.047874689102173} | |
| {"idx": 95, "text": "To find the number of girls who are not in the Girl Scouts, we can follow these steps:\n\n**Step 1: Find the number of boys.**\nThe total number of students is 200.\n$\\text{Number of boys} = \\frac{2}{5} \\times 200$\n$200 \\div 5 = 40$\n$40 \\times 2 = 80$ boys.\n\n**Step 2: Find the number of girls.**\nSubtract the number of boys from the total number of students.\n$\\text{Number of girls} = 200 - 80 = 120$ girls.\n\n**Step 3: Find the number of girls in the Girl Scouts.**\n$\\frac{2}{3}$ of the girls are in the Girl Scouts.\n$\\text{Number of girls in Girl Scouts} = \\frac{2}{3} \\times 120$\n$120 \\div 3 = 40$\n$40 \\times 2 = 80$ girls in the Girl Scouts.\n\n**Step 4: Find the number of girls not in the Girl Scouts.**\nSubtract the number of girls in the Girl Scouts from the total number of girls.\n$\\text{Number of girls not in Girl Scouts} = 120 - 80 = 40$ girls.\n\nAlternatively, if $\\frac{2}{3}$ of the girls are in the Girl Scouts, then $1 - \\frac{2}{3} = \\frac{1}{3}$ of the girls are not.\n$\\frac{1}{3} \\times 120 = 40$.\n\n#### 40", "pred": "40", "gold": "40", "correct": true, "n_new": 370, "stop": "stop", "seconds": 3.6452364921569824} | |
| {"idx": 96, "text": "To find out how many more hours Harry slept than James, we can follow these steps:\n\n1. **Identify how many hours Harry slept:**\n Harry slept 9 hours.\n\n2. **Calculate how many hours James slept:**\n James slept $\\frac{2}{3}$ of what Harry slept.\n $\\text{James's sleep} = 9 \\times \\frac{2}{3}$\n $\\text{James's sleep} = \\frac{18}{3}$\n $\\text{James's sleep} = 6$ hours.\n\n3. **Calculate the difference between Harry's and James's sleep:**\n To find how many more hours Harry slept, subtract James's sleep from Harry's sleep.\n $\\text{Difference} = 9 \\text{ hours} - 6 \\text{ hours}$\n $\\text{Difference} = 3$ hours.\n\n#### 3", "pred": "3", "gold": "3", "correct": true, "n_new": 204, "stop": "stop", "seconds": 2.3475899696350098} | |
| {"idx": 97, "text": "To solve the problem step by step:\n\n1. **Determine the volume of sauce produced per can:**\n Each can of tomatoes weighs 16 ounces. Since the tomatoes lose half their volume when cooked into sauce, each can yields:\n $16 \\text{ ounces} \\times \\frac{1}{2} = 8 \\text{ ounces of sauce per can}$.\n\n2. **Determine how many cans were used:**\n Freda made 32 ounces of sauce in total. To find the number of cans used, divide the total sauce volume by the volume produced per can:\n $32 \\text{ ounces} \\div 8 \\text{ ounces/can} = 4 \\text{ cans}$.\n\n3. **Determine the total number of tomatoes:**\n Each can contains 3 tomatoes. Since she used 4 cans, the total number of tomatoes is:\n $4 \\text{ cans} \\times 3 \\text{ tomatoes/can} = 12 \\text{ tomatoes}$.\n\n#### 12", "pred": "12", "gold": "12", "correct": true, "n_new": 226, "stop": "stop", "seconds": 2.614431381225586} | |
| {"idx": 98, "text": "To find the number of cars that drove through the traffic jam in the first 15 minutes, we can follow these steps:\n\n1. **Identify the total number of cars that drove through the jam:**\n The total number of cars originally on the motorway was 30.\n However, 5 cars took an exit, meaning they did not drive through the traffic jam.\n Total cars that drove through = $30 - 5 = 25$ cars.\n\n2. **Identify the number of cars that drove through in the second 15 minutes:**\n The problem states that 20 cars drove through in the remaining 15 minutes.\n\n3. **Calculate the number of cars that drove through in the first 15 minutes:**\n We subtract the cars from the second period from the total number of cars that drove through.\n Cars in the first 15 minutes = (Total cars that drove through) - (Cars in the second 15 minutes)\n Cars in the first 15 minutes = $25 - 20 = 5$ cars.\n\n#### 5", "pred": "5", "gold": "5", "correct": true, "n_new": 241, "stop": "stop", "seconds": 3.0749197006225586} | |
| {"idx": 99, "text": "To find out how many potted plants Mary will remain with, we can follow these steps:\n\n1. **Calculate the number of plants Mary currently has on her window ledges:**\n Mary has 40 window ledges, and each ledge has 2 potted plants.\n $40 \\times 2 = 80$ plants.\n\n2. **Add the new plants she received:**\n Mary received 18 new plants yesterday.\n $80 + 18 = 98$ total plants.\n\n3. **Calculate how many plants she will give away:**\n She plans to give 1 plant from each of her 40 window ledges to friends and family.\n $40 \\times 1 = 40$ plants to be given away.\n\n4. **Calculate the final total:**\n Subtract the number of plants she is giving away from her total number of plants.\n $98 - 40 = 58$ plants.\n\nMary will remain with 58 potted plants.\n\n#### 58", "pred": "58", "gold": "58", "correct": true, "n_new": 232, "stop": "stop", "seconds": 2.8459880352020264} | |