prompt
listlengths 1
1
| reward_model
dict | data_source
stringclasses 1
value | extra_info
dict |
|---|---|---|---|
[
{
"content": "A rectangular billboard is 5 meters tall. Its length is 3 times its height. What is the area of the billboard in square meters?\n\n### Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "75",
"style": "rule"
}
|
numina_math
|
{
"index": 2200,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Lisa works as a freelance graphic designer and charges $25 per hour. She has the opportunity to attend a professional development workshop that lasts for 6 hours and costs $120. If Lisa decides to attend the workshop, what is her opportunity cost in terms of lost earnings and the cost of the workshop? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "270",
"style": "rule"
}
|
numina_math
|
{
"index": 2201,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Julie is preparing for a marathon by running laps around a track. Each lap is 400 meters long. She plans to run 10 laps each day for 6 days, but on the 7th day, she plans to run double the number of laps she runs on a regular day. How many meters will Julie run in total over the 7 days? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "32000",
"style": "rule"
}
|
numina_math
|
{
"index": 2202,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A school had 420.5 students enrolled at the beginning of the year. During the mid-year, 294 students left the school. If the school was able to enroll new students at a rate of 2.8 students per day for 21 days, how many students were enrolled at the end of the year? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "185.3",
"style": "rule"
}
|
numina_math
|
{
"index": 2203,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a treasure hunt, the participants must find a series of clues that lead to the final treasure. Each clue provides a number that indicates how many steps to take in a specific direction. The first clue directs the participants to take 15 steps north, the second clue directs them to take 8 steps east, and the third clue directs them to take 12 steps south. How many steps must they take west to return to the starting point? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "8",
"style": "rule"
}
|
numina_math
|
{
"index": 2204,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Jack and Jill can complete a project together in 8 hours. Jack can complete the project alone in 12 hours. How long will it take Jill to complete the project alone? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "24",
"style": "rule"
}
|
numina_math
|
{
"index": 2205,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A farmer has 200 acres of land. He wants to plant wheat on two-thirds of his land and use one-fourth of the remaining land for vegetable farming. How many acres of land will be used for vegetable farming? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "16.67",
"style": "rule"
}
|
numina_math
|
{
"index": 2206,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A library has a collection of books. Initially, 60% of the books are fiction and the remaining are non-fiction. After donating 40 fiction books and adding 20 non-fiction books, the percentage of fiction books in the collection becomes 55%. How many books were in the library initially? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "800",
"style": "rule"
}
|
numina_math
|
{
"index": 2207,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a survey, 60% of people like chocolate, 40% like vanilla, and 20% like both. If 300 people were surveyed, how many people like only chocolate or only vanilla? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "180",
"style": "rule"
}
|
numina_math
|
{
"index": 2208,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A hiking trail is 15 kilometers long. If Jack has walked 3/5 of the trail, how many kilometers has he walked, and how many kilometers does he have left to complete the trail? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "6",
"style": "rule"
}
|
numina_math
|
{
"index": 2209,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Lily has a chocolate bar divided into 8 equal pieces. She ate 1/4 of the chocolate bar before lunch and another 3/8 after lunch. How many pieces of the chocolate bar does Lily have left? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "3",
"style": "rule"
}
|
numina_math
|
{
"index": 2210,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "The price of a laptop decreased by 20% and is now being sold for $800. What was the original price of the laptop? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1000",
"style": "rule"
}
|
numina_math
|
{
"index": 2211,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Two trains, Train A and Train B, start from the same station at the same time and travel in opposite directions. Train A travels at a speed that is 20% faster than Train B. If Train B travels at 60 miles per hour, how far apart will the trains be after 3 hours? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "396",
"style": "rule"
}
|
numina_math
|
{
"index": 2212,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah bought 5 packs of markers, each costing $3. She also bought a notebook that cost $7. If Sarah paid a total of $30, how much change did she receive? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "8",
"style": "rule"
}
|
numina_math
|
{
"index": 2213,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Simplify the expression: $\\frac{\\sqrt{64}}{8} \\times \\frac{9}{3}$ Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "3",
"style": "rule"
}
|
numina_math
|
{
"index": 2214,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sophia is preparing gift bags for a party. Each gift bag contains 5 candies and 3 small toys. She plans to prepare a total of 16 gift bags. If she decides to keep one-quarter of the total gift bags for herself and distribute the rest, how many candies and small toys will she distribute? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "36",
"style": "rule"
}
|
numina_math
|
{
"index": 2215,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A farm has 120 cows. The number of sheep is (5/4) of the number of cows, and it is also (3/8) of the number of chickens. How many chickens are there on the farm? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "400",
"style": "rule"
}
|
numina_math
|
{
"index": 2216,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Mitch is a freelancer. She works 5 hours every day from Monday to Friday and 3 hours every Saturday and Sunday. If she earns $3 per hour on weekdays and double that rate on weekends, how much does she earn every week? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "111",
"style": "rule"
}
|
numina_math
|
{
"index": 2217,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "The population of a town is currently 5,000 people. The population grows by 200 people each year. If another nearby town has a current population of 4,000 people and grows by 300 people each year, in how many years will the populations of the two towns be equal? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "10",
"style": "rule"
}
|
numina_math
|
{
"index": 2218,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Emily is planning a road trip. She knows that her car uses 1 gallon of fuel for every 25 miles driven. If the total distance of her trip is 500 miles and fuel costs $3.50 per gallon, how much will she spend on fuel for the entire trip? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "70",
"style": "rule"
}
|
numina_math
|
{
"index": 2219,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A local community center is planning to plant trees in a new park. They planted 45 maple trees and 35 birch trees. The number of oak trees they planted is 1.5 times the total number of maple and birch trees combined. How many oak trees were planted? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "120",
"style": "rule"
}
|
numina_math
|
{
"index": 2220,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In preparation for his art exhibit, Jacob plans to create a series of paintings. He plans to paint 2 paintings on the first day, and he will increase the number of paintings he completes each day by 3 more than the previous day. If he continues this pattern for 7 days, how many paintings will he have completed in total by the end of the 7th day? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "77",
"style": "rule"
}
|
numina_math
|
{
"index": 2221,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Simplify the expression $\\frac{1}{\\frac{1}{\\frac{3}{4}} + \\frac{1}{\\frac{5}{6}}}$. Express your answer as a common fraction. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\frac{15}{38}",
"style": "rule"
}
|
numina_math
|
{
"index": 2222,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A company’s initial investment in a project is $5,000. The value of the investment grows by 10% each year. After how many years will the investment value be approximately $8,000? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "5",
"style": "rule"
}
|
numina_math
|
{
"index": 2223,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Jessica is planning to save for a new laptop that costs $1,800. She has set a goal to buy it within a year (12 months). If she already has $300 saved and plans to save an equal amount each month from her monthly budget, how much does she need to save each month to reach her goal? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "125",
"style": "rule"
}
|
numina_math
|
{
"index": 2224,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Two gardeners, Alex and Ben, are working together to plant flowers in a garden. Alex can plant 10 flowers in 15 minutes, while Ben can plant 15 flowers in 30 minutes. If they work together, how long will it take them to plant 50 flowers? Express your answer in minutes. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "42.86",
"style": "rule"
}
|
numina_math
|
{
"index": 2225,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Find the greatest common factor (GCF) of 84 and 126. Show your work step by step. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "84",
"style": "rule"
}
|
numina_math
|
{
"index": 2226,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A rectangular garden has a length of 15 meters and a width of 20 meters. Jill wants to place a bench at a point that is equidistant from all four corners of the garden. What is the distance from this point to any corner of the garden? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "12.5",
"style": "rule"
}
|
numina_math
|
{
"index": 2227,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Let the roots of the quadratic equation \\(2x^2 - 7x + c = 0\\) be \\(\\alpha\\) and \\(\\beta\\). If the sum of the roots is equal to the product of the roots, find the value of \\(c\\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "7",
"style": "rule"
}
|
numina_math
|
{
"index": 2228,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Lisa had a certain number of marbles. She gave away 5 marbles to her friend and then squared the number of marbles she had left. If she originally had 10 marbles, how many marbles did she have after giving away the 5 and squaring the remaining amount? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "25",
"style": "rule"
}
|
numina_math
|
{
"index": 2229,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Lisa is currently 12 years old, and her brother Tom is 20 years old. In how many years will Tom be 1.5 times as old as Lisa's current age? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "4",
"style": "rule"
}
|
numina_math
|
{
"index": 2230,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A jacket originally priced at $79.99 is now sold at a discount price of $59.49. How much money is saved by buying the jacket at the discount price? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "20.50",
"style": "rule"
}
|
numina_math
|
{
"index": 2231,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "What is the last digit of \\(7^{123}\\)? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "3",
"style": "rule"
}
|
numina_math
|
{
"index": 2232,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Emily is planning a birthday party and wants to buy decorations and snacks. She spends $50 on decorations and $3 per snack pack. If she buys 20 snack packs, how much does she spend in total? Additionally, if she charges her friends $5 per person and invites 15 friends, how much money does she collect? Calculate her net expenditure by subtracting the amount collected from the total amount spent. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "35",
"style": "rule"
}
|
numina_math
|
{
"index": 2233,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A student was solving a math problem that involved adding and subtracting several numbers. The problem stated: \"Calculate the sum of 45 and 27, then subtract 18 from the result, and finally add 12.\" The student made a mistake and got 80 as the final answer. Identify the error made by the student and determine the correct answer. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "66",
"style": "rule"
}
|
numina_math
|
{
"index": 2234,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah is saving money for a new laptop. She starts with $200 in her savings account. Each month, she saves an additional $200. After 3 months, she decides to spend 25% of her total savings on a new phone. How much money does she have left in her savings account after buying the phone? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "600",
"style": "rule"
}
|
numina_math
|
{
"index": 2235,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Given the piecewise function \n\\[ g(x) = \n\\begin{cases}\n5x + 3 & \\text{if } x \\le 2, \\\\\nbx + 1 & \\text{if } x > 2,\n\\end{cases}\n\\]\nfind the value of \\( b \\) such that the function \\( g(x) \\) is continuous at \\( x = 2 \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "6",
"style": "rule"
}
|
numina_math
|
{
"index": 2236,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In five years, Maria will be three times as old as her younger brother Alex. Currently, Maria is 24 years older than Alex. How old are Maria and Alex now? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "31",
"style": "rule"
}
|
numina_math
|
{
"index": 2237,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A car travels at a constant speed of 60 miles per hour for 3 hours and then at a constant speed of 45 miles per hour for 2 hours. How many more miles did the car travel at 60 miles per hour compared to 45 miles per hour? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "90",
"style": "rule"
}
|
numina_math
|
{
"index": 2238,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "If $\\log_2 (x - 1) = 5$, find the value of $x$. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "33",
"style": "rule"
}
|
numina_math
|
{
"index": 2239,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah wants to buy a new laptop that costs $800. The store is offering a 15% discount on all electronics. After applying the discount, Sarah also needs to pay a sales tax of 8% on the discounted price. Calculate the total amount Sarah needs to pay for the laptop. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "734.40",
"style": "rule"
}
|
numina_math
|
{
"index": 2240,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A factory produces widgets at a rate of 3 widgets every 10 minutes. If the factory operates for 8 hours a day, how many widgets does the factory produce in a week (assuming it operates 7 days a week)? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1008",
"style": "rule"
}
|
numina_math
|
{
"index": 2241,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A store is having a 25% off sale on all items. If a customer buys a jacket originally priced at $80 and a pair of shoes originally priced at $60, how much does the customer pay in total after the discount? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "105",
"style": "rule"
}
|
numina_math
|
{
"index": 2242,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah is training for a marathon and runs at a constant speed. She plans to run a total of 26 miles. After running for 1.5 hours, she realizes she has 8 miles left to run. What is her running speed in miles per hour? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "12",
"style": "rule"
}
|
numina_math
|
{
"index": 2243,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Tom needs to lower a rope down 6 stories. One story is 10 feet. The only rope being sold is 20 feet long but you lose 25% of each piece when lashing them together. How many pieces of rope will he need to buy? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "4",
"style": "rule"
}
|
numina_math
|
{
"index": 2244,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Let \\( f(x) = 4x^4 - 3x^3 + 2x^2 - x + 5 \\). Evaluate \\( f(3) \\), and then determine the quotient and remainder when \\( f(x) \\) is divided by \\( x - 3 \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "263",
"style": "rule"
}
|
numina_math
|
{
"index": 2245,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A recipe calls for a mix of sugar and flour in the ratio of 2:5. If you have 700 grams of flour, how much sugar do you need to maintain the ratio? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "280",
"style": "rule"
}
|
numina_math
|
{
"index": 2246,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah is driving on a highway where the speed limit is 65 miles per hour. She drives 195 miles in 3 hours. What is Sarah's average speed, and did she stay within the speed limit? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "65",
"style": "rule"
}
|
numina_math
|
{
"index": 2247,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A car rental company charges a fixed fee of $50 plus $10 per hour for renting a car. If a customer has only $150 to spend, for how many hours can they rent the car? Use the slope-intercept form to solve the problem. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "10",
"style": "rule"
}
|
numina_math
|
{
"index": 2248,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Given the linear function \\( g(x) = 4x - 5 \\), find the value of \\( g(-2) \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "-13",
"style": "rule"
}
|
numina_math
|
{
"index": 2249,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Samantha went shopping for clothes and bought a jacket and a pair of shoes. The jacket costs $80, and the shoes cost $50. She received a 25% discount on the jacket. Calculate the total amount she spent on both items after applying the discount to the jacket. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "110",
"style": "rule"
}
|
numina_math
|
{
"index": 2250,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah has a collection of 84 marbles. She wants to divide them equally among her 7 friends, but she also wants to keep 12 marbles for herself. After distributing the marbles to her friends, how many marbles does each friend receive? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "10",
"style": "rule"
}
|
numina_math
|
{
"index": 2251,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a school fundraiser, students are selling chocolate bars and cookies. Each chocolate bar costs $1 and each cookie costs $0.50. If the total revenue from selling 20 items (chocolate bars and cookies) is $15, how many chocolate bars were sold? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "10",
"style": "rule"
}
|
numina_math
|
{
"index": 2252,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A garden is designed in the shape of a square with each side measuring 1/2 yard. This square garden is then divided into smaller rectangles, each measuring 1/4 yard by 1/8 yard. How many smaller rectangles can fit into the entire square garden? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "8",
"style": "rule"
}
|
numina_math
|
{
"index": 2253,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A factory operates 8 hours a day and produces 240 widgets per hour. Each widget takes 5 minutes to package. If there are 4 workers packaging the widgets, how many hours will it take for the workers to package all the widgets produced in one day? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "40",
"style": "rule"
}
|
numina_math
|
{
"index": 2254,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A store is having a sale where all items are 25% off. If a customer buys a jacket that originally costs $120 and a pair of shoes that originally costs $80, how much will the customer pay in total after the discount is applied to both items? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "150",
"style": "rule"
}
|
numina_math
|
{
"index": 2255,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Johnny has a collection of nickels, dimes, and quarters worth $6.50. He has twice as many dimes as nickels, and the total number of coins is 50. How many of each type of coin does Johnny have? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "14",
"style": "rule"
}
|
numina_math
|
{
"index": 2256,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A model car is built to a scale of 1:20, which means that 1 unit on the model represents 20 units on the real car. If the model car is 15 inches long, how long is the real car in feet? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "25",
"style": "rule"
}
|
numina_math
|
{
"index": 2257,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a triangle, the degree measures of the angles are in the ratio \\(2:3:5\\). What is the degree measure of the largest angle of the triangle? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "90",
"style": "rule"
}
|
numina_math
|
{
"index": 2258,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "During the summer, David decides to track the number of laps he swims in the pool each day. On Monday, he swims 12 laps. On Tuesday, he swims twice the number of laps he swam on Monday. On Wednesday, he swims three times the number of laps he swam on Tuesday. How many laps did David swim in total over these three days? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "108",
"style": "rule"
}
|
numina_math
|
{
"index": 2259,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Given the function \\( f(x) = 3x^2 + 2x - 5 \\), find \\( f(4) \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "51",
"style": "rule"
}
|
numina_math
|
{
"index": 2260,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In how many ways can a committee of 3 members be chosen from a group of 8 people? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "56",
"style": "rule"
}
|
numina_math
|
{
"index": 2261,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Ryan had $50. He decided to buy 3 comic books at $8 each and 2 action figures at $12 each. After making these purchases, how much money does Ryan have left? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2",
"style": "rule"
}
|
numina_math
|
{
"index": 2262,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah wants to save money for a new laptop that costs $1,200. She decides to save $50 each week. After saving for 15 weeks, she spends $200 on a surprise expense. How many more weeks will Sarah need to save to afford the laptop? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "13",
"style": "rule"
}
|
numina_math
|
{
"index": 2263,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah is running a small business selling handmade candles. Last month, she sold 40 candles at $15 each and 25 candles at $20 each. She also had $200 in expenses. If Sarah wants to calculate her average profit per candle sold, how should she proceed, and what is the average profit per candle? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "13.85",
"style": "rule"
}
|
numina_math
|
{
"index": 2264,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Let $\\mathbf{u} = \\begin{pmatrix} 1 \\\\ 2 \\\\ 3 \\end{pmatrix}$, $\\mathbf{v} = \\begin{pmatrix} 4 \\\\ 5 \\\\ 6 \\end{pmatrix}$, and $\\mathbf{w} = \\begin{pmatrix} 7 \\\\ 8 \\\\ 9 \\end{pmatrix}$. Calculate the scalar triple product $\\mathbf{u} \\cdot (\\mathbf{v} \\times \\mathbf{w})$, and determine the volume of the parallelepiped formed by these vectors. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "0",
"style": "rule"
}
|
numina_math
|
{
"index": 2265,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Tommy has a collection of 47 marbles. He bought 25 more marbles at the store. Then, he gave away 18 marbles to his friends. How many marbles does Tommy have now? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "54",
"style": "rule"
}
|
numina_math
|
{
"index": 2266,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "What is the smallest integer greater than 1 that has exactly three positive divisors, and the largest prime number less than 50? What is the sum of these two numbers? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "51",
"style": "rule"
}
|
numina_math
|
{
"index": 2267,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "If the ratio of the number of apples to oranges in a basket is 3:5 and there are a total of 64 fruits in the basket, how many apples and oranges are there? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "40",
"style": "rule"
}
|
numina_math
|
{
"index": 2268,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A company needs to form a 5-member committee from 10 employees. Among these employees, 3 are managers and 7 are regular employees. How many different committees can be formed if at least one manager must be included? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "231",
"style": "rule"
}
|
numina_math
|
{
"index": 2269,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A store offers a 25% discount on a jacket that originally costs $120. If a customer has a coupon for an additional $\\frac{1}{3}$ off the discounted price, what is the final price the customer pays for the jacket? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "60",
"style": "rule"
}
|
numina_math
|
{
"index": 2270,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Samantha is planning to buy snacks for a party. She finds that a 24-pack of soda costs $7.20 and a 12-pack of soda costs $4.80. She also wants to buy chips, where a large bag costs $3.50 and a small bag costs $2.00. She decides to buy the pack of soda and bag of chips that offer the best value for their price per unit. What is the total amount in cents she will spend if she buys the best value options for both soda and chips? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "920",
"style": "rule"
}
|
numina_math
|
{
"index": 2271,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A gardener is planning to plant flowers in a square-shaped flower bed. The cost to plant flowers per square foot is $3. If the perimeter of the flower bed is 40 feet, how much will it cost to plant flowers in the entire flower bed? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "300",
"style": "rule"
}
|
numina_math
|
{
"index": 2272,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah is driving to visit her friend who lives 150 miles away. She plans to drive at a constant speed of 60 miles per hour. After driving for 1 hour and 30 minutes, she takes a 15-minute break. After the break, she continues driving at the same speed. How long will it take Sarah in total to reach her friend's house? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2.75",
"style": "rule"
}
|
numina_math
|
{
"index": 2273,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a survey of 50 students, it was found that 30 students like reading, 25 students like sports, and 10 students like both reading and sports. How many students do not like either reading or sports? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "5",
"style": "rule"
}
|
numina_math
|
{
"index": 2274,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Given the polynomial \\( P(x) = x^3 - 3x^2 + x - 3 \\), factorize it completely and then simplify the expression \\(\\frac{P(a)}{a - 1}\\) for \\(a = 1\\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "undefined",
"style": "rule"
}
|
numina_math
|
{
"index": 2275,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A cyclist travels to a nearby town at an average speed of 15 km/h and returns at an average speed of 10 km/h. If the round trip takes a total of 5 hours, how far is the town from the cyclist's starting point? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "30",
"style": "rule"
}
|
numina_math
|
{
"index": 2276,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A bookstore buys books at a cost price of $80 each. The bookstore wants to apply a discount of 25% on the selling price, such that after the discount, the final price paid by the customer is $90. What should be the selling price before the discount is applied? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "120",
"style": "rule"
}
|
numina_math
|
{
"index": 2277,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A small island has an initial population where every year 20% of the population leaves the island. After 3 years, the population is found to be 512. What was the initial population of the island? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1000",
"style": "rule"
}
|
numina_math
|
{
"index": 2278,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Solve for \\( x \\) in the equation \\( \\log_{2} (x^2 - 3x + 2) = \\log_{2} (x^2 - 4) + 1 \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2",
"style": "rule"
}
|
numina_math
|
{
"index": 2279,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Consider the function \\( f(x, y, z) = x + y + z \\) subject to the constraint \\( xyz = 27 \\). Find the maximum value of \\( f(x, y, z) \\) where \\( x, y, \\) and \\( z \\) are positive integers. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "29",
"style": "rule"
}
|
numina_math
|
{
"index": 2280,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a school, 45% of the students are boys, 35% are girls, and the rest are teachers. If the total number of individuals in the school is 1000, how many individuals are teachers? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "200",
"style": "rule"
}
|
numina_math
|
{
"index": 2281,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a small city, there are \\(5\\) parks, each in the shape of a square. The side lengths of these parks are in the ratio \\(1:2:3:4:5\\). If the total perimeter of all five parks combined is \\(240\\) meters, what is the side length of the smallest park? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "4",
"style": "rule"
}
|
numina_math
|
{
"index": 2282,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A car travels 60 miles in 1 hour. If the car were to double its speed, how far would it travel in 3 hours? How much farther would this be compared to its original speed over the same time period? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "180",
"style": "rule"
}
|
numina_math
|
{
"index": 2283,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Let \\( g(x) = 2x^2 + 3x - 4 \\) and \\( h(x) = x^2 - 2x + 1 \\). Find the value of \\( g(h(2)) \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1",
"style": "rule"
}
|
numina_math
|
{
"index": 2284,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A theater has a seating arrangement such that the first row has 10 seats, the second row has 12 seats, the third row has 14 seats, and so on, increasing by 2 seats each row. If the theater has 25 rows in total, how many seats are there in the entire theater? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "850",
"style": "rule"
}
|
numina_math
|
{
"index": 2285,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Lily is planning her workout schedule for the week. She works out for 30 minutes each day from Monday to Friday, but on Saturday and Sunday, she doubles her workout time. What is the total amount of time Lily spends working out during the week? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "4.5",
"style": "rule"
}
|
numina_math
|
{
"index": 2286,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah has a budget of $50 for buying fruits. She wants to buy apples, bananas, and oranges. Apples cost $1.20 each, bananas cost $0.75 each, and oranges cost $1.50 each. If Sarah buys 10 apples, 8 bananas, and 6 oranges, how much money will she have left after the purchase? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "23",
"style": "rule"
}
|
numina_math
|
{
"index": 2287,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A pair of pants costs $28 and the price of a top is twice that of a pair of pants. If a store offers a 10% discount on the total cost of buying one pair of pants and one top, how much does the outfit cost after the discount? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "75.60",
"style": "rule"
}
|
numina_math
|
{
"index": 2288,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah works on her project for 2 hours every day. Over a span of 18 days, she spends a portion of her time each day organizing her materials, which takes 15 minutes per day. How much total time does she spend on the actual project work over these 18 days? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "31.5",
"style": "rule"
}
|
numina_math
|
{
"index": 2289,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A group of friends wants to equally share the cost of a $240 gift. If each friend contributes $15, how many friends are in the group? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "16",
"style": "rule"
}
|
numina_math
|
{
"index": 2290,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Given the parametric equations \\( x(t) = 2t + 3 \\) and \\( y(t) = t^2 - 1 \\), find the value of \\( x(t)^2 - y(t) \\) when \\( t = 5 \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "145",
"style": "rule"
}
|
numina_math
|
{
"index": 2291,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Three friends, Alice, Bob, and Carol, are dividing a sum of money they won in a contest. Alice gets twice as much money as Bob, and Carol gets three times as much money as Bob. If the total amount of money won is $720, how much money does each friend get? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "360",
"style": "rule"
}
|
numina_math
|
{
"index": 2292,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah is planning a birthday party and needs to rent chairs and tables. Each table costs $15 to rent, and each chair costs $5 to rent. She rents 8 tables and 40 chairs. How much does she spend in total? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "320",
"style": "rule"
}
|
numina_math
|
{
"index": 2293,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A cyclist travels at a constant speed of 15 miles per hour. If he travels for 3 hours, then takes a break for 1 hour, and then continues to travel for another 2 hours at the same speed, what is the total distance he travels? Additionally, if he took the same journey but wanted to complete it in 4 hours instead of 6 hours (including the break), what would be the average speed he needs to maintain? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "18.75",
"style": "rule"
}
|
numina_math
|
{
"index": 2294,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Solve for \\( x \\) in the equation \\( \\log_2(8) + \\log_4(16) = \\log_{16}(2^x) \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "20",
"style": "rule"
}
|
numina_math
|
{
"index": 2295,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "The temperature in Celsius can be converted to Fahrenheit using the formula \\( F = \\frac{9}{5}C + 32 \\). If the temperature in Fahrenheit is 95 degrees, what is the temperature in Celsius? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "35",
"style": "rule"
}
|
numina_math
|
{
"index": 2296,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Find the sum of the arithmetic series from \\( \\frac{1}{2} \\) to \\( \\frac{10}{2} \\) and simplify the result. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "13.75",
"style": "rule"
}
|
numina_math
|
{
"index": 2297,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A point \\( A (2, 5) \\) is reflected over the y-axis to obtain point \\( B \\), and then reflected over the x-axis to obtain point \\( C \\). What are the coordinates of point \\( C \\), and what is the sum of the coordinates of point \\( C \\)? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "-7",
"style": "rule"
}
|
numina_math
|
{
"index": 2298,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A company produces 250 units of a product each day. Due to an unexpected surge in demand, the company needs to estimate how many units they will produce in the next quarter (3 months). Assuming there are 30 days in each month, approximately how many units will they produce in the next quarter? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "22500",
"style": "rule"
}
|
numina_math
|
{
"index": 2299,
"name": "numina_math",
"split": "train"
}
|
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