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[ { "content": "Answer the following problem. Explain your reasoning step by step. When you are finished, give your answer in this format: <answer>(your answer)</answer>.\n\n# Problem\nIn mid-May, the river flowing through Moreland is five feet deep. By mid-June, the river is 10 feet deeper than mid-May. By mid-J...
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[ "<think>\n<sample>\n\nSure, let's break down the problem step by step:\n\n1. **Mid-May Depth**:\n - The river is 5 feet deep at mid-May.\n\n2. **Mid-June Depth**:\n - By mid-June, the river is 10 feet deeper than it was at mid-May.\n - Therefore, the depth of the river at mid-June = Mid-May depth + 10 feet\n ...
45
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[ [ { "comparison_type": "mathematical", "correct_answer": "45", "evaluation_method": "math_equivalence", "extracted_answer": "45", "is_equivalent": true }, { "comparison_type": "mathematical", "correct_answer": "45", "evaluation_method": "math_equivalence",...
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[ { "content": "Answer the following problem. Explain your reasoning step by step. When you are finished, give your answer in this format: <answer>(your answer)</answer>.\n\n# Problem\nThe carousel at the fair has 3 blue horses, three times that many purple horses, twice as many green horses as purple horses, and...
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[ "<think>\n<sample>\n\nTo solve this problem, let's break it down into steps:\n\n### Step 1: Determine the number of each type of horse.\n- We know there are 3 blue horses.\n- The number of purple horses is three times the number of blue horses. Therefore, we calculate:\n \\[\n \\text{Number of purple horses} = 3 ...
33
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[ [ "33", "33", "33", "33" ] ]
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[ { "content": "Answer the following problem. Explain your reasoning step by step. When you are finished, give your answer in this format: <answer>(your answer)</answer>.\n\n# Problem\nAlex is saving up for a new car. He already has $14,500 saved up and the car costs $14,600. He decides that to make the last of t...
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[ "<think>\n<sample>\n\nSure! Let's break down the problem step by step:\n\n1. **Initial Savings**: Alex already has $14,500 saved.\n2. **Car Cost**: The car costs $14,600.\n3. **Total Amount Needed**: To find out how much more money Alex needs, we subtract his current savings from the total cost of the car.\n \\[\...
800
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[ { "comparison_type": "mathematical", "correct_answer": "800", "evaluation_method": "math_equivalence", "extracted_answer": "800", "is_equivalent": true } ]
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[ [ "800", "800", "800", "800", "800" ] ]
[ [ { "confidence": 0.95, "extraction_type": "internal", "original_span": "800", "pattern_used": "\\boxed{...}", "position": 1736, "span_end": 1739, "span_start": 1736, "span_text": "800" }, { "confidence": 0.95, "extraction_type": "internal", ...
[ [ { "comparison_type": "mathematical", "correct_answer": "800", "evaluation_method": "math_equivalence", "extracted_answer": "800", "is_equivalent": true }, { "comparison_type": "mathematical", "correct_answer": "800", "evaluation_method": "math_equivalenc...
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[ { "content": "Answer the following problem. Explain your reasoning step by step. When you are finished, give your answer in this format: <answer>(your answer)</answer>.\n\n# Problem\nAniyah has 6 times as many birthday candles as Ambika. If Ambika has four birthday candles, how many birthday candles will they h...
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[ "<think>\n<sample>\n\nSure! Let's break down the problem step by step:\n\n1. **Determine the number of candles Aniyah has**:\n - Ambika has 4 candles.\n - Aniyah has 6 times as many candles as Ambika.\n - Therefore, Aniyah has \\( 6 \\times 4 = 24 \\) candles.\n\n2. **Calculate the total number of candles**:\...
14
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[ { "content": "Answer the following problem. Explain your reasoning step by step. When you are finished, give your answer in this format: <answer>(your answer)</answer>.\n\n# Problem\nKevin has been for a run and wants to calculate how far he traveled. He ran at 10 miles per hour for half an hour, 20 miles per h...
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[ "<think>\n<sample>\n\nTo solve this problem, we need to calculate the distance Kevin ran during each segment of his run and then sum these distances to get the total distance.\n\n### Step 1: Calculate the distance for the first segment\n- Speed: 10 miles per hour (mph) \n- Time: 30 minutes = 0.5 hours\n\nDistance ...
17
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[ { "comparison_type": "mathematical", "correct_answer": "17", "evaluation_method": "math_equivalence", "extracted_answer": "17", "is_equivalent": true } ]
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[ [ { "comparison_type": "mathematical", "correct_answer": "17", "evaluation_method": "math_equivalence", "extracted_answer": "(17)", "is_equivalent": true }, { "comparison_type": "mathematical", "correct_answer": "17", "evaluation_method": "math_equivalence...
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[ { "content": "Answer the following problem. Explain your reasoning step by step. When you are finished, give your answer in this format: <answer>(your answer)</answer>.\n\n# Problem\nSarah uses 1 ounce of shampoo, and one half as much conditioner as shampoo daily. In two weeks, what is the total volume of sham...
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[ "<think>\n<sample>\n\nSure, let's break down the problem step by step:\n\n1. **Determine Daily Usage**:\n - Sarah uses 1 ounce of shampoo each day.\n - She uses half as much conditioner as shampoo, which means she uses \\( \\frac{1}{2} \\) ounce of conditioner each day.\n\n2. **Calculate Weekly Usage**:\n - T...
21
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[ { "comparison_type": "mathematical", "correct_answer": "21", "evaluation_method": "math_equivalence", "extracted_answer": "21", "is_equivalent": true } ]
[ [ true, true, true, true, true ] ]
[ [ "21", "21", "21", "21", "21" ] ]
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[ [ { "comparison_type": "mathematical", "correct_answer": "21", "evaluation_method": "math_equivalence", "extracted_answer": "21", "is_equivalent": true }, { "comparison_type": "mathematical", "correct_answer": "21", "evaluation_method": "math_equivalence",...
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[ { "content": "Answer the following problem. Explain your reasoning step by step. When you are finished, give your answer in this format: <answer>(your answer)</answer>.\n\n# Problem\nViggo's age was 10 years more than twice his younger brother's age when his brother was 2. If his younger brother is currently 10...
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[ "<think>\n<sample>\n\nTo solve this problem, let's break it down into steps:\n\n### Step 1: Determine Viggo's Age When His Brother Was 2 Years Old\n\nAccording to the information given:\n- Viggo's age was 10 years more than twice his younger brother's age.\n- His younger brother was 2 years old at that time.\n\nTwi...
32
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[ { "comparison_type": "mathematical", "correct_answer": "32", "evaluation_method": "math_equivalence", "extracted_answer": "32", "is_equivalent": true } ]
[ [ true, true, true, true ] ]
[ [ "32", "32", "32", "32" ] ]
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[ [ { "comparison_type": "mathematical", "correct_answer": "32", "evaluation_method": "math_equivalence", "extracted_answer": "32", "is_equivalent": true }, { "comparison_type": "mathematical", "correct_answer": "32", "evaluation_method": "math_equivalence",...
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[ { "content": "Answer the following problem. Explain your reasoning step by step. When you are finished, give your answer in this format: <answer>(your answer)</answer>.\n\n# Problem\nLyanna set up a food bank to collect food to give to the homeless in her local town. In the first week, 40 pounds of food were do...
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[ "<think>\n<sample>\n\nSure, let's break down the problem step by step:\n\n1. **First Week Donations**:\n - Lyanna received 40 pounds of food from the people of her local town.\n \n2. **Second Week Donations**:\n - The donations doubled compared to the first week.\n - Therefore, the second week donation = \\...
36
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[ { "content": "Answer the following problem. Explain your reasoning step by step. When you are finished, give your answer in this format: <answer>(your answer)</answer>.\n\n# Problem\nA dental office gives away 2 toothbrushes to every patient who visits. His 8 hour days are packed and each visit takes .5 hours....
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[ "<think>\n<sample>\n\nSure, let's break down the problem step by step:\n\n1. **Determine the number of patients served per day**:\n - Each visit takes 0.5 hours.\n - The dentist works for an 8-hour day.\n - Number of visits per day = Total working time / Time per visit\n \\[\n \\text{Number of visits per ...
160
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[ { "content": "Answer the following problem. Explain your reasoning step by step. When you are finished, give your answer in this format: <answer>(your answer)</answer>.\n\n# Problem\nAfter five years, Ron will be four times as old as Maurice. If Ron's age now is 43, how old is Maurice now?\n\nGive your answer i...
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[ "<think>\n<sample>\n\nTo solve this problem, let's break it down into steps:\n\n1. **Identify the given information:**\n - After five years, Ron will be four times as old as Maurice.\n - Ron's current age is 43.\n\n2. **Define variables for their ages:**\n - Let \\( R \\) represent Ron's current age.\n - Le...
7
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