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8 lines
No EOL
2.8 KiB
JSON
8 lines
No EOL
2.8 KiB
JSON
{
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"question": "I have 10 liters of orange drink that are two-thirds water and I wish to add it to 15 liters of pineapple drink that is three-fifths water. But as I pour it, I spill one liter of the orange drink. How much water is in the remaining 24 liters?",
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"answer": "There are 15 x 3/5 = <<15*3/5=9>>9 liters of water from the 15 liters pineapple drink.\nAfter 1 liter of orange drink was spilled, there were 10 - 1 = <<10-1=9>>9 liters of orange drink left.\nOut of the 9 liters, 9 x 2/3 = <<9*2/3=6>>6 liters are water.\nThus, there are a total of 9 + 6 = <<9+6=15>>15 liters of water out of the 24 liters.\n#### 15",
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"id_orig": 20,
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"id_shuffled": 59,
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"question_annotated": "I have {n1,10} liters of {fruit1,orange} drink that is {frac1,two-thirds} water and I wish to add it to {n2,15} liters of {fruit2,pineapple} drink that is {frac2,three-fifths} water. But as I pour it, I spill {spill,one} liters of the {fruit1,orange} drink. To make up for that, I add {spill,one} liters of water to the mix. What percentage of the final mix is water?\n\n#init:\n- fruit1, fruit2 = sample([\"apple\", \"grape\", \"mango\", \"peach\", \"lemon\"], 2)\n- $n1 = range(9, 21)\n- $n2 = range(12, 31)\n- $frac1 = sample(fraction_alnum)\n- $frac2 = sample(fraction_alnum)\n- $spill = range(2, 11)\n\n#conditions:\n- spill < n1\n- is_int(n2 * frac2)\n- is_int((n1 - spill) * frac1)\n- is_int(n2 * frac2 + (n1 - spill) * frac1)\n- is_int((int(n2 * frac2 + (n1 - spill) * frac1) + spill) / (n1+n2) * 100)\n\n#answer: int((int(n2 * frac2 + (n1 - spill) * frac1) + spill) / (n1+n2) * 100)",
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"answer_annotated": "There are {n2} x {frac2} = <<{n2}*{frac2}={n2*frac2}>>{n2*frac2} liters of water from the {n2} liters {fruit2} drink.\nAfter {spill} liters of {fruit1} drink was spilled, there were {n1} - {spill} = <<{n1}-{spill}={n1-spill}>>{n1-spill} liters of {fruit1} drink left.\nOut of the {n1-spill} liters, {n1-spill} x {frac1} = <<{n1-spill}*{frac1}={(n1-spill)*frac1}>>{(n1-spill)*frac1} liters are water.\nThus, there are a total of {n2*frac2} + {(n1-spill)*frac1} = <<{n2*frac2}+{(n1-spill)*frac1}={n2*frac2 + (n1-spill)*frac1}>>{n2*frac2 + (n1-spill)*frac1} liters of water from the drinks. I also add {spill} liters of water. So the total amount of water is {n2*frac2 + (n1-spill)*frac1}+{spill} = {int(n2*frac2 + (n1-spill)*frac1) + spill} liters. \nWe know that the total amount of liquid in the final mix is {n1} (liters of {fruit1} drink) + {n2} (liters of {fruit2} drink) - {spill} (liters spilled) + {spill} (liters of water) = {n1+n2} liters.\nSo in total, the percentage of water in the final mix is {(int(n2 * frac2 + (n1 - spill) * frac1) + spill)} liters / {n1-spill+n2+spill} liters * 100% = {int((int(n2 * frac2 + (n1 - spill) * frac1) + spill)/(n1+n2) * 100)}%\n#### {int((int(n2 * frac2 + (n1 - spill) * frac1) + spill) / (n1+n2) * 100)}"
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} |