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abdulhakeem 2025-01-30 23:44:12 -06:00
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{
"question": "Jennifer's dog has 8 puppies, 3 of which have spots. Brandon's dog has 12 puppies, 4 of which have spots. What percentage of all the puppies have spots?",
"answer": "First find the total number of puppies: 8 puppies + 12 puppies = <<8+12=20>>20 puppies\nThen find the total number of puppies with spots: 3 puppies + 4 puppies = <<3+4=7>>7 puppies\nThen divide the number of spotted puppies by the total number of puppies and multiply by 100% to find the percentage of puppies with spots: 7 puppies / 20 puppies * 100% = 35%\n#### 35",
"id_orig": 458,
"id_shuffled": 15,
"question_annotated": "{name1, Jennifer}'s dog has {n1, 8} puppies, {k1,3} of which have spots. {name2, Brandon}'s dog has {n2,12} puppies, {k2,4} of which have spots. {name3, Gordon} has {n3, 10} dogs, each having {k3,4} puppies with spots. After a visit to the vet, {name1,Jennifer} discovered that half of his unspotted puppies actually have spots that were not visible before. What percentage of all the puppies have spots?\n\n#init:\n- name1, name2, name3 = sample(names_male, 3)\n- $n1 = range(95, 150)\n- $n2 = range(40, 65)\n- $n3 = range(50, 70)\n- $k1 = range(17, 29)\n- $k2 = range(12, 17)\n- $k3 = range(9, 17)\n\n#conditions:\n- divides(n1-k1, 2)\n- is_int(100 * (k1+(n1-k1)//2+k2+n3*k3) / (n1+n2+n3*k3))\n\n#answer: int(100 * (k1+(n1-k1)//2+k2+n3*k3) / (n1+n2+n3*k3))",
"answer_annotated": "First find the total number of puppies: {n1} puppies + {n2} puppies + {n3}*{k3} puppies = <<{n1}+{n2}+{n3}*{k3}={n1+n2+n3*k3}>>{n1+n2+n3*k3} puppies\nThen find the total number of puppies with spots: {k1} puppies + {k2} puppies + {n3*k3}= <<{k1}+{k2}+{n3*k3}={k1+k2+n3*k3}>>{k1+k2+n3*k3} puppies.\nBut after the vet visit we know that half of the {name1}'s unspotted puppies were actually spotted. So 1/2 * ({n1}-{k1}) = 1/2 * {n1-k1} = {(n1-k1)//2} puppies. We should add these to the total spotted puppies. {k1+k2+n3*k3} + {(n1-k1)//2} = {k1+k2+n3*k3+(n1-k1)//2}.\nThen divide the number of spotted puppies by the total number of puppies and multiply by 100% to find the percentage of puppies with spots: {k1+k2+n3*k3+(n1-k1)//2} puppies / {n1+n2+n3*k3} puppies * 100% = {int(100 * (k1+k2+n3*k3+(n1-k1)//2) / (n1+n2+n3*k3))}%\n#### {int(100 * (k1+k2+n3*k3+(n1-k1)//2) / (n1+n2+n3*k3))}"
}