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abdulhakeem 2025-01-30 23:44:12 -06:00
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{
"question": "Mia and Emma are currently 16 years apart in age. If Mia, who is younger than Emma, is 40 years old, what's the average of their ages?",
"answer": "If Mia is 40 years old, Emma is 40+16 = <<40+16=56>>56 years old.\nThe sum of their ages is 56+40 = <<56+40=96>>96 years\nThe average age of the two is 96/2 = <<96/2=48>>48 years\n#### 48",
"id_orig": 1277,
"id_shuffled": 31,
"question_annotated": "{name1,Mia}, {name2,Emma} are currently {age_diff,16} years apart in age. {name1,Mia} and {name3,Rose} are currently {age_diff2,15} years apart. {name1,Mia}, who is younger than {name2,Emma} but older than {name3, Rose}, will be {age1,40} in {next,4} years. How much younger is {name3,Rose} than the average age of all three?\n\n\n#init:\n- name1, name2, name3 = sample(names, 3)\n- $age_diff = range(8, 30)\n- $age_diff2 = range(7, 20)\n- $age1 = range(15, 75)\n- $next = range(4, 11)\n\n#conditions:\n- is_int((3*(age1-next) + age_diff - age_diff2) / 3)\n- (age1-next) - age_diff2 > 0\n- ((3*(age1-next) + age_diff - age_diff2) // 3) - (age1-next-age_diff2) > 5\n\n#answer: ((3*(age1-next) + age_diff - age_diff2) // 3) - (age1-next-age_diff2)",
"answer_annotated": "If {name1} is {age1} years old in {next} years. So {name1} is {age1} - {next} = {age1-next} years old.\nSo {name2} is {age1-next}+{age_diff} = <<{age1-next}+{age_diff}={age1-next+age_diff}>>{age1-next+age_diff} years old.\nIf {name1} is {age1-next} years old, {name3} is {age1-next}-{age_diff2} = <<{age1-next}-{age_diff2}={age1-next-age_diff2}>>{age1-next-age_diff2} years old.\nThe sum of their ages is {age1-next+age_diff}+{age1-next} + {age1-next-age_diff2} = <<{age1-next+age_diff}+{age1-next}+{age1-next-age_diff2}={3*(age1-next)+age_diff - age_diff2}>>{3*(age1-next)+age_diff-age_diff2} years\nThe average age of the three is {3*(age1-next)+age_diff-age_diff2}/3 = <<{3*(age1-next)+age_diff-age_diff2}/3={(3*(age1-next)+age_diff-age_diff2)//3}>>{(3*(age1-next)+age_diff-age_diff2)//3} years.\nSo {name3} is {(3*(age1-next)+age_diff-age_diff2)//3} - {age1-next-age_diff2} = {(3*(age1-next)+age_diff-age_diff2)//3 - (age1-next-age_diff2)} years younger than the average.\n#### {(3*(age1-next)+age_diff-age_diff2)//3 - (age1-next-age_diff2)}"
}