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abdulhakeem 2025-01-30 23:44:12 -06:00
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{
"question": "Comet Halley orbits the sun every 75 years. Bill's dad saw the Comet when he was 30 years old. Bill saw the comet a second time when he was three times the age his father was when he saw the Comet. How old was Bill when he saw the Comet for the first time?",
"answer": "Bill saw the Comet for the second time when he was 30 years * 3= <<30*3=90>>90 years old.\nComet Halley can be seen every 75 years, so Bill saw the comet for the first time when he was 90 years - 75 years = <<90-75=15>>15 years old.\n#### 15",
"id_orig": 991,
"id_shuffled": 73,
"question_annotated": "Comet {comet_name,Halley} orbits the Sun every {orbit_period,75} years. {name,Bill}'s {relative,dad} saw the comet when he was {relative_age,30} years old. {name,Bill} saw the comet for the second time when he was {multiple,three times} the age his {relative,father} was when he first saw the comet. How much older is {name,Bill}'s {relative,grandfather} than {name,Bill}?\n\n#init:\n- comet_name = sample(['Halley', 'Hale-Bopp', 'Hyakutake', 'Encke'])\n- name = sample(names_male)\n- relative = sample(['dad', 'father', 'uncle'])\n- $orbit_period = list(range(15, 66))*2\n- $relative_age = range(15, 51)\n- $multiple = sample(multi_times)\n\n#conditions:\n- relative_age < orbit_period\n- multiple * relative_age < 120\n- multiple * relative_age > orbit_period\n- is_int(multiple * relative_age - orbit_period)\n- relative_age-(multiple * relative_age - orbit_period) > 20\n- relative_age + orbit_period < 120\n- relative_age-(multiple * relative_age - orbit_period) > 0\n\n#answer: relative_age-(multiple * relative_age - orbit_period)",
"answer_annotated": "{name} saw the comet for the second time when he was {relative_age} years * {multiple}= <<{relative_age}*{multiple}={relative_age*multiple}>>{relative_age*multiple} years old.\nComet {comet_name} can be seen every {orbit_period} years, so {name} saw the comet for the first time when he was {relative_age*multiple} years - {orbit_period} years = <<{relative_age*multiple}-{orbit_period}={relative_age*multiple-orbit_period}>>{relative_age*multiple-orbit_period} years old.\nWe know that {relative}'s age when he saw the Comet for the first time was {relative_age}. So the age difference between {name} and his {relative} is: {relative_age} - {(multiple * relative_age - orbit_period)} = {relative_age-(multiple * relative_age - orbit_period)}\n#### {relative_age-(multiple * relative_age - orbit_period)}"
}