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8 lines
No EOL
2.4 KiB
JSON
8 lines
No EOL
2.4 KiB
JSON
{
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"question": "Elise is learning to write and decides to keep re-writing the alphabet until she knows it. She writes it in full twice, writes half of it once, then re-writes everything she has already written. How many letters has Elise written in total?",
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"answer": "Elise has written the alphabet twice which is a total of 26 * 2 = <<26*2=52>>52 letters.\nShe then writes half the alphabet, which is 26 / 2 = <<26/2=13>>13 letters.\nSo far, this is a total of 52 + 13 = <<52+13=65>>65 letters.\nWriting this again means she has doubled the number of letters she has written, so she has written a total of 65 * 2 = <<65*2=130>>130 letters.\n#### 130",
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"id_orig": 546,
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"id_shuffled": 55,
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"question_annotated": "{name,Elise} is learning to write and decides to keep re-writing the {alphabets,alphabet} until she knows it. She writes it in full {n1,twice}, writes {frac,half} of it once, then re-writes everything she has already written. After some rest, again she re-writes everything she has written so far. How many letters has {name,Elise} written in total?\n\n#init:\n- name = sample(names_female)\n- $alphabets = sample([(\"alphabet\", 26), (\"hiragana (with 48 letters)\", 48), (\"farsi alphabet (with 32 letters)\", 32), (\"arabic abjad (with 28 letters)\", 28) ])\n- $n1 = sample(multi_times)\n- $frac = sample(fraction_alnum)\n\n#conditions:\n- is_int(alphabets * frac)\n\n#answer: 4 * (alphabets * n1 + alphabets * frac)",
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"answer_annotated": "{name} has written the alphabets {n1} time(s) which is a total of {alphabets} * {n1} = <<{alphabets}*{n1}={alphabets*n1}>>{alphabets*n1} letters.\nShe then writes {frac} the {alphabets}, which is {alphabets} * {frac} = <<{alphabets}*{frac}={int(alphabets*frac)}>>{int(alphabets*frac)} letters.\nSo far, this is a total of {alphabets*n1} + {int(alphabets*frac)} = <<{alphabets*n1}+{int(alphabets*frac)}={alphabets*n1 + int(alphabets*frac)}>>{alphabets*n1 + int(alphabets*frac)} letters.\nRe-writing all of this again means she has doubled the number of letters she has written, so she has written a total of {alphabets*n1 + int(alphabets*frac)} * 2 = <<{alphabets*n1 + int(alphabets*frac)}*2={2*(alphabets*n1 + int(alphabets*frac))}>> {2*(alphabets*n1 + int(alphabets*frac))} letters. \nShe then re-writes all of {2*(alphabets*n1 + int(alphabets*frac))} again after rest, so the final answer is {2*(alphabets*n1 + int(alphabets*frac))} * 2 = {4*(alphabets*n1 + int(alphabets*frac))}.\n#### {4*(alphabets*n1 + int(alphabets*frac))}"
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} |