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abdulhakeem 2025-01-30 23:44:12 -06:00
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{
"question": "Katy makes coffee using teaspoons of sugar and cups of water in the ratio of 7:13. If she used a total of 120 teaspoons of sugar and cups of water, calculate the number of teaspoonfuls of sugar she used.",
"answer": "The total ratio representing the ingredients she used to make the coffee is 7+13 = <<7+13=20>>20\nSince the fraction representing the number of teaspoons she used is 7/20, she used 7/20*120 = <<7/20*120=42>>42\n#### 42",
"id_orig": 116,
"id_shuffled": 5,
"question_annotated": "{name,Katy} makes {drink,coffee} using teaspoons of sugar and cups of water in a ratio of {m,7}:{n,13}. She also uses {p,12} tablespoons of milk for every {nn,7} cups of water, and uses {pc,5} tablespoons of heavy cream for every teaspoon of sugar. She used a total of {x,120} teaspoons of sugar, cups of water, tablespoons of cream, and tablespoons of milk. How many teaspoons of sugar did she use?\n\n#init:\n- name = sample(names_female)\n- drink = sample(['coffee', 'tea'])\n- $m = range(44, 101)\n- $n = range(5, 51)\n- $p = range(5, 12)\n- $nn = range(2, 25)\n- $x = range(100, 250, 10)\n- $pc = range(2, 6)\n\n#conditions: \n- divides(p*n, nn)\n- m + n + p * (n/nn) + pc * m < x\n-is_int(x*(m/(m+n+p*n//nn+pc*m)))\n\n\n#answer: int(x*(m/(m+n+p*n//nn+pc*m)))",
"answer_annotated": "{name} uses {pc} tablespoons of cream for every teaspoon of sugar. For {m} teaspoons of sugar, she uses {pc} * {m} = {pc*m} tablespoons of heavy cream.\n{name} uses {p} tablespoons of milk for every {nn} cups of water. For {n} cups water she uses {p}*{n}/{nn} = {p*n//nn} tablespoons of milk.\nThe total ratio representing the ingredients she used to make the {drink} is {m} sugar +{n} water +{p*n//nn} milk + {pc*m} heavy cream= <<{m}+{n}+{p*n//nn}+{pc*m}={m+n+p*n//nn+pc*m}>>{m+n+p*n//nn+pc*m}.\nSince the fraction representing the number of teaspoons of sugar she used is {m}/{m+n+p*n//nn+pc*m}, she used {m}/{m+n+p*n//nn+pc*m}*{x} = <<{m}/{m+n+p*n//nn+pc*m}*{x}={x*(m/(m+n+p*n//nn+pc*m))}>>{int(x*(m/(m+n+p*n//nn+pc*m)))}\n#### {int(x*(m/(m+n+p*n//nn+pc*m)))}"
}