Problem:
Jefferson Middle School has the same number of boys and girls. Threefourths of the girls and two-thirds of the boys went on a field trip. What fraction of the students on the field trip were girls?
Answer Choices:
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Solution:
Converting the given fractions to the same denominator, we see that of the girls and of the boys went on the trip. So the ratio of the number of girls to the number of boys was , and it follows that of the students on the trip were girls.
The number of boys and girls must be a common multiple of and , the denominators of the fractions given in the problem. Suppose there are boys and girls in Jefferson Middle School. Then girls and boys went on the trip, for a total of students. The fraction of girls on the trip is .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions