Jefferson Middle School has the same number of boys and girls. (3/4) of the girls and (2/3) of the boys went on a field trip. What fraction of the students on the field trip were girls?

AMC 8 2016 Problem 12

AMC8 2016 年第 12 题

比与比例★★★☆☆

Jefferson Middle School has the same number of boys and girls.

\displaystyle \frac{3}{4}

of the girls and

\displaystyle \frac{2}{3}

of the boys went on a field trip. What fraction of the students on the field trip were girls?

Jefferson 中学的男生和女生数目相同。

\displaystyle \frac{3}{4}

的女生和

\displaystyle \frac{2}{3}

的男生去郊游。那么这些去郊游的学生中，有多少比例是女生？

正确答案 · Correct Answer

Solution 1

Let there be

b

boys and

g

girls in the school. We see g=b, which means

\displaystyle \frac{3}{4} b+ \frac{2}{3} b= \frac{17}{12} b

kids went on the trip and

\displaystyle \frac{3}{4} b

kids are girls. So, the answer is

\displaystyle \frac{\frac{3}{4} b}{ \frac{17}{12} b}= \frac{9}{17}

, which is

\displaystyle \frac{9}{17}

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