In a middle-school mentoring program, a number of the sixth graders are paired with a ninth-grade student as a buddy. No ninth grader is assigned more than one sixth-grade buddy. If 13 of all the ninth graders are paired with 25 of all the sixth graders, what fraction of the total number of sixth and ninth graders have a buddy?

AMC 8 2015 Problem 16

AMC8 2015 年第 16 题

比与比例★★★☆☆

In a middle-school mentoring program, a number of the sixth graders are paired with a ninth-grade student as a buddy. No ninth grader is assigned more than one sixth-grade buddy. If \tfrac13 of all the ninth graders are paired with \tfrac25 of all the sixth graders, what fraction of the total number of sixth and ninth graders have a buddy?

在一所中学的一项导师项目中，由六年级学生和九年级学生成对组队完成项目。每个九年级学生都不能和超过 1 个六年级学生组成队友。如果的所有九年级学生和的所有六年级成对，那么已经组成队友的学生占了六年级和九年级总人数的比例是多少？

A. $\displaystyle \frac{2}{15}$
B. $\displaystyle \frac{4}{11}$
C. $\displaystyle \frac{11}{30}$
D. $\displaystyle \frac{3}{8}$
E. $\displaystyle \frac{11}{15}$

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