AMC8 2015

AMC8 2015 · Q16

AMC8 2015 · Q16. It mainly tests Linear equations, Fractions.

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 $\frac{1}{5}$ of all the ninth graders are paired with $\frac{2}{3}$ of all the sixth graders, what fraction of the total number of sixth and ninth graders have a buddy?

在中学导师计划中，一些六年级学生与九年级学生配对成为伙伴。没有九年级学生被分配超过一个六年级伙伴。如果所有九年级学生的 $\frac{1}{5}$ 与所有六年级学生的 $\frac{2}{3}$ 配对，那么六年级和九年级学生总数中有多少分数的人有伙伴？

(A) $\frac{2}{15}$ $\frac{2}{15}$

(B) $\frac{4}{11}$ $\frac{4}{11}$

(D) $\frac{3}{8}$ $\frac{3}{8}$

(E) $\frac{11}{15}$ $\frac{11}{15}$

Answer

Correct choice: (B)

正确答案：（B）

Solution

Answer (B): 2 out of every 5 sixth graders are paired with a ninth grade buddy, and 2 out of every 6 ninth graders are paired with a sixth grade buddy. (The ratios are now expressed so that the number of sixth graders matches the number of ninth graders.) So 4 out of every 11 students are in the mentoring program. The fraction is $\frac{4}{11}$.

答案（B）：每 5 名六年级生中有 2 人与九年级伙伴配对，而每 6 名九年级生中有 2 人与六年级伙伴配对。（现在用这样的比例表示，使六年级生的人数与九年级生的人数相匹配。）所以每 11 名学生中有 4 人在辅导项目中。所求分数为 $\frac{4}{11}$。

Topics