Question

在一个中学导师项目中，一些六年级学生与一名九年级学生配成伙伴。没有九年级学生被分配超过一名六年级伙伴。如果所有九年级学生的 $\dfrac{1}{3}$ 与所有六年级学生的 $\dfrac{2}{5}$ 配成伙伴，那么六年级和九年级学生总数中有伙伴的比例是多少？

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

$\dfrac{2}{15}$

$\dfrac{4}{11}$

$\dfrac{11}{30}$

$\dfrac{3}{8}$

$\dfrac{11}{15}$

答案：B

知识点：比与比例分数

难度评级：1300

视频讲解：

Click to load, then click again to play

文字解答：

设六年级学生有 $s$ 人，九年级学生有 $n$ 人。配对的九年级学生数等于配对的六年级学生数，所以 $\dfrac13 n=\dfrac25 s.$

得 $5n=6s$ ，所以 $n:s=6:5$ 。学生总数对应 $11$ 份。

配对的九年级学生占全体学生的 $\dfrac13\cdot\dfrac6{11}=\dfrac2{11}$ ，配对的六年级学生占全体学生的 $\dfrac25\cdot\dfrac5{11}=\dfrac2{11}$ 。合计有 $\dfrac4{11}$ 的学生有伙伴。

所以正确答案是 B。

Let there be $s$ sixth graders and $n$ ninth graders. The number of paired ninth graders equals the number of paired sixth graders, so $\dfrac13 n=\dfrac25 s.$

This gives $5n=6s$ , so $n:s=6:5$ . The total number of students is therefore proportional to $11$ parts.

The paired ninth graders make up $\dfrac13\cdot\dfrac6{11}=\dfrac2{11}$ of all students, and the paired sixth graders make up $\dfrac25\cdot\dfrac5{11}=\dfrac2{11}$ of all students. Altogether, $\dfrac4{11}$ of the students have a buddy.

Thus, B is the correct answer.

2015 AMC 8 第 16 题

答案：B

难度评级：1300

视频讲解：

文字解答：

其他年份的第 16 题