Question

在一所小学，三年级、四年级、五年级学生每天平均分别跑 $12$ 、 $15$ 、 $10$ 分钟。三年级学生人数是四年级的两倍，四年级学生人数是五年级的两倍。这些学生每天平均跑多少分钟？

At an elementary school, the students in third grade, fourth grade, and fifth grade run an average of $12,$ $15,$ and $10$ minutes per day, respectively. There are twice as many third graders as fourth graders, and twice as many fourth graders as fifth graders. What is the average number of minutes run per day by these students?

$12$

$\dfrac{37}{3}$

$\dfrac{88}{7}$

$13$

$14$

答案：C

知识点：平均数比与比例

难度评级：1070

解答：

不妨设五年级有一人，则四年级有两人，三年级有四人。

这样做可以，因为平均数不受学生人数整体倍数的影响。

总跑步时间为分钟。总人数为 $1 + 2 + 4 = 7$ ，所以平均数为 $\dfrac{88}{7}$ 。 $12 \cdot 4 + 15 \cdot 2 + 10 = 88$

所以正确答案是 C。

WLOG, let there be one fifth grader. This then tells us that there are two fourth graders and four third graders.

We can do this, since we are only interested in the average, which is not impacted by the exact number of students.

The total number of minutes the students spend running is $12 \cdot 4 + 15 \cdot 2 + 10 = 88$ minutes. The total number of students is $1 + 2 + 4 = 7.$ The average is then $\dfrac{88}{7}.$

Thus, C is the correct answer.

2011 AMC 10A 第 5 题

答案：C

难度评级：1070

解答：

其他年份的第 5 题