AMC10 2011 A

AMC10 2011 A · Q5

AMC10 2011 A · Q5. It mainly tests Weighted average.

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?

在一所小学，三、四年级和五年级学生的平均每天跑步时间分别为12、15和10分钟。三四年级学生人数是四年级学生的两倍，四年级学生人数是五年级学生的两倍。这些学生的平均每天跑步分钟数是多少？

(A) 12 12

(B) $\frac{37}{3}$ $\frac{37}{3}$

(D) 13 13

(E) 14 14

Answer

Correct choice: (C)

正确答案：（C）

Solution

Let $N$ equal the number of fifth graders. Then there are $2N$ fourth graders and $4N$ third graders. The total number of minutes run per day by the students is $4N \cdot 12 + 2N \cdot 15 + N \cdot 10 = 88N$. There are a total of $4N + 2N + N = 7N$ students, so the average number of minutes run by the students per day is $\frac{88N}{7N} = \frac{88}{7}$.

设五年级学生数为$N$，则四年级学生为$2N$，三年级学生为$4N$。学生每天总跑步时间为$4N \cdot 12 + 2N \cdot 15 + N \cdot 10 = 88N$。总学生数为$4N + 2N + N = 7N$，因此平均值为$\frac{88N}{7N} = \frac{88}{7}$。

Topics

AR.013 Weighted average