2011 AMC 12A 第 4 题

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

，和

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：加权平均数比与比例

难度评级：1040

小提示：

设五年级学生人数为

1

则四年级为

2

，三年级为

4

Let the number of fifth graders be

1,

so fourth graders is

2

and third graders is

4

大提示：

平均数为

\dfrac{4 \cdot 12 + 2 \cdot 15 + 1 \cdot 10}{4 + 2 + 1}

The average is

\dfrac{4 \cdot 12 + 2 \cdot 15 + 1 \cdot 10}{4 + 2 + 1}

解答：

三、四、五年级的人数比为

4 : 2 : 1

。加权平均数为

\begin{aligned} \dfrac{4\cdot12+2\cdot15+10}{7} \\ = \dfrac{48+30+10}{7} \\ = \dfrac{88}{7} \end{aligned}\text{。}

因此，正确答案是 C。

Take the grade sizes in the ratio

4 : 2 : 1

for third, fourth, and fifth grades. The weighted average is

\begin{aligned} \dfrac{4\cdot12+2\cdot15+10}{7} \\ = \dfrac{48+30+10}{7} \\ = \dfrac{88}{7}. \end{aligned}

Thus, the correct answer is C.

2011 AMC 12A 第 4 题

答案：C

难度评级：1040

小提示：

大提示：

解答：

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