2013 AMC 10B 第 6 题

Question

33

名五年级学生的平均年龄为

11

岁。他们的

55

位家长的平均年龄为

33

岁。所有这些家长和五年级学生的平均年龄是多少？

The average age of

33

fifth-graders is

11.

The average age of

55

of their parents is

33.

What is the average age of all of these parents and fifth-graders?

22

23.25

24.75

26.25

28

知识点：平均数

使用总年龄，而不是直接平均两个平均数。

Use total age, not the average of the two averages

计算

33\cdot11+55\cdot33

，再除以

88

。

Compute

33\cdot11+55\cdot33

and divide by

88

所有五年级学生和家长的年龄总和为

33\cdot 11+55\cdot 33 = 66\cdot 33\text{。}

平均年龄等于总年龄除以总人数，所以

\dfrac{66\cdot 33}{88} = \dfrac 34 \cdot 33 = 24.75\text{。}

所以正确答案是 C。

The sum of the ages of all the fifth-graders and their parents is:

33\cdot 11+55\cdot 33 = 66\cdot 33.

Then, as the average is the sum divided by the number of people, the average age must be:

\dfrac{66\cdot 33}{88} = \dfrac 34 \cdot 33 = 24.75 .

Thus, the correct answer is C .

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