2013 AMC 12B 第 5 题

Question

33

名五年级学生的平均年龄是

11

。他们的

55

位家长的平均年龄是

33

。这些家长和五年级学生全体的平均年龄是多少？

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

总平均年龄等于所有年龄总和除以总人数。

The overall average is the total of all ages divided by the total number of people

年龄总和为

55\cdot 33 + 33\cdot 11

，人数为

55+33

。

The total age is

55\cdot 33 + 33\cdot 11,

spread over

55+33

people

家长年龄总和为

55\cdot 33

，五年级学生年龄总和为

33\cdot 11

，合计

33\cdot 66

。总人数为

88

，所以平均年龄为

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

。正确答案是 C。

The parents’ ages sum to

55\cdot 33

and the fifth-graders’ to

33\cdot 11,

a total of

33\cdot 66.

Dividing by

88

people gives

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

Thus, the correct answer is C.

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