AMC12 2013 B

AMC12 2013 B · Q5

AMC12 2013 B · Q5. It mainly tests Averages (mean), Weighted average.

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?

33名五年级学生的平均年龄是11岁。他们55位家长的平均年龄是33岁。所有这些家长和五年级学生的平均年龄是多少？

(A) 22 22

(B) 23.25 23.25

(D) 26.25 26.25

(E) 28 28

Answer

Correct choice: (C)

正确答案：（C）

Solution

Answer (C): The sum of all the ages is $55\cdot 33 + 33\cdot 11 = 33\cdot 66$, so the average of all the ages is $$ \frac{33\cdot 66}{55+33}=\frac{33\cdot 66}{88}=\frac{33\cdot 3}{4}=24.75. $$

答案（C）：所有年龄的总和为$55\cdot 33 + 33\cdot 11 = 33\cdot 66$，因此所有年龄的平均数为 $$ \frac{33\cdot 66}{55+33}=\frac{33\cdot 66}{88}=\frac{33\cdot 3}{4}=24.75。 $$

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