2013 AMC 10B Problem 6

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?

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Solution

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 .

Tagged: mean