2013 AMC 10B Problem 6

Question

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

Concepts:mean

Use total age, not the average of the two averages

Compute

33\cdot11+55\cdot33

and divide by

88

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 .

Problem 6 in other years