2013 AMC 12B Problem 5

Problem 5 of 25EasierAlgebra

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 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.

Concepts: mean

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.