2013 AMC 12B Problem 5

Attempt Problem 5 of the 2013 AMC 12B below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2013 AMC 12B solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

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

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

The total age is

55\cdot 33 + 33\cdot 11,

spread over

55+33

people

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.

Problem 5 in other years