2013 AMC 12B Problem 5

Below is the professionally curated solution for Problem 5 of the 2013 AMC 12B, 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.

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Concepts:mean

Difficulty rating: 1270

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?

$22$

$23.25$

$24.75$

$26.25$

$28$

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.

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