2013 AMC 10B Problem 6

Attempt Problem 6 of the 2013 AMC 10B 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 10B solutions, or check the answer key.

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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?

$22$

$23.25$

$24.75$

$26.25$

$28$

Answer: C

Concepts:mean

Difficulty rating: 900

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 .

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