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Difference between revisions of "2013 AMC 10B Problems/Problem 6"

(Created page with "==Problem== 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? <math>\t...")
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Revision as of 17:32, 21 February 2013

Problem

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?


$\textbf{(A)}\ 22\qquad\textbf{(B)}\ 23.25\qquad\textbf{(C)}\ 24.75\qquad\textbf{(D)}\ 26.25\qquad\textbf{(E)}\ 28$

Solution

The sum of the ages of the fifth graders is $33 * 11$, while the sum of the ages of the parents is $55 * 33$. Therefore, the total sum of all their ages must be $2178$, and given $33 + 55 = 88$ people in total, their average age is $\frac{2178}{88} = \frac{99}{4} = \boxed{\textbf{(C)}\ 24.75}$.

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