2013 AMC 10B Problems/Problem 6

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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2013 AMC 10B Problems/Problem 6

Problem

Solution