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

Latest revision as of 11:10, 7 April 2013

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-==Problem==
+#REDIRECT [[2013 AMC 12B Problems/Problem 5]]
-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>\textbf{(A)}\ 22\qquad\textbf{(B)}\ 23.25\qquad\textbf{(C)}\ 24.75\qquad\textbf{(D)}\ 26.25\qquad\textbf{(E)}\ 28</math>
-==Solution==
-The sum of the ages of the fifth graders is <math>33 * 11</math>, while the sum of the ages of the parents is <math>55 * 33</math>. Therefore, the total sum of all their ages must be <math>2178</math>, and given <math>33 + 55 = 88</math> people in total, their average age is <math>\frac{2178}{88} = \frac{99}{4} = \boxed{\textbf{(C)}\ 24.75}</math>.