Difference between revisions of "2013 AMC 12B Problems/Problem 5"
(Created page with "==Problem== The average age of <math>33</math> fifth-graders is <math>11</math>. The average age of <math>55</math> of their parents is <math>33</math>. What is the average age o...") |
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<math>\textbf{(A)}\ 22 \qquad \textbf{(B)}\ 23.25 \qquad \textbf{(C)}\ 24.75 \qquad \textbf{(D)}\ 26.25 \qquad \textbf{(E)}\ 28</math> | <math>\textbf{(A)}\ 22 \qquad \textbf{(B)}\ 23.25 \qquad \textbf{(C)}\ 24.75 \qquad \textbf{(D)}\ 26.25 \qquad \textbf{(E)}\ 28</math> | ||
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| + | ==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>. | ||
Revision as of 15:48, 22 February 2013
Problem
The average age of 
fifth-graders is 
. The average age of 
of their parents is . What is the average age of all of these parents and fifth-graders?
Solution
The sum of the ages of the fifth graders is 
, while the sum of the ages of the parents is 
. Therefore, the total sum of all their ages must be 
, and given 
people in total, their average age is 
.
