1988 AHSME Problems/Problem 25
Problem
and are pairwise disjoint sets of people. The average ages of people in the sets and are and respectively. Find the average age of the people in set .
Solution
Let the variables , , and represent the sums of the ages of the people in sets , , and respectively. Let , , and represent the numbers of people who are in sets , , and respectively. Since the sets are disjoint, we know, for example, that the number of people in the set is and the sum of their ages is , and similar results apply for the other unions of sets. Thus we have , , , , and . Hence the answer is , which is . Notice that we did not need all three of the means of the unions of the sets - any two of them would have been sufficient to determine the answer.
See also
1988 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 24 |
Followed by Problem 26 | |
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