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2005 AMC 10A Problems/Problem 6

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Problem

The average (mean) of 20 numbers is 30, and the average of 30 other numbers is 20. What is the average of all 50 numbers?

\mathrm{(A) \ } 23\qquad \mathrm{(B) \ } 24\qquad \mathrm{(C) \ } 25\qquad \mathrm{(D) \ } 26\qquad \mathrm{(E) \ } 27

Solution

Since the average of the first 20 numbers is 30, their sum is 20\cdot30=600.

Since the average of 30 other numbers is 20, their sum is 30\cdot20=600.

So the sum of all 50 numbers is 600+600=1200

Therefore, the average of all 50 numbers is \frac{1200}{50}=24 \Longrightarrow \mathrm{(B)}

See Also

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