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2001 AMC 12 Problem 4

Problem 4 of 25EasierAlgebra

The mean of three numbers is 1010 more than the least of the numbers and 1515 less than the greatest. The median of the three numbers is 5.5. What is their sum?

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Solution

Let mm be the mean. The least number is m−10,m - 10, the greatest is m+15,m + 15, and the middle number is the median 5.5. Their sum is 3m,3m, so (m−10)+5+(m+15)=3m. (m - 10) + 5 + (m + 15) = 3m. This gives m=10,m = 10, so the sum of the three numbers is 3m=30.3m = 30. Thus, the correct answer is D.

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Concepts: mean · median (data) · linear equation

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.