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2001 AMC 10 Problem 16

Problem 16 of 25IntermediateAlgebra

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−10m-10 and the greatest is m+15,m+15, with median 5.5. Since the mean of the three is m,m, 13((m−10)+5+(m+15))=m, \begin{aligned} &\tfrac13\big((m-10)+5+(m+15)\big) \\ &\quad =m, \end{aligned} which gives m=10.m=10. The sum 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.