Problem:
The mean of three numbers is 10 more than the least of the numbers and less than the greatest. The median of the three numbers is 5 . What is their sum?
Answer Choices:
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B.
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E.
Solution:
Since the median is 5 , we can write the three numbers as , and , where
If we add these equations, we get
and solving for gives . Hence the sum of the numbers 30 .
\section*{OR}
Let be the mean of the three numbers. Then the least of the numbers is and the greatest is . The middle of the three numbers is the median, 5. So
and . Hence, the sum of the three numbers is .
The problems on this page are the property of the MAA's American Mathematics Competitions