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2011 AMC 12B Problem 3

Problem 3 of 25EasierAlgebra

LeRoy and Bernardo went on a week-long trip together and agreed to share the costs equally. Over the week, each of them paid for various joint expenses such as gasoline and car rental. At the end of the trip it turned out that LeRoy had paid AA dollars and Bernardo had paid BB dollars, where A<B.A \lt B. How many dollars must LeRoy give to Bernardo so that they share the costs equally?

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Solution

The total cost is A+B,A+B, so each person’s fair share is A+B2.\dfrac{A+B}{2}. LeRoy paid A,A, which is less than his share, so he must give Bernardo A+B2A=BA2. \dfrac{A+B}{2}-A=\dfrac{B-A}{2}. Thus, the correct answer is C.

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Concepts: algebraic manipulation

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