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Sharing costs equally

Source: AMC 10 2011 b Problem 4

February 24, 2011
AMC

Problem Statement

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<BA < B. How many dollars must LeRoy give to Bernardo so that they share the costs equally?
<spanclass=latexbold>(A)</span> A+B2<spanclass=latexbold>(B)</span> AB2<spanclass=latexbold>(C)</span> BA2<spanclass=latexbold>(D)</span> BA<spanclass=latexbold>(E)</span> A+B <span class='latex-bold'>(A)</span>\ \frac{A+B}{2} \qquad <span class='latex-bold'>(B)</span>\ \frac{A-B}{2} \qquad <span class='latex-bold'>(C)</span>\ \frac{B-A}{2} \qquad <span class='latex-bold'>(D)</span>\ B-A \qquad <span class='latex-bold'>(E)</span>\ A+B