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January 2, 2009
number theoryprime factorization

Problem Statement

If a a, b b, and c c are positive real numbers such that a(b \plus{} c) \equal{} 152, b(c \plus{} a) \equal{} 162, and c(a \plus{} b) \equal{} 170, then abc is <spanclass=′latex−bold′>(A)</span> 672<spanclass=′latex−bold′>(B)</span> 688<spanclass=′latex−bold′>(C)</span> 704<spanclass=′latex−bold′>(D)</span> 720<spanclass=′latex−bold′>(E)</span> 750 <span class='latex-bold'>(A)</span>\ 672 \qquad <span class='latex-bold'>(B)</span>\ 688 \qquad <span class='latex-bold'>(C)</span>\ 704 \qquad <span class='latex-bold'>(D)</span>\ 720 \qquad <span class='latex-bold'>(E)</span>\ 750
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