2002 AMC 12B Problem 19

If a,b, and c are positive real numbers such that a(b+c) = 152, b(c+a) = 162, and c(a+b) = 170, then abc is

\mathrm{(A)}\ 672 \qquad\mathrm{(B)}\ 688 \qquad\mathrm{(C)}\ 704 \qquad\mathrm{(D)}\ 720 \qquad\mathrm{(E)}\ 750

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.