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Part of 2013 AMC 8

Problems(1)

2013/8/15/Solving for three variables

Source:

11/27/2013
If 3p+34=903^p + 3^4 = 90, 2r+44=762^r + 44 = 76, and 53+6s=14215^3 + 6^s = 1421, what is the product of pp, rr, and ss?
<spanclass=′latex−bold′>(A)</span> 27<spanclass=′latex−bold′>(B)</span> 40<spanclass=′latex−bold′>(C)</span> 50<spanclass=′latex−bold′>(D)</span> 70<spanclass=′latex−bold′>(E)</span> 90<span class='latex-bold'>(A)</span>\ 27 \qquad <span class='latex-bold'>(B)</span>\ 40 \qquad <span class='latex-bold'>(C)</span>\ 50 \qquad <span class='latex-bold'>(D)</span>\ 70 \qquad <span class='latex-bold'>(E)</span>\ 90
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