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Direct and inverse proportions

Source: 1959 AHSME Problem 20

August 13, 2013
AMCdirect proportioninversely proportionalalgebraAMC 12

Problem Statement

It is given that xx varies directly as yy and inversely as the square of zz, and that x=10x=10 when y=4y=4 and z=14z=14. Then, when y=16y=16 and z=7z=7, xx equals: <spanclass=′latex−bold′>(A)</span> 180<spanclass=′latex−bold′>(B)</span> 160<spanclass=′latex−bold′>(C)</span> 154<spanclass=′latex−bold′>(D)</span> 140<spanclass=′latex−bold′>(E)</span> 120 <span class='latex-bold'>(A)</span>\ 180\qquad<span class='latex-bold'>(B)</span>\ 160\qquad<span class='latex-bold'>(C)</span>\ 154\qquad<span class='latex-bold'>(D)</span>\ 140\qquad<span class='latex-bold'>(E)</span>\ 120
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