## Precalculus (6th Edition)

$m=36$
$m$ varies jointly as $z$ and $p$ therefore $m=kzp$ $m=10$ when $z=2$ and $p=7.5$. Substitute these values into $m=kxy$ to obtain: $m=kpz \\10=k(7.5)(2) \\10=15k \\\frac{10}{15}=\frac{15k}{15} \\\frac{2}{3}=k$ Thus, the equation for $m$ is $m=\frac{2}{3}pz$. To find the value of $m$ when $z=6$ and $p=9$, substitute 6 to z and 9 to p in the equation above to obtain: $\require{cancel} \\m=\frac{2}{3}pz \\m=\frac{2}{3}(9)(6) \\m=\frac{2}{\cancel{3}}(\cancel{9}3)(6) \\m=2(3)(6) \\m=36$