Answer
$m=36$
Work Step by Step
$m$ 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:
$\require{cancel}
\\m=\frac{2}{3}pz
\\m=\frac{2}{3}(9)(6)
\\m=\frac{2}{\cancel{3}}(\cancel{9}3)(6)
\\m=2(3)(6)
\\m=36$
