Answer
$m=36$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Use $
m=kzp
$ and solve for the value of $k$ with the given $m,x$ and $y$ values. Then use the equation of variation to solve for the value of the unknown variable.
$\bf{\text{Solution Details:}}$
Since $m$ varies jointly as $z$ and $p$, then $m=kzp.$ Substituting the given values, $
m=10,z=2,
$ and $
p=7.5
,$ then the value of $k$ is
\begin{array}{l}\require{cancel}
m=kzp
\\\\
10=k(2)(7.5)
\\\\
10=k(15)
\\\\
\dfrac{10}{15}=k
\\\\
k=\dfrac{2}{3}
.\end{array}
Hence, the equation of variation is given by
\begin{array}{l}\require{cancel}
m=kzp
\\\\
m=\dfrac{2}{3}zp
.\end{array}
If $z=6$ and $p=9,$ then
\begin{array}{l}\require{cancel}
m=\dfrac{2}{3}zp
\\\\
m=\dfrac{2}{3}(6)(9)
\\\\
m=\dfrac{2}{\cancel3}\cancel3(2)(9)
\\\\
m=2(2)(9)
\\\\
m=36
.\end{array}
