Answer
$m=60$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Use $
m=kxy
$ 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 $x$ and $y$, then $m=kxy.$ Substituting the given values, $
m=10,x=2,
$ and $
y=14
,$ then the value of $k$ is
\begin{array}{l}\require{cancel}
m=kxy
\\\\
10=k(2)(14)
\\\\
10=k(28)
\\\\
\dfrac{10}{28}=k
\\\\
k=\dfrac{5}{14}
.\end{array}
Hence, the equation of variation is given by
\begin{array}{l}\require{cancel}
m=kxy
\\\\
m=\dfrac{5}{14}xy
.\end{array}
If $x=21$ and $y=8,$ then
\begin{array}{l}\require{cancel}
m=\dfrac{5}{14}xy
\\\\
m=\dfrac{5}{14}(21)(8)
\\\\
m=\dfrac{5}{\cancel7(2)}\cancel7(3)(8)
\\\\
m=\dfrac{5}{2}(3)(8)
\\\\
m=\dfrac{5}{\cancel2}(3)\cancel2(4)
\\\\
m=5(3)(4)
\\\\
m=60
.\end{array}