Answer
$y=\dfrac{3}{2}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Use $
y=\dfrac{k}{x}
$ and solve for the value of $k$ with the given $y$ and $x$ values. Then use the equation of variation to solve for the value of the unknown variable.
$\bf{\text{Solution Details:}}$
Since $y$ varies inversely as $x$, then $y=\dfrac{k}{x}.$ Substituting the given values, $
y=10
$ and $
x=3
,$ then the value of $k$ is
\begin{array}{l}\require{cancel}
y=\dfrac{k}{x}
\\\\
10=\dfrac{k}{3}
\\\\
3\cdot10=\dfrac{k}{3}\cdot3
\\\\
30=k
.\end{array}
Hence, the equation of variation is given by
\begin{array}{l}\require{cancel}
y=\dfrac{k}{x}
\\\\
y=\dfrac{30}{x}
.\end{array}
If $x=20,$ then
\begin{array}{l}\require{cancel}
y=\dfrac{30}{x}
\\\\
y=\dfrac{30}{20}
\\\\
y=\dfrac{3}{2}
.\end{array}
