Answer
$y=\dfrac{1}{3}$
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=20
$ and $
x=\dfrac{1}{4}
,$ then the value of $k$ is
\begin{array}{l}\require{cancel}
y=\dfrac{k}{x}
\\\\
20=\dfrac{k}{\dfrac{1}{4}}
\\\\
\dfrac{1}{4}\cdot20=\dfrac{k}{\dfrac{1}{4}}\cdot\dfrac{1}{4}
\\\\
\dfrac{1}{\cancel4}\cdot\cancel{20}^5=\dfrac{k}{\cancel{\dfrac{1}{4}}}\cdot\cancel{\dfrac{1}{4}}
\\\\
5=k
.\end{array}
Hence, the equation of variation is given by
\begin{array}{l}\require{cancel}
y=\dfrac{k}{x}
\\\\
y=\dfrac{5}{x}
.\end{array}
If $x=15,$ then
\begin{array}{l}\require{cancel}
y=\dfrac{5}{x}
\\\\
y=\dfrac{5}{15}
\\\\
y=\dfrac{1}{3}
.\end{array}
