Answer
$y=35$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Use $
x=ky
$ and solve for the value of $k$ with the given $
x
$ and $
y
$ values. Then use the equation of variation to solve for the value of the unknown variable.
$\bf{\text{Solution Details:}}$
Since $x$ varies directly as $y,$ then $
x=ky
.$ Substituting the given values, $
x=20
$ and $
y=14
,$ then the value of $k$ is
\begin{array}{l}\require{cancel}
x=ky
\\\\
20=k(14)
\\\\
\dfrac{20}{14}=k
\\\\
k=\dfrac{10}{7}
.\end{array}
Hence, the equation of variation is given by
\begin{array}{l}\require{cancel}
x=ky
\\\\
x=\dfrac{10}{7}y
.\end{array}
If $x=50,$ then
\begin{array}{l}\require{cancel}
x=\dfrac{10}{7}y
\\\\
50=\dfrac{10}{7}y
\\\\
\dfrac{7}{10}(50)=\left( \dfrac{10}{7}y \right) \dfrac{7}{10}
\\\\
\dfrac{7}{\cancel{10}}(\cancel{50}^5)=y
\\\\
y=7(5)
\\\\
y=35
.\end{array}