Answer
$x=36$
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=12
$ and $
y=4
,$ then the value of $k$ is
\begin{array}{l}\require{cancel}
12=k(4)
\\\\
\dfrac{12}{4}=k
\\\\
k=3
.\end{array}
Hence, the equation of variation is given by
\begin{array}{l}\require{cancel}
x=ky
\\\\
x=3y
.\end{array}
If $y=12,$ then
\begin{array}{l}\require{cancel}
x=3y
\\\\
x=3(12)
\\\\
x=36
.\end{array}
