If y varies directly with x, we can write the following relationship:
[tex]y=kx[/tex]where k is the constant of proportionallity. Now, when x=12, y is 5, then we get
[tex]5=k\cdot12[/tex]then, k is equal to
[tex]k=\frac{5}{12}[/tex]So, our relation is
[tex]y=\frac{5}{12}x[/tex]In order to find x, we must substitute y=12 in this last expression, that is,
[tex]12=\frac{5}{12}x[/tex]By moving 12 to the left hand side, we get
[tex]\begin{gathered} 12\times12=5x \\ 144=5x \\ x=\frac{144}{5} \\ x=28.8 \end{gathered}[/tex]then the answer is 28.8 which can be written as
[tex]28\frac{4}{5}[/tex]which corresponds to option a.
