Answer
$y=\frac{5}{6}$
Work Step by Step
To find out the solution we need to follow the four-step procedure,
Step (1): As $y$ varies directly as $x$ and inversely as ${{z}^{2}}$ varies, we have
$y=k\frac{x}{{{z}^{2}}}$
Here $k$ is a constant.
Step (2):
Substitute $x=50$ , $y=20$ and $z=5$ in the equation $y=k\frac{x}{{{z}^{2}}}$ to find the value of k.
$\begin{align}
& 20=k\frac{50}{{{5}^{2}}} \\
& k=\frac{20\times 25}{50} \\
& k=10 \\
\end{align}$
Step (3): Substitute $k=10$ in the equation $y=k\frac{x}{{{z}^{2}}}$
$y=\left( 10 \right)\frac{x}{{{z}^{2}}}$
Step (4): Substitute $x=3\,\text{ and }\,z=6$ in the above equation to get:
$\begin{align}
& y=10\times \frac{3}{{{6}^{2}}} \\
& y=\frac{30}{36} \\
& y=\frac{15}{18} \\
& y=\frac{5}{6}
\end{align}$
