Answer
$y=50$
Work Step by Step
To find out the solution we need to follow the four-step procedure:
Step (1). As $y$ varies directly as $a$ , $b$ and inversely as $\sqrt{c}$ , we have
$y=k\frac{ab}{\sqrt{c}}$
Here $k$ is a constant.
Step (2).
Substitute $a=3$ , $b=2$ , $c=25$ and $y=12$ in $y=k\frac{ab}{\sqrt{c}}$
$\begin{align}
& 12=k\frac{3\times 2}{\sqrt{25}} \\
& k=\frac{12\times 5}{6} \\
& k=10 \\
\end{align}$
Step (3). Substitute the value of $k$ into the main equation.
$y=\left( 10 \right)\frac{ab}{\sqrt{c}}$
Step (4). Substitute the values $a=5,b=3,\,\text{ and }\,c=9$ in the above equation.
That is.,
$\begin{align}
& y=10\times \frac{5\times 3}{\sqrt{9}} \\
& y=\frac{150}{3} \\
& y=50 \\
\end{align}$
