# If y varies inversely as x, how do you find x when y = 3 if y = 15 when x = 2?

Apr 25, 2016

$x = 10$

#### Explanation:

If $y$ varies inversely as $x$
then
$\textcolor{w h i t e}{\text{XXX}} \textcolor{b l u e}{x} \cdot \textcolor{red}{y} = \textcolor{g r e e n}{c}$ for some constant $c$

We are told when $\textcolor{red}{x = 2}$ then $\textcolor{b l u e}{y = 15}$
So
$\textcolor{w h i t e}{\text{XXX}} \textcolor{red}{2} \cdot \textcolor{b l u e}{15} = \textcolor{g r e e n}{c}$

$\textcolor{w h i t e}{\text{XXX}} \Rightarrow \textcolor{g r e e n}{c = 30}$
and
$\textcolor{w h i t e}{\text{XXX}} \textcolor{red}{\textcolor{red}{x}} \cdot \textcolor{b l u e}{y} = \textcolor{g r e e n}{30}$

Therefore when $\textcolor{b l u e}{y = 3}$
$\textcolor{w h i t e}{\text{XXX}} \textcolor{red}{x} \cdot \textcolor{b l u e}{3} = \textcolor{g r e e n}{30}$
$\textcolor{w h i t e}{\text{XXX}} \rightarrow \textcolor{red}{x} = 10$