# If y varies inversely as x and y = 12 when x = 3, how do you find y when x = 4?

Apr 20, 2016

$y = 9$ when $x = 4$

#### Explanation:

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

Given $y = \textcolor{red}{12}$ when $x = \textcolor{b l u e}{3}$
$\textcolor{w h i t e}{\text{XXX}} \textcolor{b l u e}{3} \cdot \textcolor{red}{12} = c$

$\textcolor{w h i t e}{\text{XXX}} \Rightarrow c = 36$

So
$\textcolor{w h i t e}{\text{XXX}} x \cdot y = 36$
and when $x = \textcolor{g r e e n}{4}$
$\textcolor{w h i t e}{\text{XXX}} \textcolor{g r e e n}{4} \cdot y = 36$

$\textcolor{w h i t e}{\text{XXX}} \Rightarrow y = 9$