# If y varies inversely as x and y = 6 when x = 18, then how do you find x when y = 10?

Sep 15, 2015

$x = 10.8$

#### Explanation:

If $y$ varies inversely as $x$ then
color(white)("XXX")xy =c color(white)("XXX")" for some constant " c

Given $\left(x , y\right) = \left(18 , 6\right)$ is a solution pair to this relation
$\textcolor{w h i t e}{\text{XXX}} \left(18\right) \left(6\right) = c$

$\rightarrow \textcolor{w h i t e}{\text{XXX}} c = 108$

$\rightarrow$ The relationship is
$\textcolor{w h i t e}{\text{XXX}} x y = 108$

therefore when $y = 10$
$\textcolor{w h i t e}{\text{XXX}} x \left(10\right) = 108$

$\rightarrow \textcolor{w h i t e}{\text{XXX}} x = 10.8$