# If x varies inversely as y and x=2 when y=8, how do you find x when y=17?

Mar 27, 2016

$x = \frac{16}{17}$

#### Explanation:

If $x$ varies inversely as $y$ then
$\textcolor{w h i t e}{\text{XXX}} y = \frac{c}{x}$ or equivalently $x y = c$
$\textcolor{w h i t e}{\text{XXXXXXXXX}}$for some constant $c$

If $x = 2$ when $y = 8$
then
$\textcolor{w h i t e}{\text{XXX}} x y = 2 \times 8 = 16 = c$

and, since $x y = 16$
$\textcolor{w h i t e}{\text{XXX}}$when $y = 17$$\textcolor{w h i t e}{\text{XXX}} x = \frac{16}{17}$