# If x varies inversely with y and x = 8 when y = 6, how do you find y when x = 10?

May 28, 2015

If $x$ varies inversely with $y$
then $x \cdot y = c$ for some constant $c$

Given $\left(x , y\right) = \left(8 , 6\right)$ is a solution to the desired inverse variation:
$\left(8\right) \cdot \left(6\right) = c$
$\rightarrow c = 48$
and the desired inverse variation is $x y = 48$

When $x = 10$
$10 y = 48$
$\rightarrow y = 4.8$