# Assume y varies inversely as x, if y=12 when x=3, how do you find x when y=6?

Oct 27, 2017

$6$

#### Explanation:

$y \text{ }$varies inversely as $x$

$\implies y \propto \frac{1}{x}$

$\implies y = \frac{k}{x} \text{ for some constant } k$

$y = 12 \text{ when } x = 3$

$\therefore 12 = \frac{k}{3} \implies k = 36$

$\therefore y = \frac{36}{x}$

$y = 6$

$6 = \frac{36}{x}$

$\implies x = \frac{36}{6} = 6$