# If y=5 when x=6, how do you find x when y=2 given y varies inversely as x?

Jun 11, 2017

$x = 15$

#### Explanation:

$y \text{ }$ varies inversely with $x \implies y \propto \frac{1}{x}$

$\therefore y = \frac{k}{x} \text{ }$ where $k \text{ }$ is the constant of proportionality

to find $\text{ } k$

$y = 5 , x = 6$

$5 = \frac{k}{6} \implies k = 30$

$\therefore y = \frac{30}{x}$

$y = 2$

$2 = \frac{30}{x}$

$x = \frac{30}{2} = 15$