# If y varies inversely as x and y=5 when x=3 how do you find x when y is 15?

Sep 8, 2017

$x = 1$

#### Explanation:

$\text{the initial statement is } y \propto \frac{1}{x}$

$\text{to convert to an equation multiply by k the constant of}$
$\text{variation}$

$\Rightarrow y = \frac{k}{x}$

$\text{to find k use the given condition}$

$y = 5 \text{ when } x = 3$

$y = \frac{k}{x} \Rightarrow k = x y = 3 \times 5 = 15$

$\text{equation is } \textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{y = \frac{15}{x}} \textcolor{w h i t e}{\frac{2}{2}} |}}}$

$\text{when } y = 15$

$x = \frac{15}{y} = \frac{15}{15} = 1$