# If y varies inversely as x, and y = 3 when x = 6, how do you find the value of x when y = 18?

Feb 26, 2018

$x = 1$

#### Explanation:

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

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

$\Rightarrow y = k \times \frac{1}{x} \Rightarrow y = \frac{k}{x}$

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

$y = \frac{k}{x} \Rightarrow k = y x = 3 \times 6 = 18$

$\text{equation is } \textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{y = \frac{18}{x}} \textcolor{w h i t e}{\frac{2}{2}} |}}}$

$\text{when "y=18" then}$

$x = \frac{18}{y} = \frac{18}{18} = 1$