# If y=3.8 when x=1.5, how do you find x when y=0.3 given that y varies inversely as x?

Jul 12, 2017

$x = 19$

#### Explanation:

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

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

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

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

$y = 3.8 \text{ when } x = 1.5$

$y = \frac{k}{x} \Rightarrow k = x y = 1.5 \times 3.8 = 5.7$

$\text{equation is } \textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{y = \frac{5.7}{x}} \textcolor{w h i t e}{\frac{2}{2}} |}}}$

$\text{when } y = 0.3$

$y = \frac{5.7}{x} \Rightarrow x = \frac{5.7}{y} = \frac{5.7}{0.3} = 19$