# If y varies inversely as x, and y = 3 when x = 6, what is x when y=18?

Apr 6, 2017

$x = 1$

#### Explanation:

$y$ varies inversely as $x$ means that

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

$\implies y = k \cdot \frac{1}{x} = \frac{k}{x}$ where $k$ is some constant.

to find $k$, substitute the given values $y = 3$ when $x = 6$

$i . e . 3 = \frac{k}{6} \implies k = 3 \cdot 6 = 18$

$\therefore$ the equation becomes:- $y = \frac{18}{x}$.

Now substituting $y = 18$ in this equation;

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

Hence $x = 1$ when $y = 18$