# Assume that y varies inversely with x. If y = 3.75 when x = 9, what is x when y = 6.75?

Sep 3, 2016

$x = 5$

#### Explanation:

If $y$ varies inversely as $x$, this means $y \propto \frac{1}{x}$ i.e. y=k×1/x, where $k$ is a constant.

Hence, $x y = k$

Now as $y = 3.75$, when $x = 9$,

k=9×3.75=33.75

And so if $y = 6.75$,

$x = \frac{k}{y} = \frac{33.75}{6.75}$

= $\frac{3375}{675}$

= (3×3×3×5×5×5)/(3×3×3×5×5)

= $5$