# If x varies inversely as y, and x = 11 when y = 15, how do you find x when y = 3?

Jun 7, 2017

$x = 55$

#### Explanation:

If $x$ varies inversely as $y$, then that means:

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

Let's multiply both sides of the equation by $x$ to find $k$.

$k = x y$

Plugging the numbers in:

$k = \left(11\right) \left(15\right) = 165$

Now, we go back to the original equation and solve for x:

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

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

Finally, plug $y = 3$ and $k = 165$:

$x = \frac{165}{3}$

$x = 55$