# If y varies inversely as x and y = 725 when x = 20, how do you find x when y is 50?

Jan 4, 2017

$x = 290$ when $y = 50$

#### Explanation:

When you are told that $y$ varies inversely as $x$, that means that

$x \cdot y = k$

where $k$ can be any single number. If you plug in the initially given numerical values for $x$ and $y$ you have

$20 \cdot 725 = 14500$

So your $k$-value becomes $14500$. Now you can say that, for this particular relation

$x y = 14500$

If you want to know your $x$-value when $y = 50$, you can plug $50$ in for $y$ and solve for $x$.

$x \cdot 50 = 14500$

so

$x = \frac{14500}{50}$

meaning that

$x = 290$.