# If y varies directly as x, and y is 180 when x is n and y is n when x is 5, what is the value of n?

Jun 25, 2017

n = 30

#### Explanation:

Let's write a proportion to represent this problem!

1. When $y = 180$, $x = n$. If we write the value of y on the top and x on the bottom, one side of the proportion is:

$\frac{180}{n}$

2. When $y = n$, $x = 5$. So the other side of the proportion would be:

$\frac{180}{n} = \frac{n}{5}$

3. Cross multiply.

$180 \left(5\right) = n \left(n\right)$
$900 = {n}^{2}$

4. Take the square root of both sides to find $n$.

$\sqrt{900} = \sqrt{{n}^{2}}$

$30 = n$

Does $\frac{180}{30}$ equal $\frac{30}{5}$?