# Z varies inversely with x and directly with y. When x=6, y= 2, z=5. What is the value of z when x=4 and y=9?

Jun 10, 2016

$z = 33.25$

#### Explanation:

As $z$ varies inversely with $x$ and directly with $y$, we can say

$z \propto \frac{y}{x}$ or $z = k \times \frac{y}{x}$, where $k$ is a constant.

Now as $z = 5$ when $x = 6$ and $y = 2$, we have

$5 = k \times \frac{2}{6}$ or $k = 5 \times \frac{6}{2} = 15$ i.e. $z = 15 \times \frac{y}{x}$

Hence, when $x = 4$ snd $y = 9$

$z = 15 \times \frac{9}{4} = \frac{135}{4} = 33.25$