# Suppose that z varies jointly as u and v and inversely as w, and that z=.8 and when u=8, v=6, w=5. How do you find z when u=3, v=10 and w=5?

Sep 26, 2017

$z = \frac{4}{5}$

#### Explanation:

$\text{the initial statement is } z \propto \frac{u v}{w}$

$\text{to convert to an equation multiply by k the constant}$
$\text{of variation}$

$\Rightarrow z = \frac{k u v}{w}$

$\text{to find k use the given condition}$

$z = 0.8 \text{ when } u = 8 , v = 6 , w = 5$

$z = \frac{k u v}{w}$

$\Rightarrow k = \frac{w z}{u v} = \frac{5 \times 0.8}{3 \times 10} = \frac{0.8}{6} = \frac{8}{60} = \frac{2}{15}$

$\text{equation is } \textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{z = \frac{2 u v}{15 w}} \textcolor{w h i t e}{\frac{2}{2}} |}}}$

$\text{when "u=3,v=10" and } w = 5$

$\Rightarrow z = \frac{2 \times 3 \times 10}{15 \times 5} = \frac{60}{75} = \frac{4}{5}$