# Suppose that y varies directly with x and inversely with z, y=18 when x=15 and z=5. How do you write the equation that models the relationship, then find y when x=21 and z=7?

Apr 1, 2018

$y = 18$

#### Explanation:

$\text{the initial statement is } y \propto \frac{x}{z}$

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

$\Rightarrow y = k \times \frac{x}{z} = \frac{k x}{z}$

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

$y = 18 \text{ when "x=15" and } z = 5$

$y = \frac{k x}{z} \Rightarrow k = \frac{y z}{x} = \frac{18 \times 5}{15} = 6$

$\text{equation is } \textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{y = \frac{6 x}{z}} \textcolor{w h i t e}{\frac{2}{2}} |}}}$

$\text{when "x=21" and "z=7" then}$

$y = \frac{6 \times 21}{7} = 18$