# If y varies jointly as x and z and inversely as w, and y = 3/2 when x=2, z=2, and w=4. How do you find the equation of variation for the given situation?

Oct 29, 2017

$y = \frac{3 x z}{2 w}$

#### Explanation:

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

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

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

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

$y = \frac{3}{2} \text{ when "x=2,z=2" and } w = 4$

$y = \frac{k x z}{w}$

$\Rightarrow k = \frac{w y}{x z} = \frac{4 \times \frac{3}{2}}{2 \times 2} = \frac{6}{4} = \frac{3}{2}$

$\text{equation is } \textcolor{red}{\overline{\underline{| \overline{\textcolor{w h i t e}{\frac{2}{2}}} \textcolor{b l a c k}{y = \frac{3 x z}{2 w}} \textcolor{w h i t e}{\frac{2}{2}} |}}}$