# If q is inversely proportional to p, and q = 3 / 2 when p = 72 how do you write the equation?

Apr 17, 2018

$q = \frac{108}{p}$

#### Explanation:

$\text{the initial statement is } q \propto \frac{1}{p}$

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

$\Rightarrow q = k \times \frac{1}{p} = \frac{k}{p}$

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

$q = \frac{k}{p} \Rightarrow k = q p = \frac{3}{2} \times 72 = 108$

$\text{equation is } \textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{q = \frac{108}{p}} \textcolor{w h i t e}{\frac{2}{2}} |}}}$