# If r varies jointly as p and q and inversely as t, then how do you find an equation for r if r=6 when p=8, q=−3, and t=3?

Jul 30, 2017

$r = - \frac{3 p q}{4 t}$

#### Explanation:

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

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

$\Rightarrow r = \frac{k p q}{t}$

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

$r = 6 \text{ when "p=8,q=-3" and } t = 3$

$r = \frac{k p q}{t}$

$\Rightarrow k p q = r t \leftarrow \textcolor{b l u e}{\text{ cross-multiplying}}$

$\Rightarrow k = \frac{r t}{p q} = \frac{6 \times 3}{8 \times - 3} = \frac{18}{- 24} = - \frac{3}{4}$

rArr" equation is " color(red)(bar(ul(|color(white)(2/2)color(black)(r=-(3pq)/(4t)color(white)(2/2)|)))