# How do you write a specific formula to describe the variation: Q varies jointly with the inverse of the sum of b and R; Q=3 when b=7, R=3?

Nov 5, 2017

See process below;

#### Explanation:

$Q \propto \frac{1}{b + R}$

$Q = \frac{1}{b + R} k$, where $k$ is constant..

$Q = \frac{k}{b + R}$

Where;

$Q = 3$

$b = 7$

$R = 3$

$3 = \frac{k}{7 + 3}$

$3 = \frac{k}{10}$

$\frac{3}{1} = \frac{k}{10}$

cross multiply..

$k = 3 \times 10$

$k = 30$

Hence the equation is..

$Q = \frac{30}{b + R}$