# If a varies inversely as b, and a = 3 when b = 4 then what is the value of b when a = 48?

Jun 16, 2016

$b = \frac{1}{4}$

#### Explanation:

This is an example of inverse proportion, or inverse variation.

To change a proportion into an equation, multiply by a constant and then use the values given to find the value of the constant.

$a \propto \frac{1}{b} \Rightarrow a = \frac{k}{b} \Rightarrow k = a b$

Find the value of k, using the a and b given.

$k = 3 \times 4 = 12$

So, $a = \frac{12}{b} \text{ can also be written as } b = \frac{12}{a}$

When $a = 48 , \text{ } b = \frac{12}{48} = \frac{1}{4}$