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

**Solution:**

The statement is a ∝ 1/b

Where inverse is 1/variable

Introduce k, which is the constant of variation or constant of proportionality to convert it into an equation

a = k × 1/b

a = k/b

In order to determine k, use a = 3 when b = 4

3 = k/4

k = 3×4 = 12

The equation here is b = 12/a

From the question as a = 48

b = 12/48 = 1/4

Therefore, b = 1/4 when a = 48.

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

**Summary:**

If a varies inversely as b, and a = 3 when b = 4 then the value of b when a = 48 is 1/4.