# If x varies inversely as y, how do you find x when y = 64 if x = 0.2 when y = 48?

May 3, 2016

$x = 0.15$

#### Explanation:

As $x \propto \frac{1}{y}$

$x = \frac{k}{y}$

As $x = 0.2$, when $y = 48$

$0.2 = \frac{k}{48}$ or $k = 0.2 \times 48 = 9.6$

Hence $y = 64$

$x = \frac{9.6}{64} = \frac{96}{10} \times 64$

= $x = \frac{32 \times 3}{10} \times \frac{1}{32 \times 2}$

or $x = \frac{3}{20} = 0.15$