Y varies inversely as x. y is 4 when x is 16. How do you find y if x is 20?

Oct 18, 2016

$y = \frac{16}{5}$

Explanation:

If y varies inversely with x, then y is inversely proportional to x.
$y \propto \frac{1}{x}$

Another way to write this is $y = \frac{k}{x}$ where $k$ is a proportionality constant.

First, find $k$ using this equation.

$y = \frac{k}{x} \text{ }$ which gives $k = x y$

$k = 16 \times 4 \textcolor{w h i t e}{a a a}$Subsitute $4$ for $y$ and $16$ for $x$.

$k = 64$

To find $y$ when $x = 20$:

plug $k = 64$ and $x = 20$ back into the original equation.

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

$y = \frac{64}{20}$

$y = \frac{16}{5}$