# If y varies inversely as x and y = 40 when x = 16, how do you find y when x = 10?

Apr 26, 2018

$y = 64$

#### Explanation:

The method for these questions always stays the same.

$y \propto \frac{1}{x} \text{ } \leftarrow$ write as an inverse proportion

$y = \frac{k}{x} \text{ } \leftarrow \times k$ to change it into an equation

$x y = k \text{ } \leftarrow$ isolate $k$

$k = 16 \times 40 = 640 \text{ } \leftarrow$ substitute to find the value of $k$

$y = \frac{640}{x} \text{ } \leftarrow$ use the value for $k$ in the equation.

Now you can find a value for $x \mathmr{and}$ y if you are given a value.

$x = 10$

$y = \frac{640}{10}$

$y = 64$