# If 20 quarts of milk contains 2 quarts of butter fat, how much pure water would be need to be added to the milk to make it 4% butter fat?

Jun 13, 2017

$\textcolor{red}{30}$ quarts of pure water would need to be added.

#### Explanation:

Suppose that the required amount of water that would need to be added was $\textcolor{red}{x}$ quarts.

The total resulting volume would be $\textcolor{b l u e}{20 + \textcolor{red}{x}}$

The ratio of butter fat (given $\textcolor{g r e e n}{2}$ quarts of butter fat) to total volume would be:
$\textcolor{w h i t e}{\text{XXX}} \frac{\textcolor{g r e e n}{2}}{\textcolor{b l u e}{20} + \textcolor{red}{x}}$

We are told that this ratio needs to be color(magenta)(4%)
and
Noting that color(magenta)(4%)=color(magenta)(4/100)=color(magenta)(2/50)

We have, as a requirement:
$\textcolor{w h i t e}{\text{XXX}} \frac{\textcolor{g r e e n}{2}}{\textcolor{b l u e}{20} + \textcolor{red}{x}} = \textcolor{m a \ge n t a}{\frac{2}{50}}$

$\Rightarrow \textcolor{b l u e}{20 + \textcolor{red}{x}} = \textcolor{g r e e n}{50}$

$\Rightarrow \textcolor{red}{x} = \textcolor{g r e e n}{50} - \textcolor{b l u e}{20} = \textcolor{red}{30}$