# How do you find how many quarts of 4% butterfat milk and 1% butterfat milk should be mixed to yield 60 quarts of 2% butterfat milk?

Jun 18, 2018

$\textcolor{b l u e}{20}$ quarts of 4% and $\textcolor{b l u e}{40}$ quarts of 1% will give $60$ quarts of 2%

#### Explanation:

Let $x$ be the number of quarts of 4% required.
This implies the number of quarts of 1% required will be $60 - x$

The total butter fact will be
$\textcolor{w h i t e}{\text{XXX}} \frac{4}{100} \cdot x + \frac{1}{100} \cdot \left(60 - x\right) = \frac{2}{100} \cdot 60$

$\textcolor{w h i t e}{\text{XXX}} \rightarrow 4 x + 60 - x = 2 \cdot 60$

$\textcolor{w h i t e}{\text{XXX}} \rightarrow 3 x + 60 = 120$

$\textcolor{w h i t e}{\text{XXX}} 3 x = 60$

$\textcolor{w h i t e}{\text{XXX}} x = 20$

So $20$ quarts of 4% are needed plus $\left(60 - 20\right) = 40$ quarts of 1%