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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?

1 Answer

Jun 18, 2018

$20$ $color(blue)20$ quarts of $4 %$ $4%$ and $40$ $color(blue)40$ quarts of $1 %$ $1%$ will give $60$ $60$ quarts of $2 %$ $2%$

Explanation:

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

The total butter fact will be
$XXX \frac{4}{100} \cdot x + \frac{1}{100} \cdot (60 - x) = \frac{2}{100} \cdot 60$ $color(white)("XXX")4/100 * x +1/100 * (60-x)=2/100 * 60$

$XXX \to 4 x + 60 - x = 2 \cdot 60$ $color(white)("XXX")rarr 4x+60-x= 2 *60$

$XXX \to 3 x + 60 = 120$ $color(white)("XXX")rarr 3x+60=120$

$XXX 3 x = 60$ $color(white)("XXX")3x=60$

$XXX x = 20$ $color(white)("XXX")x=20$

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

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