Question

find how many quarts of 6% butterfat milk and 2% butterfat milk should be mixed to yield 80 quarts of 3% butterfat milk

Answer 1

Let the quantity of 6% butterfat milk be x quarts and that of 2% butterfat milk be y quarts.

As the mixture yields 80 quarts in total,

x + y = 80 → (1)

Also, mixing x quarts of 6% butterfat milk and y quarts of 2% butterfat milk should yield 80 quarts of 3% butterfat milk.

0.06x + 0.02y = 0.03 * 80

0.06x + 0.02y = 2.4

6x + 2y = 240

On dividing the entire equation by 2,

3x + y = 120 → (2)

Subtracting (1) from (2),

3x + y = 120

-(x + y = 80)

2x = 40

x = 20

20 + y = 80

y = 60

20 quarts of 6% butterfat milk

60 quarts of 2% butterfat milk