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Question 250511: Find how many quarts of 4% butterfat milk and 1% butterfat milk should be mixed to yield 90 quarts of 3% butterfat milk.
The mixture should contain __ quarts of the 4% butterfat milk.
The mixture should contain __ quarts of the 1% butterfat milk.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! x = number of quarts at 4% butterfat.
y = number of quarts at 1% butterfat.
you want to get 90 quarts of 3% butterfat.
amount of butterfat you get in the mixture will be .03 * 90 = 2.7 quarts of butterfat.
.04 * x + .01 * y = 2.7 (equation 1)
x + y = 90 (equation 2)
equation 1 tells you how much of x and y you need to get 2.7 quarts of butterfat.
equation 2 tells you how much of x and y you need to get 90 quarts of milk total.
you need to solve these equations simultaneously so the same value of x and y satisfies both equations.
solve for x in equation 2 to get:
x = 90 - y
substitute for x in equation 1 and solve for y.
.04 * x + .01 * y = 2.7 (equation 1) becomes:
.04 * (90-y) + .01*y = 2.7
simplify by removing parentheses to get:
.04*90 - .04*y + .01*y = 2.7
simlify by performing indicated operations and combining like terms to get
3.6 - .03y = 2.7
add .03y to both sides of the equation and subtract 2.7 from both sides of the equation to get:
3.6 - 2.7 = .03y
combine like terms to get:
.9 = .03y
divide both sides of the equation by .03 to get
y = 30
if y = 30, then x = 90-y = 60
x = 60
y = 30
substitute in original equation to confirm the answer is true.
original equation is:
.04 * x + .01 * y = 2.7
substitute for x and y to get:
.04 * 60 + .01 * 30 = 2.7
this becomes 2.7 = 2.7 which is true, confirming that the answer is correct.
the answer is:
the mixture should contain 60 quarts of 4% butterfat milk.
the mixture should contain 30 quarts of 1% butterfat milk.
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