Question 250511
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.