SOLUTION: 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

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: 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      Log On


   

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) About Me  (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.