Question 1155684
x = number of quarts of 6% butterfat milk.
y = number of quarts of 3% butterfat milk.
you have 2 equations that need to be solved simultaneously.
they are:
x + y = 45
.06x + .03y = .04 * 45
simplify the second equation to get .06x + .03y = 1.8 quarts of butterfat.
solve for y in the first equation to get y = 45 - x
replace y in the second equation to get .06 * x + .03 * (45-x) = 1.8
simplify to get .06x + .03*45 - .03x = 1.8
simplify further to get .06x + 1.35 - .03x = 1.8
subtract 1.35 from both sides of the equation to get .06x - .03x = 1.8 - 1.35
combine like terms to get .03x = .45
solve for x to get x = 45 / .03 = 15
since x + y = 45, then y = 30
you have:
x = 15 and y = 30
.06 * x + .03 * y becomes .06 * 15 + .03 * 30 = 1.8 quarts of butterfat
your solution is that 15 quarts of 6% butterfat and 30 quarts of 3% butterfat must be mixed together to get 45 quarts of 4% butterfat.