SOLUTION: A liter of cream contains 9.5 percent butterfat. How much skim milk containing 5.5 percent butterfat must be added to the mixture (which is the same as the amount of cream that mus

Question 1151935: A liter of cream contains 9.5 percent butterfat. How much skim milk containing 5.5 percent butterfat must be added to the mixture (which is the same as the amount of cream that must be taken out) to obtain one liter of mixture with 6.5 percent butterfat?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
x = number of liters of cream with 9.5% butterfat.
y = number of liters of cream with 5.5% butterfat.
you have 2 equations that need to be solved simultaneously.
they are:
x + y = 1
.095x + .055y = .065 * (x + y)
since x + y = 1, then the equations become:
x + y = 1
.095x + .055y = .065
multiply both sides of the first equation by .095 and leave the second equation as is to get:
.095x + .095y = .095
.095x + .055y = .065
subtract the second equation from the first to get:
.04y = .03
solve for y to get:
y = 3/4
since x + y = 1, then x = 1/4
replace x with 1/4 and y with 3/4 in the second equation to get:
.095x + .055y = .065 becomes .095 * 1/4 + .055 * 3/4 = ..065
simplify to get .095/4 + .165/4 = .065
simplify further to get .26/4 = .065
simplify further to get .065 = .065
this confirms the solution is correct.
the solution is that 3/4 of a liter of 5.5% cream must be added to 1/4 of a liter of 9.5% cream to make 1 liter of 6.5% cream.
this also means that 3/4 of a liter of 9.5% cream must be removed.

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