Question 1151935
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.