SOLUTION: To make low-fat cottage cheese, milk containing 4% butterfat is mixed with milk containing 1% butterfat to obtain 36 gallons of a mixture containing 2% butterfat. How many gallons

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Question 779949: To make low-fat cottage cheese, milk containing 4% butterfat is mixed with milk containing 1% butterfat to obtain 36 gallons of a mixture containing 2% butterfat. How many gallons of each milk must be used? See Example 4.
1% milk ___ gal
4% milk ___ gal
Answer by josgarithmetic(39613) About Me  (Show Source):
You can put this solution on YOUR website!
ASSIGN VARIABLES
L = 1%
T = 2%, target value wanted
H = 4%
M = 36 gallons
u = amount of 1%, unknown
v = amount of 4%, unknown

MAKE EQUATIONS
%28Lu%2BHv%29%2FM=T and u%2Bv=M


SOLVE EQUATIONS FOR EACH UNKNOWN VARIABLE
Meaning, solve for u and v.
%28Lu%2BHv%29%2FM=T and u%2Bv=M
Lu%2BHv=MT, v=M-u
Lu%2BH%28M-u%29=MT
Lu%2BHM-Hu=MT
Lu-Hu=MT-HM
u%28L-H%29=M%28T-H%29
u=M%28T-H%29%2F%28L-H%29
and because L%3CT%3CH, we multiply top & bottom by -1
highlight%28u=M%28H-T%29%2F%28H-L%29%29
and including the use of the other equation,
highlight%28v=M%281-%28H-T%29%2F%28H-L%29%29%29 or whichever simpler form you want.


SUBSTITUTE THE KNOWN VALUES