Three varieties of coffee- Coffee A, Coffee B, Coffee C - are combined and roasted, yielding a 53-lb batch of coffee beans.
Twice as many pounds of Coffee C, which retails for 12.76 per lb,
are needed as Coffee A which sells for 15.99 per lb.
Coffee B retails for 12.31 per lb. How many pounds of each coffee should be used in a blend that sells for 12.82 per lb?
~~~~~~~~~~~~~~~~~~
x pounds Coffee A
2x pounds Coffee C
and (53-x-2x) = 53-3x Coffee B.
The total money equation
15.99x + 12.31*(53-3x) + 12.76*(2x) = 53*12.82.
Simplify and find x
15.99x - 12.31*3x +12.76*2x + 12.31*53 = 53*12.82
(15.99 - 12.31*3 + 12.76*2)x = 53*12.82 - 12.31*53
4.58x = 27.03
x = 27.03/4.58
x = 5.902
ANSWER. 5.902 pounds Coffee A; 11.803 pounds Coffee C, and the rest, 53-5.902 - 11.803 = 35.295 pounds Coffee B.
Solved.