Question 1156913
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?
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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


<U>ANSWER</U>.  5.902 pounds Coffee A; 11.803 pounds Coffee C, and the rest,  53-5.902 - 11.803 = 35.295 pounds Coffee B.
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Solved.