the coffee company mixes coffee worth 12 per pound with coff

the coffee company mixes coffee worth $12 per pound with coffee worth $8 per pound to produce 50 pounds of coffee worth 8.80 per pound. how many pounds of $12 coffee and how many pounds of $8 must be used

Solution

Let A pounds of $12 coffee and B pounds of $8 coffee are mixed.

Given                                                                                                  A+ B = 50...................(1)

The cost of the mixture is 12A + 8B.

On the other hand, this cost is given to be 50 x $8.80 =$440.

Thus                                                                                                 12A +8B = 440

or                                                                                                        3A +2B = 110..............(2)

                                                                                   (2) -2x (1) gives            A = .10 pounds, so B =40 pounds