Question

Three varieties of coffee long dash— Coffee​ A, Coffee​ B, and Coffee C long dash— are combined and​ roasted, yielding a 51​-lb batch of coffee beans. Twice as many pounds of Coffee​ C, which retails for ​$9.95 per​ lb, are needed as Coffee​ A, which sells for ​$15.99 per lb. Coffee B retails for ​$13.21 per lb. How many pounds of each coffee should be used in a blend that sells for ​$12.82 per​ lb?

Answer 1

Let A, B and C be the number of pounds of each brand of coffee.
A+B+C=51 (weight) which is 3A+B=51 because C=2A, B=51-3A
15.99A+13.21B+19.90A=51×12.82=653.82 (cost) I’ve used C=2A
35.89A+13.21B=653.82
Substitute for B:
35.89A+13.21(51-3A)=653.82
35.89A+673.71-39.63A=653.82
3.74A=19.89, A=117/22 pounds, B=771/22 pounds, C=117/11 pounds.
Approximate weights are A: 5.32lb, B: 35.05lb, C: 10.64lb.