How many pounds of each coffee should be used?

Question

Three varieties of coffee --- Coffee A, Coffee B, and Coffee C ---- are combined and roasted, yielding a 55-lb batch of coffee beans. Twice as many pounds of Coffee C, which retails for $9.95 per lb, are needed ad Coffee A, which sells for $14.99 per lb. Coffee B retails for $13.99 per lb. How many pounds of each coffee should be used in a blend that sells for $12.82 per lb?

Should be used __lb. of Coffee A, __lb of Coffee B and __lb. of Coffee C. (Round to two decimal places as needed.)

Answer 1

Let a be pounds of coffee A,b be pounds of coffee B, and c be pounds of coffee C.

We have 55 pounds of coffee, so a + b + c = 55

As there are twice as many pounds of c as a, c = 2a. Then, b = 55 - a - c = 55 - a -2a = 55 - 3a

As the blend sells for $12.82 and there are 55 pounds, the total price is 55 * 12.82

14.99 a + 13.99 (55 - 3a) + 9.95 (2 a) = 55 * 12.82

Multiply by 100

1499 a + 1399 (55 - 3a) + 995 (2 a) = 55 * 1282

76945 - 708 a = 70510

a = 6435/708 = 9.09

c = 2a = 18.18

b = 55 - a - c = 27.73