Need Help Please

Question

A one-pound blend of coffee uses Brazilian (50 cents per ounce), Columbian (40 cents per ounce), and Peruvian (60 cents per ounce) coffee beans and costs $8.10 per pound. The blend contains twice the weight of Brazilian beans as Columbian beans. How many ounces of each type of bean does the blend contain? 

Answer 1

From the information given we can derive three equations.

B(0.50) + C(0.40) + P(0.60) = 8.10                    B,C, & P equals the number of ounces of each coffee

B = 2C and P = 16 - B - C                                  so substituting these two values into the first equation

(2C)(0.50) + C(0.40) + [(16 - (2C) -C](0.60) = 8.10

C + 0.40 C + [9.6 - 1.8 C] = 8.10

- 0.4 C = - 1.5

C = 3.75 ounces

so B = 2(C) = 2(3.75) = 7.5 ounces

and P = 16 - 3.75 - 7.5 = 4.75 ounces

Placing these values in the first equation as a check gives:

7.5(0.50) + 3.75(0.40) + 4.75(0.60) = 8.10

3.75 + 1.50 + 2.85 = 8.10

8.10 = 8.10