A shop specializes in preparing blends of gourmet coffees. From Colombian, Costa Rican, and Kenyan coffees, the owner wishes to prepare 3-pounds bags that will sell for $8.50. The cost per pound of these coffees is $10, $6, and $8, respectively. The amount of Colombian is to be three times the amount of Costa Rican. Find the amount of each type of coffee in the blend.
A)0.825 lb Colombian , 0.275 lb Costa Rican , 1.9 lb Kenyan
B)0.675 lb Colombian , 0.225 lb Costa Rican , 2.1 lb Kenyan
C)1.125 lb Colombian , 0.375 lb Costa Rican , 1.5 lb Kenyan
D)1.125 lb Colombian , 0.375 lb Costa Rican , 3 lb Kenyan
E)1.275 lb Colombian , 0.425 lb Costa Rican , 1.3 lb Kenyan

Question

Quizplus · Accepted Answer

Let the amount of Costa Rican coffee be $x$ pounds. Since the amount of Colombian coffee is three times the amount of Costa Rican, it is $3x$ pounds. Let the amount of Kenyan coffee be $y$ pounds. The total weight of the blend is 3 pounds, so we have the equation $3x + x + y = 3$. Simplifying, we get $4x + y = 3$. The cost of the blend per pound is $\frac{8.50}{3}$ dollars, and the total cost for 3 pounds is $8.50. The cost equation based on the prices per pound of the coffees is $10(3x) + 6(x) + 8(y) = 8.50 \times 3$. Simplifying and solving these equations gives us $x = 0.375$ and $3x = 1.125$, with the remainder being Kenyan coffee, $y = 1.5$.

A Shop Specializes in Preparing Blends of Gourmet Coffees