The Coffee Shoppe sells a coffee blend made from two coffees, one costing $3.00/lb and the other costing $2.50/lb. If the blended coffee sells for $2.90/lb, find how much of each coffee is used to obtain the desired blend. (Assume the weight of the blended coffee is 100 lb.)
A) 20 lb of $3.00/lb coffee and 80 lb of $2.50/lb coffee
B) 75 lb of $3.00/lb coffee and 25 lb of $2.50/lb coffee
C) 80 lb of $3.00/lb coffee and 20 lb of $2.50/lb coffee
D) 80 lb of $3.00/lb coffee and 25 lb of $2.50/lb coffee
E) 85 lb of $3.00/lb coffee and 20 lb of $2.50/lb coffee

Question

The Coffee Shoppe sells a coffee blend made from two coffees, one costing $3.00/lb and the other costing $2.50/lb. If the blended coffee sells for $2.90/lb, find how much of each coffee is used to obtain the desired blend. (Assume the weight of the blended coffee is 100 lb.) ​
A) 20 lb of $3.00/lb coffee and 80 lb of $2.50/lb coffee
B) 75 lb of $3.00/lb coffee and 25 lb of $2.50/lb coffee
C) 80 lb of $3.00/lb coffee and 20 lb of $2.50/lb coffee
D) 80 lb of $3.00/lb coffee and 25 lb of $2.50/lb coffee
E) 85 lb of $3.00/lb coffee and 20 lb of $2.50/lb coffee

Quizplus · Accepted Answer

We can begin by setting up a system of equations. Let x be the weight of the $3.00/lb coffee and y be the weight of the $2.50/lb coffee. We know that:

x + y = 100 (since the total weight of the blended coffee is 100 lb)
3x + 2.5y = 2.9(100) (since the cost of the blended coffee is $2.90/lb)

Simplifying the second equation, we get:

3x + 2.5y = 290

Multiplying the first equation by 2.5 and subtracting it from the second equation, we get:

0.5x = 10

x = 20

Substituting x = 20 into the first equation, we get:

20 + y = 100

y = 80

Therefore, the desired blend is 20 lb of the $3.00/lb coffee and 80 lb of the $2.50/lb coffee. The best choice is C.

The Coffee Shoppe Sells a Coffee Blend Made from Two