Question

A coffee distributor needs to mix a(n) Ethiopian coffee blend that normally sells for $10.40 per pound with a Organic Free Trade coffee blend that normally sells for $14.50 per pound to create 40 pounds of a coffee that can sell for $12.25 per pound. How many pounds of each kind of coffee should they mix?

Answer 1

To create a 40-pound coffee blend selling at $12.25 per pound, mix approximately 21.95 pounds of Ethiopian coffee with 18.05 pounds of Organic Free Trade coffee.

Step-by-step explanation:

To determine how many pounds of each kind of coffee a distributor should mix to create 40 pounds of a blend that sells for $12.25 per pound, we can set up a system of equations based on the prices and total weight required.

Let x represent the pounds of the Ethiopian coffee and y represent the pounds of the Organic Free Trade coffee. We have two equations:

1. x + y = 40 (total weight of coffee)
2. 10.4x + 14.5y = 12.25(40) (total value of coffee)

By solving this system of equations, we get the following solutions:

Substitute x = 40 - y into the second equation:

10.4(40 - y) + 14.5y = 490

416 - 10.4y + 14.5y = 490

4.1y = 74

y = 74 / 4.1

y = 18.05 (approximately)

Now solve for x:

x = 40 - y

x = 40 - 18.05

x = 21.95 (approximately)

The distributor should mix approximately 21.95 pounds of Ethiopian coffee with 18.05 pounds of Organic Free Trade coffee.