A coffee distributor needs to mix a (n) Organic Free Trade coffee blend that normally sells for $8.90 per pound with a Arabian Mocha coffee blend that normally sells for $13.40 per pound to create 20 pounds of a coffee that can sell for $8.90 per pound. How many pounds of each kind of coffee should they mix?

Answer: A = 0.22

F = 19.78

Step-by-step explanation:

Let Organic Free Trade coffee = F

It normally sells for $8.90 per pound. That is 8.9F

Let Arabian Mocha coffee = A

It normally sells for $13.40 per pound. That is 13.4A

The mixture to create 20 pounds of a coffee that can sell for $8.90 per pound.

Also, they want to create 20 lbs of coffee that can sell for $8.9/lb. If we multiply each kind of coffee blend to be mixed by their respective amounts (in pounds) to be mixed then their sum should be equal to the total cost of the new coffee created, which is the selling price for the new coffee multiplied by the total amount (in pounds) created. That is,

F + A = 20 ... (1)

8.9F + 13.4A = 8.9 * 20 ... (2)

Multiply equation 1 will 8.9

8.9F + 8.9A = 178

8.9F + 13.4A = 178

Eliminate F using simultaneous equation. That is eqn 2 - eqn 1

4.5A = 1

A = 0.22

Substitute A in equation 1

F = 20 - 0.22

F = 19.78