Joseph would like to make 12 pounds of a coffee blend at a cost of $6.25. He blends Ground Chicory at $4.40 a pound with Jamaican Blue Mountain at $8.84 per pound. How much if each type of coefficient should be use?

7 pounds of Ground Chicory

5 pounds of Jamaican Blue Mountain

Step-by-step explanation:

Total pounds of coffee = 12 pounds

Cost of the final mixture per pound = $ 6.25

Since the cost per pound is $ 6.25, the cost for 12 pounds would be $ 6.65 (12)

Let Joseph blends "x" pounds of Ground Chicory at $4.40 per pound. Since, the cost of Ground Chicory per pound is $ 4.40, for x pounds the cost would be $ 4.40x

Total amount is 12 pounds from which x pounds is Ground Chicory. So, the remaining amount (12 - x) pounds will be the Jamaican Blue Mountain at $8.84 per pound. Since, the cost of Jamaican Blue Mountain per pound is $ 8.84, for (12 - x) pounds the cost would be $ 8.84 (12 - x)

Total cost of the two coffees must be equal to the cost of the final mixture.

So,

Cost of Ground Chicory + Cost of Jamaican Blue Mountain = Cost of Final Blend

Using the values in this equation, we get:

4.40x + 8.84 (12 - x) = 6.25 (12)

4.40x + 106.08 - 8.84x = 75

-4.44x = 75 - 106.08

- 4.44x = - 31.08

x = 7

Since, x represents the amount of Ground Chicory, we can conclude that 7 pounds of Ground Chicory should be used and 12 - 7 = 5 pounds of Jamaican Blue Mountain should be used to make the desired blend.