Question

A coffee distributor needs to mix a(n) Mexican Shade Grown coffee blend that normally sells for $8.30 per pound with a House coffee blend that normally sells for $13.70 per pound to create 20 pounds of a coffee that can sell for $10.73 per pound. How many pounds of each kind of coffee should they mix?

___pounds of the Mexican Shade Grown Blend
___pounds of the House Blend.

Answer 1

Answer:the number of pounds of the Mexican Shade Grown Blend that should be mixed is 11

the number of pounds of the House Blend that should be mixed is 9

Explanation:

Let x represent the number of pounds of the Mexican Shade Grown Blend that should be mixed.

Let y represent the number of pounds of the House Blend that should be mixed.

The total number of pounds of coffee created is 20. It means that

x + y = 20

The Mexican Shade Grown coffee blend normally sells for $8.30 per pound with a House coffee blend normally sells for $13.70 per pound. The mixed coffee can sell for $10.73 per pound. This means that the total cost of 20 pounds would be 20 × 10.73 = $214.6

Therefore,

8.3x + 13.7y = 214.6 - - - - - - - - - 1

Substituting x = 20 - y into equation 1, it becomes

8.3(20 - y) + 13.7y = 214.6

166 - 8.3y + 13.7y = 214.6

- 8.3y + 13.7y = 214.6 - 166

5.4y = 48.6

y = 48.6/5.4 = 9

x = 20 - y = 20 - 9

x = 11