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
Step-by-step 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
