Answer: 12.5 pounds of the gourmet brand and 37.5 pounds of the cheaper brand should be mixed.
Step-by-step explanation:
Let x represent the number of pounds of the gourmet brand of coffee that should be mixed.
Let y represent the number of pounds of the cheaper brand of coffee that should be mixed.
Each type should be mixed in order to have 50 pounds of coffee. It means that
x + y = 50
The mixed coffee would be worth $7.50 per pound. It means that the worth of the mixture would be
7.5 × 50 = $375. The gourmet coffee usually sells for $9.00 per pound. The cheaper brand sells for $7.00 per pound. It means that
9x + 7y = 375- - - - - - -- - - - - 1
Substituting x = 50 - y into equation 1, it becomes
9(50 - y) + 7y = 375
450 - 9y + 7y = 375
- 9y + 7y = 375 - 450
- 2y = - 75
y = - 75/ - 2
y = 37.5
x = 50 - y = 50 - 37.5
x = 12.5
