Solve using a system of two equations in two unknowns.
-The manager of a bulk foods establishment sells a trail mix for $7 per pound and premium cashews for $15 per pound. The manager wishes to make a 120-pound trail mix-cashew mixture
That will sell for $9 per pound. How many pounds of each should be used?
A) 75 lb of trail mix, 45 lb of cashews
B) 60 lb of trail mix, 60 lb of cashews
C) 30 lb of trail mix, 90 lb of cashews
D) 90 lb of trail mix, 30 lb of cashews

Question

Quizplus · Accepted Answer

Let x be the number of pounds of trail mix and y be the number of pounds of premium cashews.

From the problem, we know:

- x + y = 120 (the total mixture weighs 120 pounds) 
- 7x + 15y = 9(120) (the value of the mixture is $9 per pound)

Simplifying the second equation:

- 7x + 15y = 1080

Multiplying the first equation by 7 and subtracting it from the second equation:

- 7x + 15y - 7x - 7y = 1080 - 840 
- 8y = 240 
- y = 30

Substituting y = 30 into the first equation:

- x + 30 = 120 
- x = 90

Therefore, we need 90 pounds of trail mix and 30 pounds of premium cashews to make a 120-pound mixture that sells for $9 per pound.

Solve Using a System of Two Equations in Two Unknowns