the manager of a health food store sells peanuts for $7 a pound and premium cashews for $12 a pound. If he wishes to make a 50 pound cashew and peanut mix for $11 a pound, how many pounds (lb) of cashews should he use

So there should be 6 pounds of trail mix and 44 pounds of cashews.

Step-by-step explanation:

Let x = pounds of peanuts

Let y = pounds of cashews

The two amounts have add up to 50 lbs, so that gives us the first equation:

x+y=50

Next, we know that the 50-lbs mixture needs to cost $11 per pound. We can use the per lbs info for the trail mix and cashews to make equation 2:

7x + 12y = 11*14

Now use whatever method you like to solve the equations. I will choose to use substitution method:

y = 50-x

7x + 12 (50-x) = 154

7x + 600x - 15x = 154

50 = 8x

x = 6.25 or 6lbs

Use equation 1 to find y:

6+y = 50

y = 44