The manager of a bulk foods establishment sells peanuts for $6 per pound and premium cashews for $12 per pound. The manager wishes to make a 105 pound nut mixture that will sell for $10 per pound. How many pounds of peanuts should be used?

35 pounds of peanuts should be used.

Step-by-step explanation:

Let amount of peanut to be used = x

then amount of premium cashews = 105 - x

So, 6x+12 (105-x) = 105 (10)

Solving:

6x + 1260 - 12x = 1050

-6x = 1050-1260

-6x = - 210

x = - 210/-6

x = 35

So, 35 pounds of peanuts should be used.