Question

Cashews at $7.40 a pound are mixed with peanuts at $2.60 a pound. If there are 18 pounds in the mixture and the mixture sells for $5.80 per pound, how many pounds of cashews are there in the mixture?

Answer 1

I found:
`12` pounds of cashews
`6` pounds peanuts

Explanation:

Call `C` and `P` the quantities of the two; you have:
`{(C+P=18),(7.4C+2.6P=5.8*18=104.4):}`
solve the system (by substitution, for example) to get:
`C=18-P`
`7.4(18-P)+2.6P=104.4`
So:
`P=6` pounds
`C=12` pounds

This answers assumes a seller that sells at a price exactly according to the mixture. Many sellers are would be fully willing to sell you a "mixture" that is completely peanuts for them to have a profit. Assuming a seller would not sell for a loss, the answer would be "AT LEAST 6 pounds of peanuts, and AT MOST 12 pounds of cashews".