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?

1 Answer
Aug 16, 2015

Answer:

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".