A merchant has 5 pounds of mixed nuts that cost $30. He wants to add peanuts that cost $1.50 per pound and cashews that cost $4.50 per pound to obtain 50 pounds of a mixture that costs $2.90 per pound. How many pounds of peanuts are needed?

1 Answer
Sep 29, 2015

The merchant needs 29.2 pounds of peanuts to make his mixture.

Explanation:

Be P the quantity of peanuts added to the mixture and C the quantity of cashews added to the mixture. We have:

5+P+C=50 rarr P+C=45

If the mixture is to cost $2.90 per pound, then 50 pounds will cost $145. Therefore we have:

30+1.5P+4.5C=145 rarr 1.5P+4.5C=115

rarr 1.5(P+C)+3C=67.5+3C=115

rarr 3C=47.5 rarr C=47.5/3

rarr P+47.5/3=45

rarr P=45-47.5/3=(135-47.5)/3=87.5/3~~29.2