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?

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Answer 1 · 2015-09-29T16:34:29

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

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#