How many pounds of each should I buy if I have $15.00 and wish to buy five pounds of mixed nuts for a party where peanuts cost $2.20 per pound and cashews cost $4.70 per pound?

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Answer 1 · 2014-11-04T16:02:23

Let #p# be the amount of peanuts
Let #c# be the amount of cashews

Since we only need 5 pounds of nuts,
#p + c = 5#
#=> p = 5 - c#

#2.20(p) + 4.70(c) = 15.00#

#=> 2.20(5 - c) + 4.70(c) = 15.00#

#=> 2.20(5) + 2.20(-c) + 4.70c = 15.00#

#=> 11.00 - 2.20c + 4.70c = 15.00#

#=> 2.50c = 4#

#=> c = 1.6#

#p = 5 - c#

#=> p = 5 - 1.6#

#=> p = 3.4#

You should buy 1.6 lbs of cashews and 3.4 pounds of peanuts