SOLUTION: John is going to make 13 pounds of mixed nuts for a party. if keil can spend $64.50 on nuts and peanuts cost $2.50 per pound and fancy nuts cost $6.50 pound, how many pounds of eac

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Question 520163: John is going to make 13 pounds of mixed nuts for a party. if keil can spend $64.50 on nuts and peanuts cost $2.50 per pound and fancy nuts cost $6.50 pound, how many pounds of each should he buy?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let a = pounds of peanuts
Let b = pounds of fancy nuts
given:
(1) +a+%2B+b+=+13+
(2) +2.5a+%2B+6.5b+=+64.5+
----------------------
(2) +25a+%2B+65b+=+645+
(2) +5a+%2B+13b+=+129+
Multiply both sides of (1) by 5
and subtract (1) from (2)
(2) +5a+%2B+13b+=+129+
(1) +-5a+-+5b+=+-65+
+8b+=+64+
+b+=+8+
and, since
(1) +a+%2B+b+=+13+
(1) +a+=+5+
5 pounds of peanuts are needed
8 pounds of fancy nuts are needed