SOLUTION: a shop has one-pound bags of peanuts for $2 and three-pound bags of peanuts for $5.50. if you buy 5 bags and spend $17, how many of each bag did you buy?

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Question 801198: a shop has one-pound bags of peanuts for $2 and three-pound bags of peanuts for $5.50. if you buy 5 bags and spend $17, how many of each bag did you buy?

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = number of 1 pound bags
Let +b+ = number of 3 pound bags
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(1) +a+%2B+b+=+5+
(2) +2a+%2B+5.5b+=+17+
---------------------
Multiply both sides of (1) by 2
and subtract (1) from (2)
(2) +2a+%2B+5.5b+=+17+
(1) +-2a+-+2b+=+-10+
+3.5b+=+7+
+b+=+2+
and, since
(1) +a+%2B+b+=+5+
(1) +a+=+3+
You bought 3 1-pound bags and
2 3-pound bags
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check:
(2) +2a+%2B+5.5b+=+17+
(2) +2%2A3+%2B+5.5%2A2+=+17+
(2) +6+%2B+11+=+17+
(2) +17+=+17+
OK