SOLUTION: Maple syrup worth $6.00 a gallon and corn syrup worth .80 cents a gallon are used to make a mixture worth $2.36 a gallon. How many gallons of each kind of syrup are need to make 50

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Question 423406: Maple syrup worth $6.00 a gallon and corn syrup worth .80 cents a gallon are used to make a mixture worth $2.36 a gallon. How many gallons of each kind of syrup are need to make 50 gallons of the mixture?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let a = gallons of maple syrup needed
Let b = gallons of corn syrup needed
given:
(1) +%28600a+%2B+80b%29+%2F+50+=+236+
(2) +a+%2B+b+=+50+
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Multiply both sides of (2) by 80 and
subtract from (1)
(1) 600a+%2B+80b+=+11800+
(2) -80a++-+80b+=+-4000+
+520a+=+7800+
+a+=+15+
and, since,
+a+%2B+b+=+50+
+b+=+50+-+15+
+b+=+35+
15 gallons of maple syrup are needed
35 gallons of corn syrup are needed