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 needed to make

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Question 415232: 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 needed 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 $6 syrup needed
Let b = gallons of $.80 syrup needed
given:
(1) a+%2B+b+=+50
(2) %286a+%2B+.8b%29%2F50+=+2.36
----------------------
(2) 6a+%2B+.8b+=+118
(2) 60a+%2B+8b+=+1180
Multiply both sides of (1) by 8
and subtract (1) from (2)
(2) 60a+%2B+8b+=+1180
(1) -8a+-+8b+=+-400
52a+=+780
a+=+15
and
(1) a+%2B+b+=+50
15+%2B+b+=+50
b+=+35
15 gallons of $6 syrup are needed
35 gallons of $.80 syrup are needed
check answer:
(2) %286a+%2B+.8b%29%2F50+=+2.36
(2) %286%2A15+%2B+.8%2A35%29%2F50+=+2.36
+%2890+%2B+28%29%2F50+=+2.36
+118%2F50+=+2.36
118+=+118
OK