algebra 2 question. ,maple syrup

Question

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 1

First, recognize that this question is asking you to solve a system of linear equations. From the information given, you can set up two equations to solve for your two unknown values. Let m represent gallons of maple syrup and c represent gallons of corn syrup. We are told that m and c must add up to 50, so

 

(1) m + c = 50

 

In addition, we know the cost per gallon of each component so we can set up an equation that represents price.

 

(2) 6.00m + 0.80c = 2.36*50

 

Solving this system of equations, we get

 

m = 15 gallons

c = 35 gallons