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

X+Y=50 (gallons)

6.00X + 0.8Y = 118 (because 50* 2.36= 118$)

therefor
X+Y-50=0 and 6X+0.8Y-118=0
also
7X + 1.8Y - 168=0 (combining the two)
15X+1.8Y- 295= 0 (equation 2 times 2.5) (then subtract from other)
8X-127=0
X=15.875
Y= 50-X= 34.125

So you need 15.875 gallons of Maple and 34.125 gallons of Corn.

Answer 2

that is total bull.
let X represent the decimal percentage of corny syrup in the mix \[(0.00 \le X \le 1.00)\]
so, for 1 gallon,
0.80X + 6.00(1.00-X) = 2.36
0.80X + 6.00 - 6.00X = 2.36
6.00 - 5.20X = 2.36
3.64 = 5.20X
X = 3.64/5.20
X = 0.70
Therefore, for 50 gallons of the mix, 50*0.70 gallons of corn syrup are used and 50*(1-0.70) of maple are used.
So, exactly 35 gallons of corn syrup are needed and 15 gallons of maple syrup are needed.