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?
{maple syrup: _______________________a0 gallons, corn syrup: _________________________a1gallons}

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?
{maple syrup: _______________________a0 gallons, corn syrup: _________________________a1gallons}

hero · Answer

m = gallons of maple syrup
c = gallons of corn syrup

Gallons of syrup
m + c = 50

Cost of Syrup
6m + .8c = 2.36(m + c)
6m + .8c = 2.36(50)

Solve this system:
m + c = 50
6m + .8c = 2.36(50)

anonymous · Answer

M=14.2
C=35.8

hero · Answer

Close, but not quite

hero · Answer

The values for m and c are integers.

anonymous · Answer

can you explain?

hero · Answer

You need approximately 35 gallons of corn syrup and approximately 15 gallons of maple syrup to make 50 gallons of syrup.

hero · Answer

Actually....

hero · Answer

m + c = 50
6m + .8c = 50(2.36)

6m + 6c = 300
6m + .8c = 118

(6 - 6)m + (6 - .8)c = 300 - 118
0m + 5.2c = 182
5.2c = 182
     c = 182/5.2
     `c = 35`

m + c = 50
m + 35 = 50
m = 50 - 35
`m = 15`