SOLUTION: A garage owner wants to fill a 55-gallon drum with a 20% winter mixture of antifreeze for his customers. How many gallons of 100% antifreeze should he mix with some 10% antifreeze

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: A garage owner wants to fill a 55-gallon drum with a 20% winter mixture of antifreeze for his customers. How many gallons of 100% antifreeze should he mix with some 10% antifreeze       Log On


   

Question 260650: A garage owner wants to fill a 55-gallon drum with a 20% winter mixture of antifreeze for his customers. How many gallons of 100% antifreeze should he mix with some 10% antifreeze mixtures in order to fill the drum?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Let A be the amount of 100% antifreeze and B be the amount of 10% antifreeze.
1.A%2BB=55
.
.
100A%2B10B=20%2855%29=1100
2.10A%2BB=110
From eq. 1,
A=55-B
Substitute into eq. 2,
10A%2BB=110
10%2855-B%29%2BB=110
550-10B%2BB=110
-9B=-440
B=440%2F9
Then from eq. 1,
A=55-B=495%2F9-440%2F9
A=55%2F9
Use 55/9 gallons of 100% antifreeze and 440/9 gallons of 10% antifreeze.