SOLUTION: Nathan needs to make 30L of a 28% acid solution. He has 2 bottles, one containing 20% acid and the other containing 50% acid. What volume of each should he mix together to make the

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Nathan needs to make 30L of a 28% acid solution. He has 2 bottles, one containing 20% acid and the other containing 50% acid. What volume of each should he mix together to make the      Log On


   

Question 714702: Nathan needs to make 30L of a 28% acid solution. He has 2 bottles, one containing 20% acid and the other containing 50% acid. What volume of each should he mix together to make the 28% acid solution?
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
A very routine exercise. Let x = volume of the 20% acid to use and y = volume of the 50% acid to use.

%2820x%2B50y%29%2F30=28 AND x%2By=30

The numbers were picked to make the arithmetic easier to do.
Managing the percentage equation,
(2x+5y)/3=28 just by removing factor of 1=10%2F10 from left side;
2x+5y=3*28
2x+5y=84

System to solve is this:
2x%2B5y=84
x%2By=30

Possible next step is
2x%2B5y-2%28x%2By%29=84-2%2A30
5y-2y=24
3y=24
highlight%28y=8%29 liters for the 50% acid.
You can continue from here...

Also notice, if 30 liters mixture is to result, as described, then this must be some huge bottle containing the x liters of the other acid!