SOLUTION: Mrs. Smith operates a soybean farm. She buys supplies in bulk. Often the bulk products need to be custom mixed before she can use them. To apply herbicide to a large field she must

Question 29669: Mrs. Smith operates a soybean farm. She buys supplies in bulk. Often the bulk products need to be custom mixed before she can use them. To apply herbicide to a large field she must mix a solution of 67% herbicide with a solution of 46% herbicide to form 42 liters of a 55% solution. How much of the 67% solution must she use?
Answer by bmauger(101) (Show Source):
You can put this solution on YOUR website!
A mild variation talking about acid instead of herbicide (same concept) can be found on this site using the Mixing Acids Solver

Solved by pluggable solver: Mixing Acids

This problem can be solved by a system of equations. The first step though is to define your variables correctly. Because our unknowns are volumes, we can call the volume of solution A a and the volume of B b.
We know from the problem that the total volume is 42. Since that total is made up of combining A & B, we can write it as their sum:

The other equation is devised by realizing that the amount of acid contributed by each solution is equal to its volume times its percentage. Thus acid a would contribute a times 67 and b would contribute b * 46. The final volume of acid will also be equal to the (42) times the final percentage of this solution (55). This gives:

We have now successfully converted from English to math and can solve our two equations. In this example, it's easier done with substitution. Rewriting our first equation solving for a, we get:

Substituting this into to equation 2 for a gives:
Distributing on left & solving right side gives:
Rearrange combining b's and constants to get:
Dividing both sides by -21 gives:
don't forget the units mL.
This can then be put back into the equation:
substituting for b gives:
giving the volume a as:
mL.