How much of the 30% solution should the chemist use?

Question

A chemist is mixing a 30% salt solution with a 20% salt solution to make 40 L of a new solution that will contain 25% salt. How much of the 30% solution should the chemist use?

Answer 1

Let x = amount of 30% salt solution.  

Then, 40 - x = amount of 20% salt solution

 

Salt content of first solution + salt content of second solution  = 

     salt content of the mixture

 

So, 0.30x + 0.20(40 - x) = 0.25(40)

 

     0.30x + 8 - 0.20x = 10

 

                         0.10x = 2

 

                                 x = 20

 

ANSWER:  mix 20L of 30% solution with 20L of 20% solution to                            obtain 40L of 25% solution

Answer 2

You could write out equations for this, but there's a quicker way to think about it.

 

The starting solutions are 30% and 20% and the ending solution is 25%.  25 is halfway between 20 and 30, or it's the AVERAGE of 20 and 30.  That means that he's going to be using the SAME amount of each.  Since there will be 40 L of the new solution, he'd have to use 20 L of each starting solution to end up with 40.  So the answer is 20 L of the 30% solution.