Question

How many gallons of a 3% salt solution must be mixed with 50 gallons of a 7% solution to obtain a 5% solution?

Answer 1

50 gallons

Explanation:

This was an interesting question. And here is how I tackled it.

What is required is a 5% solution, and this is made up by adding an unknown volume (we'll call that v) of a 3% solution to 50 gallons of a 7% solution.

So, the above can be expressed as:

7% solution + 3% solution = 5% solution

So:
(7 x 50) + (3 x v) = 5 x (50 + v)
350 + 3v = 250 + 5v
350 - 250 + 3v = 5v
100 + 3v = 5v
100 = 5v - 3v
100 = v(5 - 3)
100 = 2v

Therefore v = 50 gallons

Hence, you need to add 50 gallons of the 3% solution to the 50 gallons of the 7% solution and that will give 100 gallons of a 5% solution.