Question

A chemist is mixing a 30% salt solution with a 15% salt solution to make 30 L of a new solution that will contain 20% salt. How much of each of the original solutions should the chemist use?

Answer 1

Answer:

• 10 L of 30%
• 20 L of 15%

Step-by-step explanation:

Let x represent the amount of the higher-concentration solution. The 30-x is the amount of the lower-concentration solution. The amount of salt in the final mix is ...

  0.30x +0.15(30-x) = 0.20(30)

  0.15x +4.5 = 6 . . . simplify

  0.15x = 1.5 . . . . . subtract 4.5

  x = 10 . . . . . . . . divide by 0.15

  30-x = 20

The chemist should use 10 L of 30% solution and 20 L of 15% solution.

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Additional comment

Here, as with all mixture problems, the fraction of the mix that is composed of the higher-concentration solution is ...

  fraction that is high% = (mix% - low%)/(high% -low%)

  = (20 -15)/(30 -15) = 5/15 = 1/3

So, 1/3(30 L) = 10 L is 30% solution, and the remaining 20 L is 15% solution.

Once you know this generic solution, you can often work these in your head.