Mixing two solutions to one concentration

Question

You mix 3 liters of a 20\% salt solution with 1 liter of a 60\% salt solution. Solve in your head. What is the concentration of the mixture? Aim: under 10 seconds.

Accepted Answer

Concentration blends as a volume-weighted average. The volumes are in ratio 3 : 1, so the result sits 	frac{1}{4} of the way from 20\% toward 60\% (only a quarter of the mix is the strong stuff): 20\% + \frac{1}{4}(60\% - 20\%) = 20\% + \frac{1}{4}(40\%) = 20\% + 10\% = 30\%. The direct route agrees: \frac{3 \cdot 20 + 1 \cdot 60}{4} = \frac{60 + 60}{4} = 30\%. Takeaway. A mixture concentration is a weighted average by amount, sitting closer to whichever component you have more of. Move along the gap by the minority component's fraction and the arithmetic stays trivial.

Mixing two solutions to one concentration

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