How to Find the Concentration After Mixing

Two salt solutions of different strengths are mixed. Mixing does not change the salt itself, so the salt from both is added and divided by the combined weight.

$w_1$ and $w_2$ are the weights of the two solutions, $c_1$ and $c_2$ their concentrations as percentages, and $c$ the concentration after mixing. The combined weight and the salt it holds are shown as well.

Example

An 8 percent solution weighing 200 g is mixed with a 3 percent solution weighing 300 g. That gives $c = (200 \times 8 + 300 \times 3) \div (200 + 300) = 2500 \div 500 = 5$ percent, and the 500 g holds $500 \times 5 \div 100 = 25$ g of salt.

It is not the average of the concentrations

The average of 8 and 3 is 5.5, but the answer is 5. The heavier solution pulls the result towards its own concentration, and here the 3 percent solution is the heavier of the two at 300 g. Only when both weigh the same does the answer match the plain average.

Notes

To add plain water, set one of the concentrations to 0. Adding 100 g of water to 100 g of a 10 percent solution leaves 200 g at 5 percent.

Concentrations belong between 0 and 100. If both weights are 0 there is nothing to divide by, so no concentration exists.