Two solutions of salt water contain 0.06% and 0.21% salt respectively. A lab technician wants to make 1 liter of solution which contains 0.12% salt. How much of each solution should she use?

The volume of the first solution will be called "x", while the one from the second will be "y". The salt content on the first solution is "0.0006*x", while the salt content on the second solution is "0.0021*y", and the sum of these two values must be the same as the one in the final solution, so we have:

0.0006*x + 0.0021*y = 0.0012

And the sum of volumes must be equal to 1 liter.

x + y = 1

We have the equation system:

x + y = 1 (1)

0.0006*x + 0.0021*y = 0.0012 (2)

Isolating the "x" variable in the first equation and applying it in the second we have:

x = 1 - y

0.0006*(1-y) + 0.0021*y = 0.0012

0.0006 - 0.0006*y + 0.0021*y = 0.0012

0.0015*y = 0.0006

y = 0.0006/0.0015 = 0.4

x = 1 - 0.4 = 0.6

The first solution must have 0.6 l and the second one 0.4 l.