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

Step-by-step explanation:

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.