One antifreeze solution is 31% alcohol and another is 15% alcohol. How much of each mixture should be added to make 28 L a solution that is 27% alcohol?

Let

x = volume of the 31% solution

y = volume of the 15% solution

We want a solution with a total volume of 28 L, so

x + y = 28

For each liter of either solution, there is a contribution of 0.31 L and 0.15 L of alcohol, respectively. In the resulting solution, we want a concentration of 27% alcohol, which comes out to 0.27 * 28 L = 7.56 L. So

0.31 x + 0.15 y = 7.56

The first equation says

y = 28 - x

Substitute this into the second equation and solve for x, then for y:

0.31 x + 0.15 (28 - x) = 7.56

0.31 x + 4.2 - 0.15 x = 7.56

0.16 x = 3.36

x = 21

y = 28 - x

y = 7