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
