Let
<em>x</em> = volume of the 31% solution
<em>y</em> = volume of the 15% solution
We want a solution with a total volume of 28 L, so
<em>x</em> + <em>y</em> = 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 <em>x</em> + 0.15 <em>y</em> = 7.56
The first equation says
<em>y</em> = 28 - <em>x</em>
Substitute this into the second equation and solve for <em>x</em>, then for <em>y </em>:
0.31 <em>x</em> + 0.15 (28 - <em>x</em>) = 7.56
0.31 <em>x</em> + 4.2 - 0.15 <em>x</em> = 7.56
0.16 <em>x</em> = 3.36
<em>x </em>= 21
<em>y</em> = 28 - <em>x</em>
<em>y</em> = 7