Suppose you add x oz of 10% alcohol to y oz of pure alcohol. Then the mixture has a total volume of x + y oz, and we want to end up with 16 oz so that
x + y = 16
For each oz of the solution 10% used, 0.1 oz of alcohol is contributed, and each oz of pure alcohol contributes 1 oz of alcohol. The mixture is supposed to have a concentration of 14%, which comes out to 0.14*16 = 2.24 oz of alcohol. Then
0.1 x + 1 y = 2.24
Solve for y in both equations:
y = 16 - x
y = 2.24 - 0.1 x
Set them equal to one another and solve for x, then for y.
16 - x = 2.24 - 0.1 x
13.76 = 0.9 x
x = 13.76/0.9 ≈ 15.29
y = 16 - 15.29 ≈ 0.71
So you need about 15.29 oz of 10% alcohol and 0.71 oz of pure alcohol to get the desired mixture.
