How to Solve a Mixing Problem

Suppose a dishonest bartender decides to water down the liquor to make it last longer. He knows the customers will notice if he dilutes liquor below 30% alcohol by volume. If he has a half full 750 ml bottle of 40% ABV liquor, how much water can he add?

Let x = # of ml of water added

Half of 750 ml is 375 ml, and 40% of it is alcohol. 

The amount of alcohol in the liquor already (0.4)*750/2 = 150 ml. The other 225 ml is water. 

150/(375 + x) = 0.3

150 = (0.3)(375 + x)

500 = 375 + x

125 = x

x = 125 ml of water

If we add that 125 ml to the 375 ml we started with, we get 500 ml total, which will fit in a 750 ml bottle.