SOLUTION: A 2.5 L container has a mixture of 25% alcohol. How many liters of the mixture must be drained out and replaced with pure alcohol in order to obtain a mixture containing 40% alcoho

Let W be the volume to drain off from 2.5 liters of the original mixture.


Step 1:  Draining.  After draining,  you have 2.5-W liters of the 25% mixture.


Step 2:  Replacing.  Then you add W liters of the pure alcohol (the replacing step).

                     After the replacing,  you have the same total liquid volume of 2.5 liters.


It contains  0.25(2.5-W) + W  of the pure alcohol.


So, your "concentration equation" is


 = 0.4.    (1)


The setup is done and completed.


Now you need to solve your basic equation  (1).


0.25*(2.5-W) + W = 0.4*2.5

0.25*2.5 - 0.25W + W = 0.4*2.5

0.75W = 1 - 0.625

W =  = 0.5.


Answer.  0.5  of a liter of the original mixture should be drained and replaced with the pure alcohol.