SOLUTION: How many liters of pure alcohol must be added to 15 liters of 20% solution to obtain a mixture which is 30% alcohol

Let V be the volume of the pure alcohol to add.


Then the volume of the 30% mixture is (15+V) liters, and you have this equation 


    0.2*15 + V = 0.3*(15+V).    (1)


It says that the pure alcohol amount in ingredients (left side) us the same as the alcohol amount in the final mixture (right side).



From this equation, you have

    0.2*15 + V = 0.3*15 + 0.3V

    V   - 0.3V = 0.3*15 - 0.2*15

    V =  = 2.143 liters (approximately).


CHECK.  I will check equation (1):  

        Left side  is  0.2*15 + 2.143 = 5.143 liters of the pure alcohol;

        Right side is  0.3*(15+2.143) = 5.143 liters of the pure alcohol.

              ! Precisely correct !