SOLUTION: a lab tech needs to make a 60-liter batch of a 40% acid solution, how can the lab tech combine a batch of an acid solution that is pure acid with another that is 20% to get desired

Let x = the volume of the pure acid (in liters),
and y = the volume of the 20% acid solution to combine with.

Then you have two equations 

x +    y = 60,       (1)    (for the total combined volume)
x + 0.2y = 0.4*60.   (2)    (for the acide amount)

Rewrite the system by simplifying (2):

x +    y = 60,       (1')
x + 0.2y = 24.       (2')

From (1'), express x = 60-y and substitute it into (2'). You will get a single equation for the unknown y:

(60-y) + 0.2y = 24.

Simplify and solve it:

60 - y + 0.2y = 24,
60 - 0.8y = 24,
60 - 24 = 0.8y,
36 = 0.8y,

y =  = 45 liters of the 40% acid solution.

Now, x = 60 - 45 = 15 liters of pure acid.