How many liters of a 60% acid solution would need to be mixed with a 75% acid solution to get 20L of a 72% acid solution?

All the other similar problems leading up to this one I haven't had trouble with, but this one and others like it where you're only given the amount of the end product and not of the initial ones, like "how many liters of x% solution need to be mixed into 5L of y% solution to get a z% solution?", are just kicking my butt. The book says the answer is "4 Liters," but doesn't explain the formula for such a problem in the text, and doesn't show any work. Everything I've tried has given me high or low numbers and often decimals, so I'm thinking I'm not setting up the formula properly or I'm not simplifying properly. Here's what I've pulled out so far:

Rate | Amount | Amt of Pure Acid 60% | x | .60(x) 75% | (x-20) | .75(x-20) 72% | 20 | .72*20 = 14.4 L x(.60) + (x-20) = 14.4 +20 to both sides x(.60) + x = 34.4 Divide by .6 2x = 57 1/3 Divide by 2 28 3/5

Where am I going wrong here? I'm about ready to pull my hair out.

**Edited by Kamikaze_Badger, 08 April 2012 - 09:47 PM.**