Call x the number of young and y the number of old. We know that x+y=5000 from the first sentence. Now we have to express the way they lie into an equation. If 20% of the young people, or x, say that they are old, how will this change the number from the real number?

Another way to look at it, when asked are you old, who will say yes? 20% of the young people and 90% of the old right?

So (.2)x+(.9)y claim to be old. If 34% claim to be old, that is 34% of 5,000 people or (.34)(5000). Set this equal to the above equation and now you have two variables and two equations.