SOLUTION: Peter and Paul are two friends. The sum of their ages is 35 years. Peter is twice as old as Paul was when Peter was as old as Paul is now. What is the present age of Peter?

We let  

Paul's age now = x
Peter's age now = y

x + y = 35

Let z = the number of years it has been since Peter was as old as 
Paul is now.

Paul's age back then = x-z,
Peter's age back then = y-z.

So Peter's age back then = Paul's age now:

y-z = x

y = 2(x-z)

So we have the system of equations:



Solve that system and get x = 15,   y = 20,   z = 5

So Paul is 15, Peter is 20.  5 years ago,
Paul was 10, and Peter was 15.

So Peter is now 20, and that is twice as old as Paul was back then (10).
Paul now (15) is as old as Peter was back then (15).

So it checks.

Edwin