Question 365530
Peter and Paul are two friends. The sum of their ages is 35 years. Peter is twice as old as Paul was <font color = "red">when</font> Peter was as old as Paul is now. What is the present age of Peter?
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Let x = Peter's present age
Let y = Paul's present age
Let z = the number of years ago indicated by the word "<font color = "red">when</font>" above.
x - z = Peter's age z years ago
y - z = Paul's age z years ago
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>>The sum of their ages is 35 years.<<
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So x + y = 35</pre>>>Peter is twice as old as Paul was when Peter was as old as Paul is now.<<
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We first need to express how old Paul was <font color = "red">when</font> Peter was as old as Paul is now.

That was z years ago, so z years ago, Peter was x - z, and that is the age Paul
is now, so

x - z = y

But Paul was y - z then 

We are told that Peter is now twice that (Paul's age then), so

x = 2(y - z) 
x = 2y - 2z

So we have the system of equations:

x + y = 35
x - z = y
x = 2y - 2z

Lining them up makes the system easier to solve:

x +  y      = 35
x -  y -  z =  0
x - 2y + 2z =  0

I assume you can solve that.  If not post again asking how.

Solution:  x=20, y=15, z=5

So Peter is 20, Paul is 15, and the number of years ago is 5

You were only asked for Peter's age, so the answer is 20.

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Let's check with the words:

The sum of their ages is 35 years. 

That checks because 20 + 15 = 35 

Peter is twice as old as Paul was when Peter was as old as Paul is now. 

Now it has been 5 years since Peter was as old as Paul is now, for 5 years ago
Peter was 15 and that's how old Paul is now.  But 5 years ago Paul was 10, and
so Peter, who is now 20, is now twice as old as Paul was then.

Edwin</pre>