SOLUTION: John is twice as old as Jane was when he was as old as she is now. The sum of their age is 63. How old is John and Jane

Let x be the John's present age and y be the Jane's present age.


When John was as old as Jane is now ?  - Answer: (x-y) years ago.

What was Jane's age then?  - Answer: y - (x-y) years, or, which is the same, 2y - x was Jane's age then.



The condition says:

x = 2 *(2y-x),   or  

x= 4y - 2x,      or

3x = 4y.         (1)



The second equation is 

x + y = 63.      (2)



From (2), express x = 63-y and substitute it into (2), replacing x. You will get

3*(63-y) = 4y,   or

189 - 3y = 4y  --->  189 = 7y  --->  y =  = 27.


Answer.  Jane is 27 years old.  John is  = 36 years old.