Answer by ikleyn(52776)   (Show Source): You can put this solution on YOUR website!
 .

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

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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.




Solved.





For similar solved problems see the lesson



    - Really intricate age word problem



in this site.







There is a bunch of lessons on age word problems 



    - Age problems and their solutions



    - A fresh formulation of a traditional age problem



    - Really intricate age word problem (*)



    - Selected age word problems from the archive



    - Age problem for the day of April, 1 



    - OVERVIEW of lessons on age problems



in this site.





Read them and become an expert in solving age problems.





Also, you have this free of charge online textbook in ALGEBRA-I in this site



    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.





The referred lessons are the part of this online textbook under the topic "Age word problems".







 

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