Question 1067594
.
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
~~~~~~~~~~~~~~~~~~~~~~~~~~


<pre>
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 = {{{189/7}}} = 27.


<U>Answer</U>.  Jane is 27 years old.  John is {{{(27*4)/3}}} = 36 years old.
</pre>

Solved.


For similar solved problems see the lesson

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/age/Really-intricate-age-word-problem.lesson>Really intricate age word problem</A>

in this site.



There is a bunch of lessons on age word problems 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/age/Age-problems-and-their-solutions.lesson>Age problems and their solutions</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/age/Fresh-formulation-of-a-traditional-age-problem.lesson>A fresh formulation of a traditional age problem</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/age/Really-intricate-age-word-problem.lesson>Really intricate age word problem</A> (*)

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/age/Selected-age-word-problems-from-the-archive.lesson>Selected age word problems from the archive</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/age/Age-problem-for-the-day-of-April-1.lesson>Age problem for the day of April, 1</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/age/04-OVERVIEW-of-lessons-on-age-problems.lesson>OVERVIEW of lessons on age problems</A>

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

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-I - YOUR ONLINE TEXTBOOK</A>.


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