Question 1195485
.
Lola is 9 years older than Maggie, and in 1 year Maggie’s age will have 
the same two digits as Lola’s age, but in reverse order. How old is Lola now?  
~~~~~~~~~~~~~~~~~


<pre>
I will explain the solution to you in easy informal manner.


I will consider everything in next your, when Lola is still 9 years older than Maggie,

their ages are reversed two-digit numbers, and their difference is 9 years.



It is useful to know, that 

    (1)  the difference of any two-digit number x and its reversed y 
         is ALWAYS multiple to 9:  |x - y| = 9k, 

and 

    (2)  if "a" and "b" are the digits of such numbers, then |a-b| = k.



In our case, it means that the difference of the digits is 1:  |a - b| = 1
(since |x - y| = 9 = 9*1).


    +---------------------------------------------------------+
    |    So, our digits are two consecutive integer numbers.  |
    +---------------------------------------------------------+


And it is ALL the information, which we can extract from the given input.


Having only this information, we may conclude that their ages next your can be

   (Lola,Maggie) = (21,12), (32,23), (43,34), . . . , (98,89).


So, 8 different solutions are possible, and the problem DOES NOT provide any additional info
to select a unique solution from these 8 possible solutions.



      You can check it on your own, that all conditions, 
            imposed by the problem, are held.



Thus, it is {{{highlight(OBVIOUS)}}} that in the given formulation the problem is {{{highlight(INCOMPLETE)}}} :

    it gives 8 possible solutions, but it is IMPOSSIBLE 
    to select some a UNIOQUE soliton from these 8 solutions.
</pre>

At this point, my explanation is complete.



======================


The solution can be done formally, and it would be appropriate, if you solve such problem
for the first time in your life.


But my interior voice says me that, &nbsp;<U>under right educational curriculum</U>, &nbsp;the student
obtains such problem, &nbsp;when he &nbsp;(or she) &nbsp;is just familiar to some degree with problems
that include reversed numbers.


Then such  " lightened " &nbsp;explanation works better . . . 



////////////////



For word problems on two-digit reversed integer numbers, &nbsp;see the lesson

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/misc/Word-problems-on-interchanging-digits-of-numbers.lesson>Word problems on reversing digits of numbers</A>

in this site.


From this lesson, &nbsp;learn that properties of reversed numbers, &nbsp;which I used in my solution.



Happy learning &nbsp;(&nbsp;!&nbsp;)



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The fact that the given problem is &nbsp;INCOMPLETE &nbsp;and, &nbsp;THEREFORE, &nbsp;is &nbsp;DEFECTIVE,

does not surprise me : &nbsp;at this forum, &nbsp;I see defective incoming problems &nbsp;EVERY &nbsp;DAY,

and even &nbsp;SEVERAL &nbsp;TIMES &nbsp;per day.