document.write( "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?
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Algebra.Com's Answer #827986 by ikleyn(52811) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "Lola is 9 years older than Maggie, and in 1 year Maggie’s age will have
\n" ); document.write( "the same two digits as Lola’s age, but in reverse order. How old is Lola now?
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document.write( "I will explain the solution to you in easy informal manner.\r\n" );
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document.write( "I will consider everything in next your, when Lola is still 9 years older than Maggie,\r\n" );
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document.write( "their ages are reversed two-digit numbers, and their difference is 9 years.\r\n" );
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document.write( "It is useful to know, that \r\n" );
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document.write( "    (1)  the difference of any two-digit number x and its reversed y \r\n" );
document.write( "         is ALWAYS multiple to 9:  |x - y| = 9k, \r\n" );
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document.write( "and \r\n" );
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document.write( "    (2)  if \"a\" and \"b\" are the digits of such numbers, then |a-b| = k.\r\n" );
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document.write( "In our case, it means that the difference of the digits is 1:  |a - b| = 1\r\n" );
document.write( "(since |x - y| = 9 = 9*1).\r\n" );
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document.write( "    +---------------------------------------------------------+\r\n" );
document.write( "    |    So, our digits are two consecutive integer numbers.  |\r\n" );
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document.write( "And it is ALL the information, which we can extract from the given input.\r\n" );
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document.write( "Having only this information, we may conclude that their ages next your can be\r\n" );
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document.write( "   (Lola,Maggie) = (21,12), (32,23), (43,34), . . . , (98,89).\r\n" );
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document.write( "So, 8 different solutions are possible, and the problem DOES NOT provide any additional info\r\n" );
document.write( "to select a unique solution from these 8 possible solutions.\r\n" );
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document.write( "      You can check it on your own, that all conditions, \r\n" );
document.write( "            imposed by the problem, are held.\r\n" );
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document.write( "Thus, it is  that in the given formulation the problem is  :\r\n" );
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document.write( "    it gives 8 possible solutions, but it is IMPOSSIBLE \r\n" );
document.write( "    to select some a UNIOQUE soliton from these 8 solutions.\r\n" );
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\n" ); document.write( "\n" ); document.write( "At this point, my explanation is complete.\r
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\n" ); document.write( "\n" ); document.write( "The solution can be done formally, and it would be appropriate, if you solve such problem
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\n" ); document.write( "\n" ); document.write( "But my interior voice says me that, under right educational curriculum, the student
\n" ); document.write( "obtains such problem, when he (or she) is just familiar to some degree with problems
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\n" ); document.write( "\n" ); document.write( "Then such \" lightened \" explanation works better . . . \r
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\n" ); document.write( "\n" ); document.write( "For word problems on two-digit reversed integer numbers, see the lesson\r
\n" ); document.write( "\n" ); document.write( " - Word problems on reversing digits of numbers\r
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\n" ); document.write( "\n" ); document.write( "From this lesson, learn that properties of reversed numbers, which I used in my solution.\r
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\n" ); document.write( "\n" ); document.write( "Happy learning ( ! )\r
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\n" ); document.write( "\n" ); document.write( "The fact that the given problem is INCOMPLETE and, THEREFORE, is DEFECTIVE,\r
\n" ); document.write( "\n" ); document.write( "does not surprise me : at this forum, I see defective incoming problems EVERY DAY,\r
\n" ); document.write( "\n" ); document.write( "and even SEVERAL TIMES per day.\r
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