document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1195485>Question 1195485</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 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?  <BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #827987 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13203)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=827987\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The difference in their ages next year, when their two ages have the same digits but in reverse order, will still be 9 years.<br><BR>\n" );
document.write( "When the digits of a 2-digit number are reversed, the difference between the original number and the new number is 9 times the difference between the two digits.  This is easily proved algebraically; but you can see it with a few examples....<BR>\n" );
document.write( "74-47 = 27 = 9(3) = 9(7-4)<BR>\n" );
document.write( "82-28 = 54 = 9(6) = 9(8-2)<BR>\n" );
document.write( "43-34 = 9 = 9(1) = 9(4-3)<br><BR>\n" );
document.write( "Since in this problem the difference in their ages is 9, their ages 1 year from now will both have two digits whose difference is 1.<br><BR>\n" );
document.write( "But there is no unique solution to that.  Their ages next year could be 21 and 12, or 32 and 23, or 43 and 34, or..., or 98 and 89.<br><BR>\n" );
document.write( "So the problem is defective....<br><BR>\n" );
document.write( "ANSWER: no unique solution<br><BR>\n" );
document.write( "We quickly see that there is no unique solution if we try to solve the problem with formal algebra.<br><BR>\n" );
document.write( "1 year from now, Lola's age and Maggie's age will have the same two digits, so let Lola's age be \"AB\" and Maggie's age be \"BA\".  Algebraically, then, their ages will be<br><BR>\n" );
document.write( "Lola: 10A+B<BR>\n" );
document.write( "Maggie: 10B+A<br><BR>\n" );
document.write( "The difference in their ages then will be 9 years:<br><BR>\n" );
document.write( "(10A+B)-(10B+A) = 9<BR>\n" );
document.write( "10A+B-10B-A = 9<BR>\n" );
document.write( "9A-9B = 9<BR>\n" );
document.write( "A-B = 1<br><BR>\n" );
document.write( "That's as far as we can go with the given information, so the problem has no unique solution.<br>\r<BR>\n" );
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