document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=275504>Question 275504</A>: <I><SPAN STYLE=\"word-break: break-all;\"> if you take a certain two-digit number and reverse its digits to get another two-digit number, then add these two numbers together, their sum is 132. what is the original number? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #854111 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13327)</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=854111\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "While a formal algebraic solution was probably wanted, note that you can also work this problem using logical reasoning and the basic process of adding two 2-digit numbers.  In \"coded\" form, you have this addition, where A and B are the two digits of the original number and S is the sum of those two digits (S is not a digit, because the sum of the two 2-digit numbers is 3 digits):<br><PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "   A B\r\n" );
document.write( " + B A\r\n" );
document.write( " ------\r\n" );
document.write( "   S S</PRE><BR>\n" );
document.write( "Now that sum has the sum \"S\" in the 10s column and also in the units column, so the value of that sum is 10S + 1S = 11S.<br><BR>\n" );
document.write( "But the sum is 132, so 11S = 132, so S = 132/11 = 12.<br><BR>\n" );
document.write( "So we know that the sum of the two digits A and B is 12.<br><BR>\n" );
document.write( "However, we have no other information to use to find a unique solution to the problem.  So the original number can be any 2-digit number in which the sum of the two digits is 12: 39, 48, 57, 66, 75, 84, or 93.  Notice that the statement of the problem did not require the two digits of the original number to be different, so 66 is one of the possible answers.<br><BR>\n" );
document.write( "ANSWERS: any of the numbers 39, 48, 57, 66, 75, 84, or 93<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );