document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=722277>Question 722277</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The product of a two-digit number and the same number with its digits reversed is 3154. Find the sum of the two numbers. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #442727 by </B><A HREF=/tutors/aboutme.mpl?userid=DrBeeee><B>DrBeeee(684)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=DrBeeee><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=442727\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I know the answer is 38*83 = 3154<BR>\n" );
document.write( "So the sum is 38+83 = 121<BR>\n" );
document.write( "However I've been unable to derive it. Sorry.<BR>\n" );
document.write( "I've got<BR>\n" );
document.write( "(1) n1 = 10x + y and<BR>\n" );
document.write( "(2) n2 = 10y + x <BR>\n" );
document.write( "Therefore the sum is<BR>\n" );
document.write( "(3) n1 + n2 = 11x + 11y or<BR>\n" );
document.write( "(4) sum = 11(x+y)<BR>\n" );
document.write( "But I can't come up with 3 and 8 for x and y.<BR>\n" );
document.write( "Nor can I solve <BR>\n" );
document.write( "(5) n1*n2 = 3154<BR>\n" );
document.write( "We know that n1 (or n2) has to be greater than 32 in order to get a second two digit number for the product.<BR>\n" );
document.write( "Maybe we can say both are greater than 32 which means x or y has to be 3, then try 33*33, 34*43, 35*53, 36*63, 37*73, 38*83, 39*93. Indeed<BR>\n" );
document.write( "the answer appear, but mathematician can't accept trial and error. There's got to be a better way. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );