document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=269364>Question 269364</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A number consist of two digit whose sum is 5. When the digits are reversed, tne number becomes greater by 9.Find the number: </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #197434 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=197434\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A number consist of two digit whose sum is 5. When the digits are reversed, tne number becomes greater by 9.Find the number:<BR>\n" );
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document.write( "It has to be 14 or 23<BR>\n" );
document.write( "It's 23<BR>\n" );
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document.write( "The difference when you reverse digits is always a multiple of 9.<BR>\n" );
document.write( "1*9<BR>\n" );
document.write( "2*9<BR>\n" );
document.write( "3*9<BR>\n" );
document.write( "4*9 etc<BR>\n" );
document.write( "The multiplier of 9 is the difference between the digits.<BR>\n" );
document.write( "eg, for 37, the difference is 4, so 4*9 will be the change when the digits are reversed.<BR>\n" );
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document.write( "For your problem, the multiplier of 9 is 1, so the difference between the digits is 1.<BR>\n" );
document.write( "That makes the problem simpler:<BR>\n" );
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document.write( "The sum of the digits is 5<BR>\n" );
document.write( "The difference of the digits is 1<BR>\n" );
document.write( "u + t = 5<BR>\n" );
document.write( "u - t = 1<BR>\n" );
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document.write( "2u = 6<BR>\n" );
document.write( "u = 3<BR>\n" );
document.write( "t = 2<BR>\n" );
document.write( "--> 23<BR>\n" );
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document.write( "The long way:<BR>\n" );
document.write( "10t + u = 10u + t - 9<BR>\n" );
document.write( "t + u = 5<BR>\n" );
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document.write( "9t - 9u = -9<BR>\n" );
document.write( "t - u = -1<BR>\n" );
document.write( "t + u = 5<BR>\n" );
document.write( "2t = 4<BR>\n" );
document.write( "t = 2<BR>\n" );
document.write( "u = 3<BR>\n" );
document.write( "--> 23\r<BR>\n" );
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