document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=280832>Question 280832</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The sum of the digits of a two digit number is 14. If 36 is subtracted from the number, the resulting number is the original number with its digits interchangeable. 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 #204089 by </B><A HREF=/tutors/aboutme.mpl?userid=oberobic><B>oberobic(2304)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=oberobic><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=204089\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> When doing sum of digits problems, you have to remember that numbers like 'xy' are not being multiplied.<BR>\n" );
document.write( "Consider the number 23.<BR>\n" );
document.write( "It really is not \"one\" number, but instead it means 2*10 + 3*1.<BR>\n" );
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document.write( "So the number is 'xy' but that is NOT x*y, it's just 'x' next to 'y'.<BR>\n" );
document.write( "The value of the number 'xy' = 10x + y.<BR>\n" );
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document.write( "x + y = 14  :: given<BR>\n" );
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document.write( "36 is a value, so to subtract it, you have to calculate the value of xy:<BR>\n" );
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document.write( "10x+y -36 = 10y + x<BR>\n" );
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document.write( "Setting up a system of equations:<BR>\n" );
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document.write( "10x + y - 36 - 10y - x = 0<BR>\n" );
document.write( "9x - 9y = 36<BR>\n" );
document.write( "x - y = 4<BR>\n" );
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document.write( "x + y = 14<BR>\n" );
document.write( "x - y = 4<BR>\n" );
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document.write( "adding<BR>\n" );
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document.write( "2x = 18<BR>\n" );
document.write( "x = 9<BR>\n" );
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document.write( "x + y = 14<BR>\n" );
document.write( "given x = 9<BR>\n" );
document.write( "y = 5<BR>\n" );
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document.write( "so the original number, 'xy', appears to be 95.<BR>\n" );
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document.write( "checking...<BR>\n" );
document.write( "'yx' would be 59.<BR>\n" );
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document.write( "so, is 95 - 36 = 59?<BR>\n" );
document.write( "Yes, it is.<BR>\n" );
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document.write( "Answer:<BR>\n" );
document.write( "The number is 95.<BR>\n" );
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document.write( "Done. </SPAN>\n" );
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