document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=480647>Question 480647</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The sum of the digits of a two-digit number is 13. When the digits are reversed, the new number is 27 more than the original number. What is the original number?\r<BR>\n" );
document.write( "\n" );
document.write( "(The worksheet says at the top \"Applying Systems\") </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #329142 by </B><A HREF=/tutors/aboutme.mpl?userid=Anthea+Lawn><B>Anthea Lawn(22)</B></A><img src=\"/images/stars/stars-07.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Anthea+Lawn><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=329142\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Lets say the 2 digit number is xy<BR>\n" );
document.write( "That is to say the \"tens\" digit is x and the \"units\" digit is y   (ie. by xy we don't mean x times y)\r<BR>\n" );
document.write( "\n" );
document.write( "So the value of the original number is 10x + y (because the x is in the \"tens\" column, just like 35 is 3 times 10 plus 5 for example)\r<BR>\n" );
document.write( "\n" );
document.write( "If you reverse the digits then the value of the new number is 10y + x\r<BR>\n" );
document.write( "\n" );
document.write( ".. and we know that this number is 27 more than the original .. so ...\r<BR>\n" );
document.write( "\n" );
document.write( "(10y + x) = (10x + y) + 27\r<BR>\n" );
document.write( "\n" );
document.write( "Take an x away from each side\r<BR>\n" );
document.write( "\n" );
document.write( "10y = 9x + y + 27\r<BR>\n" );
document.write( "\n" );
document.write( "Take a y away from each side\r<BR>\n" );
document.write( "\n" );
document.write( "9y = 9x + 27\r<BR>\n" );
document.write( "\n" );
document.write( ".. and we can divide both sides by 9 to make it a bit simpler\r<BR>\n" );
document.write( "\n" );
document.write( "y = x + 3\r<BR>\n" );
document.write( "\n" );
document.write( "So we are looking for a 2 digit number in which one digit is 3 more than the other.\r<BR>\n" );
document.write( "\n" );
document.write( "We are also told that the sum of the digits is 13\r<BR>\n" );
document.write( "\n" );
document.write( "x + y = 13\r<BR>\n" );
document.write( "\n" );
document.write( "Since we know that y = x + 3 (from above) we can substitute for y\r<BR>\n" );
document.write( "\n" );
document.write( "x + (x + 3) = 13\r<BR>\n" );
document.write( "\n" );
document.write( "So x = 5 which means that y = 8\r<BR>\n" );
document.write( "\n" );
document.write( "Therefore the original number was 58, which when reversed becomes 85 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );