document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=277285>Question 277285</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The sum of the digits  of a two- digit number is 14. When the digits are reversed, the new number is 36 more than the original number. 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 #201930 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=201930\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> When solving number problems like these, we have to keep in mind the place values.<BR>\n" );
document.write( "For example, the number 23 actually means 2*10 + 3*1.<BR>\n" );
document.write( "Since the numbers are unknown in this word problem, we can call them 'xy'.<BR>\n" );
document.write( "BUT keep in mind that they are just standing next to each other, they're not being multiplied.<BR>\n" );
document.write( "The value would be 10x + y.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "We are told some characteristics of the number 'xy'...<BR>\n" );
document.write( "x + y = 14<BR>\n" );
document.write( ".<BR>\n" );
document.write( "That's easy, but the second statement is harder to set up.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Remember, the VALUE of 'xy' is 10x + y.<BR>\n" );
document.write( "So, reversing the digits to be 'yx' would change the VALUE to 10y + x.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "We're told<BR>\n" );
document.write( "10y + x is 36 more than 10x + y, which algebraically is<BR>\n" );
document.write( "10y+x = 10x+y+36<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Rearranging this equation we have:<BR>\n" );
document.write( "x + 10y = 10x + y + 36<BR>\n" );
document.write( "x -10x + 10y - y = 36<BR>\n" );
document.write( "-9x + 9y = 36<BR>\n" );
document.write( "dividing by 9<BR>\n" );
document.write( "-x + y = 4<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Now we have to the two equations<BR>\n" );
document.write( "x + y = 14<BR>\n" );
document.write( "-x  + y = 4<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Adding we obtain<BR>\n" );
document.write( "2y = 18<BR>\n" );
document.write( "y = 9<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Since x+y = 14, then x = 14-9 = 5<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Checking...<BR>\n" );
document.write( "xy = 59<BR>\n" );
document.write( ".<BR>\n" );
document.write( "yx = 95<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Is 95 = 59 + 36??<BR>\n" );
document.write( "Yes.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Answer:<BR>\n" );
document.write( "The original number was 59.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Done </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );