document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1207727>Question 1207727</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The sum of the digits of a two-digit number is 5. If 9 is subtracted from the number, the digits will be interchanged. Find the number. \r<BR>\n" );
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document.write( "I had completed this much:\r<BR>\n" );
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document.write( "assume ab is a number, a being in the 10's place and b being in the units place. <BR>\n" );
document.write( "ab=10a+b<BR>\n" );
document.write( "a+b=5<BR>\n" );
document.write( "9-(10a+b)=(10b+a)\r<BR>\n" );
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document.write( "But I am now confused on to what to substitute and how to do it.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #845753 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13203)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=845753\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Here is an important note regarding the work you show in trying to set up the problem.<br><BR>\n" );
document.write( "The statement of the problem says \"if 9 is subtracted from the number...\"<br><BR>\n" );
document.write( "You need to pay attention to what the whole phrase says, and not just write math symbols representing the given words.<br><BR>\n" );
document.write( "\"9\" is SUBTRACTED FROM the number.  The mathematical expression representing those words has to show that the 9 is being subtracted:<BR>\n" );
document.write( "(the number) minus (9) --> (10a+b)-9  --  not \"9-(10a+b)\", as you show in your work.<br><BR>\n" );
document.write( "Then a formal algebraic solution can be obtained from this correct expression as shown in the response from the other tutor.<br><BR>\n" );
document.write( "This is a common type of problem on competitive math contest exams.  If a formal algebraic solution is not needed, note that when the digits of a 2-digit number are reversed, the difference between the original number and the new number is always 9 times the difference between the two digits.<br><BR>\n" );
document.write( "In this problem, the sum of the two digits is 5, and the difference between the two numbers is 9 = 9*1, so the difference between the two digits is 1.<br><BR>\n" );
document.write( "So the sum of the two digits is 5 and the difference between the two digits is 1; that means the two digits are 2 and 3.<br><BR>\n" );
document.write( "Finally, since 9 was subtracted from the original number to get the new number, the original number is larger than the new number; that makes the original number 32 and the new number 23.<br><BR>\n" );
document.write( "ANSWER: 32<br><BR>\n" );
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