document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1209008>Question 1209008</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Sophie's favorite number is a two-digit number.  If she reverses the digits, the result is $45$ less than her favorite number.  The sum of the digits in her favorite number is $6$.  What is Sophie's favorite number?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #847568 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=847568\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "For the original number we have<BR>\n" );
document.write( "t = tens digit<BR>\n" );
document.write( "u = units digit<BR>\n" );
document.write( "That constructs 10t+u\r<BR>\n" );
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document.write( "For instance if the number is 23 then t = 2 and u = 3.<BR>\n" );
document.write( "10t+u = 10*2+3 = 23.\r<BR>\n" );
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document.write( "The digits of Sophie's mystery number add to 6.<BR>\n" );
document.write( "t+u = 6 which solves to <font color=blue>u = 6-t</font><BR>\n" );
document.write( "This will be useful in a substitution later.\r<BR>\n" );
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document.write( "10u+t is the result of reversing the digits. This is 45 less than her favorite number.\r<BR>\n" );
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document.write( "swapped = original - 45<BR>\n" );
document.write( "10u + t = 10t+u - 45<BR>\n" );
document.write( "10(<font color=blue>u</font>) + t = 10t+<font color=blue>u</font> - 45<BR>\n" );
document.write( "10(<font color=blue>6-t</font>) + t = 10t+<font color=blue>6-t</font> - 45<BR>\n" );
document.write( "60-10t+t = 10t+6-t-45<BR>\n" );
document.write( "60-9t = 9t-39<BR>\n" );
document.write( "-9t-9t = -39-60<BR>\n" );
document.write( "-18t = -99<BR>\n" );
document.write( "t = -99/(-18)<BR>\n" );
document.write( "t = 5.5<BR>\n" );
document.write( "We do not get a whole number result for the tens digit, so there must be a typo somewhere in your question. <BR>\n" );
document.write( "Perhaps the digits add to something else other than 6? <BR>\n" );
document.write( "Or maybe the \"45\" should be another value?<BR>\n" );
document.write( "I would ask your teacher for clarification.<BR>\n" );
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