document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=187305>Question 187305</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The sum of the digits of a two-digit number is 11. If 45 is added to the number, the result is the number reversed. 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 #140426 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=140426\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "10s digit: <i>x</i>\r<BR>\n" );
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document.write( "1s digit: <i>y</i>\r<BR>\n" );
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document.write( "So:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \  x + y = 11 \ \ \Rightarrow\ \ x = 11 - y\">\r<BR>\n" );
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document.write( "Also the number is then:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \  10x + y\">\r<BR>\n" );
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document.write( "And the number with the digits reversed is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \  10y + x\">\r<BR>\n" );
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document.write( "And we are given that:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \  10x + y + 45 = 10y + x \ \ \Rightarrow\ \ 9x - 9y = -45 \ \ \Rightarrow\ \ x - y = -5\">\r<BR>\n" );
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document.write( "Substituting:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \  (11 - y) - y = 5 \ \ \Rightarrow\ \ -2y = -16 \ \ \Rightarrow\ \ y = 8 \ \ \Rightarrow\ \ x = 3\">\r<BR>\n" );
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document.write( "And the number is 38.\r<BR>\n" );
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document.write( "Note that 38 + 45 = 83 and 3 + 8 = 11, so the answer checks.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
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document.write( " </SPAN>\n" );
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