document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=672743>Question 672743</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If a two digit number is decreased by 45, the original number will be reversed.  The number is 5 less than 8 times the sum of its digits.  What is the number?  (According to the answer in my book; they are showing 10x and x and no x and y or t and u).  I need to know how they are doing it with just x and 10x.   </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #418463 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=418463\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let x = the 10's digit<BR>\n" );
document.write( "let y = the units<BR>\n" );
document.write( "then<BR>\n" );
document.write( "10x+y = the original number<BR>\n" );
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document.write( "Write an equation for each statement; simplify:<BR>\n" );
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document.write( "\"If a two digit number is decreased by 45, the original number will be reversed.\"<BR>\n" );
document.write( "10x + y - 45 = 10y + x<BR>\n" );
document.write( "10x - x = 10y -y + 45<BR>\n" );
document.write( "9x = 9y + 45<BR>\n" );
document.write( "Simplify, divide thru by 9<BR>\n" );
document.write( "x = y + 5<BR>\n" );
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document.write( "\" The number is 5 less than 8 times the sum of its digits.\"<BR>\n" );
document.write( "10x + y = 8(x+y) - 5<BR>\n" );
document.write( "10x + y = 8x + 8y - 5<BR>\n" );
document.write( "10x - 8x = 8y - y - 5<BR>\n" );
document.write( "2x = 7y - 5<BR>\n" );
document.write( "Replace x with (y+5), from the 1st statment<BR>\n" );
document.write( "2(y+5) = 7y - 5<BR>\n" );
document.write( "2y + 10 = 7y - 5<BR>\n" );
document.write( "Get everything positive here<BR>\n" );
document.write( "10 + 5 = 7y - 2y<BR>\n" );
document.write( "15 = 5y<BR>\n" );
document.write( "y = 15/5<BR>\n" );
document.write( "y = 3<BR>\n" );
document.write( "then<BR>\n" );
document.write( "x = 3 + 5<BR>\n" );
document.write( "x = 8<BR>\n" );
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document.write( "83 = the original number<BR>\n" );
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document.write( "See if that checks out in the 1st statement<BR>\n" );
document.write( "\"If a two digit number is decreased by 45, the original number will be reversed.<BR>\n" );
document.write( "83 - 45 = 38; confirms our solution\r<BR>\n" );
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document.write( "  </SPAN>\n" );
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