document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=28142>Question 28142</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help us write out this equation. I couldn't find anything like this problem in your previous answers. This problem is word for word from my son's algebra book.\r<BR>\n" );
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document.write( "The sum of the digits of a two-digit number is 9. If the digits are reversed, the new number is 27 less than the original. Find the original number.\r<BR>\n" );
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document.write( "Thanks a billion in advance for your help. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #15335 by </B><A HREF=/tutors/aboutme.mpl?userid=longjonsilver><B>longjonsilver(2297)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=longjonsilver><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=longjonsilver><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=15335\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let the number be written as xy, where x is the number of tens and y in the number of units.\r<BR>\n" );
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document.write( "x+y = 9 --eqn1\r<BR>\n" );
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document.write( "original number is (10x + y)<BR>\n" );
document.write( "reversed number is (10y + x)\r<BR>\n" );
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document.write( "reversed = original - 27<BR>\n" );
document.write( "(10y + x) = (10x + y) - 27<BR>\n" );
document.write( "10y + x = 10x + y - 27<BR>\n" );
document.write( "9y - 9x = -27<BR>\n" );
document.write( "or -9y + 9x = 27 ... just reversing all signs (equivalent to moving all terms to opposite side of equals sign)\r<BR>\n" );
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document.write( "so -9y + 9x = 27 is <BR>\n" );
document.write( "9x - 9y = 27 --eqn2\r<BR>\n" );
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document.write( "so we have 2 equations and 2 unknowns...possible to solve.<BR>\n" );
document.write( "x + y = 9 -- multiply by 9<BR>\n" );
document.write( "9x - 9y = 27\r<BR>\n" );
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document.write( "9x + 9y = 81<BR>\n" );
document.write( "9x - 9y = 27<BR>\n" );
document.write( "and add together giving 18x = 108<BR>\n" );
document.write( "--> x = 6<BR>\n" );
document.write( "therefore y must be 3\r<BR>\n" );
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document.write( "so numbers are 63 and 36 and their difference is 27...correct.\r<BR>\n" );
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document.write( "jon.<BR>\n" );
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