document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1054978>Question 1054978</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In a number of two digits, the sum of the digits is 14. If the digits are interchanged, the resulting number is 18 less than the original number. 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 #670194 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=670194\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let x equal the first digit of the original number.<BR>\n" );
document.write( "let y equal the second digit of the original number.\r<BR>\n" );
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document.write( "the original number is equal to 10x + y.\r<BR>\n" );
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document.write( "if you reverse the digits, then the number with the digits reversed is equal to 10y + x.\r<BR>\n" );
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document.write( "x + y = 14\r<BR>\n" );
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document.write( "10x + y = 10y + x - 18\r<BR>\n" );
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document.write( "simplify the second equation to get:\r<BR>\n" );
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document.write( "9x - 9y = -18\r<BR>\n" );
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document.write( "solve for x in the first equation to get x = 14 - y\r<BR>\n" );
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document.write( "replace x with 14 - y in the second equation to get:\r<BR>\n" );
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document.write( "9 * (14 - y) - 9y = -18\r<BR>\n" );
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document.write( "simplify to get 126 - 9y - 9y = -18\r<BR>\n" );
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document.write( "combine like terms to get 126 - 18y = -18\r<BR>\n" );
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document.write( "add 18 to both sides of the equation and add 18y to both sides of the equation to get:\r<BR>\n" );
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document.write( "126 + 18 = 18y\r<BR>\n" );
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document.write( "combine like terms to get 144 = 18y\r<BR>\n" );
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document.write( "divide both sides of the equation by 18 to get 144/18 = y\r<BR>\n" );
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document.write( "simplify to get 8 = y\r<BR>\n" );
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document.write( "since x + y = 14, then x must be equal to 6.\r<BR>\n" );
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document.write( "x + y = 14 becomes 14 = 14 which is true.\r<BR>\n" );
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document.write( "10x + y = 10y + x - 18 becomes 60 + 8 = 80 + 6 - 18 which becomes 68 = 86 - 18 which becomes 68 = 68 which is true.\r<BR>\n" );
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document.write( "the original number is 10x + y which is equal to 68.\r<BR>\n" );
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document.write( "the number with the digits reversed is equal to 10y + x which is equal to 86.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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