document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=77841>Question 77841</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The sum of the digits of a two-digit number equals 1/7 of the number. If the digits are reversed, the new number is 27 less than the original number. Find the original number. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #55808 by </B><A HREF=/tutors/aboutme.mpl?userid=ptaylor><B>ptaylor(2198)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ptaylor><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=ptaylor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=55808\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let 10x+y=the number\r<BR>\n" );
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document.write( "We are told that x+y=(1/7)(10x+y)----------------eq 1\r<BR>\n" );
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document.write( "We are also told that:\r<BR>\n" );
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document.write( "10y+x=(10x+y)-27----------------------------------eq 2\r<BR>\n" );
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document.write( "Simplifying eq 1:\r<BR>\n" );
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document.write( "x+y=(10/7)x+(1/7)y  multiply each term by 7\r<BR>\n" );
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document.write( "7x+7y=10x+y  subtract 10x and also y from both sides\r<BR>\n" );
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document.write( "7x-10x+7y-y=10x-10x+y-y  collect like terms\r<BR>\n" );
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document.write( "-3x+6y=0 subtract 6y from both sides and divide both sides by -3<BR>\n" );
document.write( "x=2y---------------------------eq 1 simplified\r<BR>\n" );
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document.write( "Simplifying eq 2:\r<BR>\n" );
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document.write( "10y+x=10x+y-27  subtract 10x and also y from both sides\r<BR>\n" );
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document.write( "10y-y+x-10x=10x-10x+y-y-27  collect like terms\r<BR>\n" );
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document.write( "9y-9x=-27 multiply each term by -1 and divide each term by 9\r<BR>\n" );
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document.write( "x-y=3--------------------------------eq 2 simplified<BR>\n" );
document.write( "Substitute x=2y from eq 1 into eq 2\r<BR>\n" );
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document.write( "2y-y=3 or <BR>\n" );
document.write( "y=3--------------substitute into eq 1\r<BR>\n" );
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document.write( "x=2y=2*3=6\r<BR>\n" );
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document.write( "10x+y=60+3=63---------------------------the number\r<BR>\n" );
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document.write( "CK\r<BR>\n" );
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document.write( "sum of the digits of the number (6+3) = 1/7 of the number<BR>\n" );
document.write( "9=1/7(63)--------------ok<BR>\n" );
document.write( "If the digits are reversed, the new number is 27 less than the original number:<BR>\n" );
document.write( "36=63-27<BR>\n" );
document.write( "36=36--------------ok\r<BR>\n" );
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document.write( "Hope this helps---ptaylor\r<BR>\n" );
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document.write( " </SPAN>\n" );
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