document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=129107>Question 129107</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0030700396/algebrahomeworkh>Algebra !</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> The sum of the digits of a two-digit number is 8. If 16 is added to the orginal number, the result is 3 times the original number with its digits reversed. Find the orginal number. This is the problum and  have no idea how to do it because i was gone when we learned this and i have bin working on this for litterly 2 hours please help me </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #94398 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=94398\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let x=one of the digits---the 10's digit<BR>\n" );
document.write( "And let y=the other digit---the unit digit\r<BR>\n" );
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document.write( "Now we are told that x+y=8-------------------------eq1\r<BR>\n" );
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document.write( "We know that the original number can be written as:\r<BR>\n" );
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document.write( "10x+y  now if we add 16 to this, we get (10x+y)+16 -------1\r<BR>\n" );
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document.write( "If we reverse the digits of the original number, we get:\r<BR>\n" );
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document.write( "10y+x and three time this number is:\r<BR>\n" );
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document.write( " 3(10y+x)----2\r<BR>\n" );
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document.write( "We are told that 1=2, so:\r<BR>\n" );
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document.write( "(10x+y)+16=3(10y+x)  get rid of parens\r<BR>\n" );
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document.write( "10x+y+16=30y+3x  subtract 10x and also y from both sides:\r<BR>\n" );
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document.write( "10x-10x+y-y+16=30y-y+3x-10x  collect like terms\r<BR>\n" );
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document.write( "16=29y-7x or<BR>\n" );
document.write( "-7x+29y=16-----------------------------------------eq2\r<BR>\n" );
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document.write( "substitute x=8-y from eq1 into eq2 and we have:\r<BR>\n" );
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document.write( "-7(8-y)+29y=16 get rid of parens\r<BR>\n" );
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document.write( "-56+7y+29y=16  add 56 to both sides\r<BR>\n" );
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document.write( "-56+56+7y+29y=16+56  collect like terms\r<BR>\n" );
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document.write( "36y=72  divide both sides by 36\r<BR>\n" );
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document.write( "y=2--------------------------------------the unit digit\r<BR>\n" );
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document.write( "substitute y=2 into eq1 and we get:\r<BR>\n" );
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document.write( "x+2=8  subtract 2 from both sides\r<BR>\n" );
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document.write( "x+2-2=8-2  collect like terms\r<BR>\n" );
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document.write( "x=6-----------------the 10's digit\r<BR>\n" );
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document.write( "Thus, the original number is 62\r<BR>\n" );
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document.write( "CK\r<BR>\n" );
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document.write( "6+2=8<BR>\n" );
document.write( "8=8<BR>\n" );
document.write( "and\r<BR>\n" );
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document.write( "62+16=3*26\r<BR>\n" );
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document.write( "78=78\r<BR>\n" );
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document.write( "Hope this helps---ptaylor<BR>\n" );
document.write( " </SPAN>\n" );
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