document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=66333>Question 66333</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/093979862x/algebrahomeworkh>An Incremental Development</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> The sum of the digits of a two-digit number is 15. if the digits are reversed, the new number is only 9 more than the original number. What was 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 #47040 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=47040\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The sum of the digits of a two-digit number is 15. if the digits are reversed, the new number is only 9 more than the original number. What was the original number?\r<BR>\n" );
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document.write( "Letx=1st digit<BR>\n" );
document.write( "And y= 2nd digit\r<BR>\n" );
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document.write( "Now we are told that x+y=15------------our first equation\r<BR>\n" );
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document.write( "But the first number is 10x+y\r<BR>\n" );
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document.write( "Now we are also told that if the digits are reversed the new number (10y+x) is 9 more that the first number (10x+y).  So:\r<BR>\n" );
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document.write( "10y+x=10x+y+9 collecting like terms, we have\r<BR>\n" );
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document.write( "9y=9x+9  divide by 9<BR>\n" );
document.write( "y=x+1 or<BR>\n" );
document.write( "x-y=-1------------our second equation\r<BR>\n" );
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document.write( "(1) x+y=15<BR>\n" );
document.write( "(2) x-y=-1\r<BR>\n" );
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document.write( "Add (1) and (2)<BR>\n" );
document.write( "2x=14<BR>\n" );
document.write( "x=7 first digit  \r<BR>\n" );
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document.write( "substitute x=7 in (1)<BR>\n" );
document.write( "7+y=15<BR>\n" );
document.write( "y=15-7<BR>\n" );
document.write( "y=8  second digit\r<BR>\n" );
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document.write( "So our first number was 78 and our second number was 87\r<BR>\n" );
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document.write( "ck\r<BR>\n" );
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document.write( "7+8=15<BR>\n" );
document.write( "15=15<BR>\n" );
document.write( "87 is 9 more than 78\r<BR>\n" );
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document.write( "Hope this helps -----ptaylor<BR>\n" );
document.write( " </SPAN>\n" );
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