document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=32011>Question 32011</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/1888469544/algebrahomeworkh>Beginning Algebra</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> A number consists of two digits whose sum is five.  When the digits are reversed, the number is increased by nine.  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 #18552 by </B><A HREF=/tutors/aboutme.mpl?userid=mbarugel><B>mbarugel(146)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mbarugel><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=18552\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Hello!<BR>\n" );
document.write( "Let's call X to the first digit and Y to the second digit. The two digit number is then written as:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10X+%2B+Y ALIGN=MIDDLE  ALT=\"10X+%2B+Y\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "For example, if the digits are 3 and 7 (the number is 37), then the above expression yields:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2A3+%2B+7+=+37 ALIGN=MIDDLE  ALT=\"10%2A3+%2B+7+=+37\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "We know that the sum of the digits is 5, so we get the equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=X%2BY=5 ALIGN=MIDDLE  ALT=\"X%2BY=5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "We also know that when we reverse the number, it increases by 9. This implies that:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10Y%2BX+=+10X%2BY%2B9 ALIGN=MIDDLE  ALT=\"10Y%2BX+=+10X%2BY%2B9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9Y+-+9X+=+9 ALIGN=MIDDLE  ALT=\"9Y+-+9X+=+9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Y+-+X+=+1 ALIGN=MIDDLE  ALT=\"Y+-+X+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "We can isolate Y from this equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Y+=+1+%2B+X ALIGN=MIDDLE  ALT=\"Y+=+1+%2B+X\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "And replace it in the previous one:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=X%2B1%2BX+=+5 ALIGN=MIDDLE  ALT=\"X%2B1%2BX+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now solve for X:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2B2X+=+5 ALIGN=MIDDLE  ALT=\"1%2B2X+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=X+=+2 ALIGN=MIDDLE  ALT=\"X+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since the sum is 5, then Y must be 3. Therefore, the number is 23.\r<BR>\n" );
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document.write( "I hope this helps!<BR>\n" );
document.write( "Get more answers at <a  rel=nofollow HREF=http://www.onlinemathanswers.com>Online Math Answers.com</a>!<BR>\n" );
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