document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=133852>Question 133852</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The sum of the digits of a two-digit number is 13. If the digits are reversed, the new number is 4 less than twice the original number. Find the original number.\r<BR>\n" );
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document.write( "I an very confused with this problem.\r<BR>\n" );
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document.write( "It's be greatly appreciated if I could get help! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #97894 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=97894\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 10s digit: x<BR>\n" );
document.write( "1s digit: y\r<BR>\n" );
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document.write( "The original number:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5Bo%5D=10x%2By ALIGN=MIDDLE  ALT=\"n%5Bo%5D=10x%2By\"   DISABLED_style= \"max-width:90%; height:auto;\" >, because a number like 24 could be represented as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2A10%2B4 ALIGN=MIDDLE  ALT=\"2%2A10%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Reversing the digits makes a new number: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5Bn%5D=10y%2Bx ALIGN=MIDDLE  ALT=\"n%5Bn%5D=10y%2Bx\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Twice the original number is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2810x%2By%29 ALIGN=MIDDLE  ALT=\"2%2810x%2By%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and 4 less than that is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2810x%2By%29-4 ALIGN=MIDDLE  ALT=\"2%2810x%2By%29-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > which we know to be equal to the new number, so:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10y%2Bx=2%2810x%2By%29-4 ALIGN=MIDDLE  ALT=\"10y%2Bx=2%2810x%2By%29-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Simplify:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10y%2Bx=20x%2B2y-4 ALIGN=MIDDLE  ALT=\"10y%2Bx=20x%2B2y-4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10y-2y%2Bx-20x=-4 ALIGN=MIDDLE  ALT=\"10y-2y%2Bx-20x=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8y-19x=-4 ALIGN=MIDDLE  ALT=\"8y-19x=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since we know that the sum of the digits is 13, we can say <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By=13 ALIGN=MIDDLE  ALT=\"x%2By=13\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or in other words, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=13-x ALIGN=MIDDLE  ALT=\"y=13-x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Substitute:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%2813-x%29-19x=-4 ALIGN=MIDDLE  ALT=\"8%2813-x%29-19x=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=104-8x-19x=-4 ALIGN=MIDDLE  ALT=\"104-8x-19x=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-27x=-108 ALIGN=MIDDLE  ALT=\"-27x=-108\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=4 ALIGN=MIDDLE  ALT=\"x=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the 10s digit of the original number (and the ones digit of the new number) is 4.  Therefore the ones digit of the original number must be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13-4=9 ALIGN=MIDDLE  ALT=\"13-4=9\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and the original number must be 49.\r<BR>\n" );
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document.write( "Check:<BR>\n" );
document.write( "Number is: 49<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2B9=13 ALIGN=MIDDLE  ALT=\"4%2B9=13\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2A49-4=98-4=94 ALIGN=MIDDLE  ALT=\"2%2A49-4=98-4=94\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is the original number with the digits reversed. </SPAN>\n" );
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