document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=557651>Question 557651</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A two-digit number is eight times the sim of its digits. When the number is added to the number obtained by reversing the digits, the sum is 99. Find the original number.\r<BR>\n" );
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document.write( "(I tried 10x+y=8(x+y), 10x+y+10y+x=99) It didn't work though...<BR>\n" );
document.write( "Thanks! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #362699 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=362699\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let tens digit be x and units digit be y.<BR>\n" );
document.write( "The value of the number is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10x%2By ALIGN=MIDDLE  ALT=\"10x%2By\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "The sum of its digits is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By ALIGN=MIDDLE  ALT=\"x%2By\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "\"A two-digit number is eight times the sum of its digits\" translates into<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10x%2By=8%28x%2By%29 ALIGN=MIDDLE  ALT=\"10x%2By=8%28x%2By%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10x%2By=8x%2B8y ALIGN=MIDDLE  ALT=\"10x%2By=8x%2B8y\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10x-8x=8y-y ALIGN=MIDDLE  ALT=\"10x-8x=8y-y\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x=7y ALIGN=MIDDLE  ALT=\"2x=7y\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Since x and y are digits, the only solution is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=7 ALIGN=MIDDLE  ALT=\"x=7\"   DISABLED_style= \"max-width:90%; height:auto;\" > with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2 ALIGN=MIDDLE  ALT=\"y=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x=7y ALIGN=MIDDLE  ALT=\"2x=7y\"   DISABLED_style= \"max-width:90%; height:auto;\" >tells you that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x ALIGN=MIDDLE  ALT=\"2x\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a multiple of 7 or zero, so x must be a multiple of 7, and can only be 7. So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x=2%2A7=14=7y ALIGN=MIDDLE  ALT=\"2x=2%2A7=14=7y\"   DISABLED_style= \"max-width:90%; height:auto;\" >, which leads to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2 ALIGN=MIDDLE  ALT=\"y=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >).<BR>\n" );
document.write( "So the number is 72.<BR>\n" );
document.write( "When you reverse the digits, you get 27, which added to 72 is 99, but why that was added to the problem is a mystery to me.  </SPAN>\n" );
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