document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=724360>Question 724360</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Need help with set up please!! I know the answer is 83 through playing with numbers, but I need to show it algebraically. thanks in advance\r<BR>\n" );
document.write( "\n" );
document.write( "The tens digit of a two-digit number is 5 more than the units digit. If \"the number\" is divided by the sum of its digits, the partial quotient is 7 and the remainder is 6. 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 #443712 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5399)</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=443712\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" > = tens digit<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" > = units digit<BR>\n" );
document.write( "so the value of the number is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10a%2Bb ALIGN=MIDDLE  ALT=\"10a%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" > and<BR>\n" );
document.write( "the sum of the digits is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Bb ALIGN=MIDDLE  ALT=\"a%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The tens digit is 5 more than the units digit translates as<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=b%2B5 ALIGN=MIDDLE  ALT=\"a=b%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "Now comes the hard part:<BR>\n" );
document.write( "If \"the number\" is divided by the sum of its digits, the partial quotient is 7 and the remainder is 6 translates as<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10a%2Bb=7%28a%2Bb%29%2B6 ALIGN=MIDDLE  ALT=\"10a%2Bb=7%28a%2Bb%29%2B6\"   DISABLED_style= \"max-width:90%; height:auto;\" > (dividend = divisor x quotient + remainder)<BR>\n" );
document.write( " <BR>\n" );
document.write( "Another way to see that:<BR>\n" );
document.write( "The number divided by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Bb ALIGN=MIDDLE  ALT=\"a%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" > is 7 plus the fraction that we get when we divide the remainder by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Bb ALIGN=MIDDLE  ALT=\"a%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2810a%2Bb%29%2F%28a%2Bb%29=7%2B6%2F%28a%2Bb%29 ALIGN=MIDDLE  ALT=\"%2810a%2Bb%29%2F%28a%2Bb%29=7%2B6%2F%28a%2Bb%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Multiplying times <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Bb ALIGN=MIDDLE  ALT=\"a%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" > both sides of the equal sign we get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10a%2Bb=7%28a%2Bb%29%2B6 ALIGN=MIDDLE  ALT=\"10a%2Bb=7%28a%2Bb%29%2B6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "Anyway,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10a%2Bb=7%28a%2Bb%29%2B6 ALIGN=MIDDLE  ALT=\"10a%2Bb=7%28a%2Bb%29%2B6\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10a%2Bb=7a%2B7b%2B6 ALIGN=MIDDLE  ALT=\"10a%2Bb=7a%2B7b%2B6\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3a%2Bb=7b%2B6 ALIGN=MIDDLE  ALT=\"3a%2Bb=7b%2B6\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3a=6b%2B6 ALIGN=MIDDLE  ALT=\"3a=6b%2B6\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3a%2F3=%286b%2B6%29%2F3 ALIGN=MIDDLE  ALT=\"3a%2F3=%286b%2B6%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=2b%2B2 ALIGN=MIDDLE  ALT=\"a=2b%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now we have a system of linear equations:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28a=b%2B5%2Ca=2b%2B2%29 ALIGN=MIDDLE  ALT=\"system%28a=b%2B5%2Ca=2b%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2b%2B2=b%2B5 ALIGN=MIDDLE  ALT=\"2b%2B2=b%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%2B2=5 ALIGN=MIDDLE  ALT=\"b%2B2=5\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=5-2 ALIGN=MIDDLE  ALT=\"b=5-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28b=3%29 ALIGN=MIDDLE  ALT=\"highlight%28b=3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28a=b%2B5%2Cb=3%29 ALIGN=MIDDLE  ALT=\"system%28a=b%2B5%2Cb=3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=3%2B5 ALIGN=MIDDLE  ALT=\"a=3%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28a=8%29 ALIGN=MIDDLE  ALT=\"highlight%28a=8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );