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" );
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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 #443713 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=443713\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let a = the 10's digit<BR>\n" );
document.write( "let b = the units<BR>\n" );
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document.write( "10a+b = \"the number\"<BR>\n" );
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document.write( "Write an equation for each statement<BR>\n" );
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document.write( "\"The tens digit of a two-digit number is 5 more than the units digit.\"<BR>\n" );
document.write( "a = b + 5<BR>\n" );
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document.write( "\"If \"the number\" is divided by the sum of its digits, the partial quotient is 7 and the remainder is 6.\"<BR>\n" );
document.write( "subtract the remainder (6) from the number to get an even 7<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%2810a%2Bb-6%29%29%2F%28%28a%2Bb%29%29 ALIGN=MIDDLE  ALT=\"%28%2810a%2Bb-6%29%29%2F%28%28a%2Bb%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 7<BR>\n" );
document.write( "multiply both sides by (a+b)<BR>\n" );
document.write( "10a + b - 6 = 7(a+b)<BR>\n" );
document.write( "10a + b - 6 = 7a + 7b<BR>\n" );
document.write( "10a - 7a = 7b - b + 6<BR>\n" );
document.write( "3a = 6b + 6<BR>\n" );
document.write( "simplify, divide by 3<BR>\n" );
document.write( "a = 2b + 2<BR>\n" );
document.write( "Replace a with (b+5)<BR>\n" );
document.write( "b + 5 = 2b + 2<BR>\n" );
document.write( "5 - 2 = 2b - b<BR>\n" );
document.write( "b = 3, <BR>\n" );
document.write( "then<BR>\n" );
document.write( "a = 3 + 5<BR>\n" );
document.write( "a = 8<BR>\n" );
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document.write( "83 is the number<BR>\n" );
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document.write( ":\r<BR>\n" );
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document.write( "Check this, divide 83 by 11, 7 a remainder of 6\r<BR>\n" );
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document.write( "  </SPAN>\n" );
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