document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1109194>Question 1109194</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 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 (answer) 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 #724199 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=724199\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The tens digit of a two-digit number is 5 more than the units digit.<BR>\n" );
document.write( " If \"the number\" is divided by the sum of its digits, the partial quotient (answer) is 7 and the remainder is 6.<BR>\n" );
document.write( " Find the number.<BR>\n" );
document.write( "let a = the 10's digit<BR>\n" );
document.write( "let b = the units<BR>\n" );
document.write( "then<BR>\n" );
document.write( "10a+b = \"the number\"<BR>\n" );
document.write( ":<BR>\n" );
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" );
document.write( ":<BR>\n" );
document.write( "If \"the number\" is divided by the sum of its digits, the partial quotient (answer) is 7 and the remainder is 6.<BR>\n" );
document.write( "  Subtracting the remainder make the quotient an integer<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%2810a%29%2B+b+-+6%29%2F%28a%2Bb%29 ALIGN=MIDDLE  ALT=\"%28%2810a%29%2B+b+-+6%29%2F%28a%2Bb%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( "combine like terms on the left<BR>\n" );
document.write( "10a - 7a + b - 7b = 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), from the first equation/statement<BR>\n" );
document.write( "(b+5) - 2b = 2<BR>\n" );
document.write( "b - 2b = 2 - 5<BR>\n" );
document.write( "-b = -3<BR>\n" );
document.write( "b = 3<BR>\n" );
document.write( "then, obviously;<BR>\n" );
document.write( "a = 8<BR>\n" );
document.write( " Find the number. 83 is the number <BR>\n" );
document.write( ":<BR>\n" );
document.write( ";<BR>\n" );
document.write( "Check<BR>\n" );
document.write( "(83-6)/11 = 7  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );