document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1118220>Question 1118220</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Brian buses tables at a local cafe. To bus a table, he must clear the dirty dishes and reset the table for the next set of customers. One night he noticed that for every three-fifths of a table that he bused, another table of customers would get up and leave. He also noticed that right after he finished busing a table, a new table of customers would come into the restaurant. However, once every table was empty (no diners were left in the restaurant), nobody else came into the restaurant. Suppose there were six tables with customers and one unbused table. How many new tables of customers would come in before the restaurant was empty? After the last table of customers had left, how many tables were unbused? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #733567 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=733567\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> When <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13 ALIGN=MIDDLE  ALT=\"13\"   DISABLED_style= \"max-width:90%; height:auto;\" > sets of customers had left the cafe<BR>\n" );
document.write( "( <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6 ALIGN=MIDDLE  ALT=\"6\"   DISABLED_style= \"max-width:90%; height:auto;\" > sets who where seating at their tables initially,<BR>\n" );
document.write( "and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13-6=7 ALIGN=MIDDLE  ALT=\"13-6=7\"   DISABLED_style= \"max-width:90%; height:auto;\" > sets who entered and left the cafe),<BR>\n" );
document.write( "Brian has bused <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13%283%2F5%29=39%2F5=7%264%2F5 ALIGN=MIDDLE  ALT=\"13%283%2F5%29=39%2F5=7%264%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > tables,<BR>\n" );
document.write( "so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%287%29 ALIGN=MIDDLE  ALT=\"highlight%287%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > new tables of customers had come in,<BR>\n" );
document.write( "and Brian rushed to lock the door before an 8th set of customers could come in.<BR>\n" );
document.write( "At that point the number of unbused tables was<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2B13-7%264%2F5=highlight%286%261%2F5%29 ALIGN=MIDDLE  ALT=\"1%2B13-7%264%2F5=highlight%286%261%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( " <BR>\n" );
document.write( "STEPWISE:<BR>\n" );
document.write( "As Brian has bused <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F5 ALIGN=MIDDLE  ALT=\"3%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > of a table, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" > table-ful of customers leaves, so now Brian has <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" > more table to bus,<BR>\n" );
document.write( "to be added to the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F5 ALIGN=MIDDLE  ALT=\"2%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > left to do of the table he is busing.<BR>\n" );
document.write( "For each set of customers that leaves the restaurant,<BR>\n" );
document.write( "the number of tables unbused increases by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F5 ALIGN=MIDDLE  ALT=\"2%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(compared to the number unbused when the previous set of customers left).<BR>\n" );
document.write( "As Brian has bused <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%283%2F5%29=3 ALIGN=MIDDLE  ALT=\"5%283%2F5%29=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > tables, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2A1=5 ALIGN=MIDDLE  ALT=\"5%2A1=5\"   DISABLED_style= \"max-width:90%; height:auto;\" > table-ful of customers have left,<BR>\n" );
document.write( "but at the same time new customers have filled <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > tables.<BR>\n" );
document.write( "The number of tables in use has decreased by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5-3=2 ALIGN=MIDDLE  ALT=\"5-3=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" > tables emptied.<BR>\n" );
document.write( "As Brian has bused <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%283%2F5%29=6 ALIGN=MIDDLE  ALT=\"10%283%2F5%29=6\"   DISABLED_style= \"max-width:90%; height:auto;\" > tables, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2A1 ALIGN=MIDDLE  ALT=\"10%2A1\"   DISABLED_style= \"max-width:90%; height:auto;\" > table-ful of customers have left,<BR>\n" );
document.write( "but at the same time new customers have filled <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6 ALIGN=MIDDLE  ALT=\"6\"   DISABLED_style= \"max-width:90%; height:auto;\" > tables,<BR>\n" );
document.write( "leaving <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6-10%2B6=2 ALIGN=MIDDLE  ALT=\"6-10%2B6=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > tables occupied.<BR>\n" );
document.write( "After that, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2B1=3 ALIGN=MIDDLE  ALT=\"2%2B1=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > more table-fuls of diners will have to leave for the cafe to be empty,<BR>\n" );
document.write( "because by the time the customers in those <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > occupied tables leave,<BR>\n" );
document.write( "Brian will have bused <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%283%2F5%29=6%2F5=1%261%2F5 ALIGN=MIDDLE  ALT=\"2%283%2F5%29=6%2F5=1%261%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > table,<BR>\n" );
document.write( "but as he finished busing one table, another table became occupied.<BR>\n" );
document.write( "As the last <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > table-fuls of customers left,<BR>\n" );
document.write( "a total of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2B3=13 ALIGN=MIDDLE  ALT=\"10%2B3=13\"   DISABLED_style= \"max-width:90%; height:auto;\" > table-fuls of customers had left,<BR>\n" );
document.write( "Brian had bused <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13%283%2F5%29=39%2F5=7%264%2F5 ALIGN=MIDDLE  ALT=\"13%283%2F5%29=39%2F5=7%264%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > tables,<BR>\n" );
document.write( "while the number of tables to be bused had increased by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13 ALIGN=MIDDLE  ALT=\"13\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "so after Brian locked the door, the number of unbused tables was<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2B13-7%264%2F5=6%261%2F5 ALIGN=MIDDLE  ALT=\"1%2B13-7%264%2F5=6%261%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > . </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );