document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=853428>Question 853428</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a caterer is planning a large dinner party for 1001 guests. Each table must seat and equal number of guests, more than 1 guest and fewer than 20. Determine the number of possible table sizes. If the caterers use 7 person tables, how many tables will they need? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #514098 by </B><A HREF=/tutors/aboutme.mpl?userid=JulietG><B>JulietG(1812)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=JulietG><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=JulietG><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=514098\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If there are 7 people per table, simply divide 1001/7 to get 143 tables.<BR>\n" );
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document.write( "For the others, the key is here: Each table must seat and equal number of guests<BR>\n" );
document.write( "So only table seatings that evenly go into 1001 can be considered.  Which numbers 2-19 are factors of 1001? 2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19<BR>\n" );
document.write( "We can immediately toss the even ones. 3,5,7,9,11,13,15,17,19<BR>\n" );
document.write( "We know that 5's don't fit. 3,7,9,11,13,17,19<BR>\n" );
document.write( "Divide 1001 by the numbers to find the possibilities where there is no remainder: 7, 11, 13<BR>\n" );
document.write( "Those are the only 3 table sizes that work.<BR>\n" );
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