document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=802025>Question 802025</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In a math society the members were discussing how to divide the cost of their $3120 bill.  It was agreed that each member should pay an equal amount.  However 4 members resigned leaving remaining members to pay an extra $26 each.  How many members did the society originally have? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #483755 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=483755\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> In a math society the members were discussing how to divide the cost of their $3120 bill.<BR>\n" );
document.write( " It was agreed that each member should pay an equal amount.<BR>\n" );
document.write( " However 4 members resigned leaving remaining members to pay an extra $26 each.<BR>\n" );
document.write( " How many members did the society originally have?<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Let x = no. of original members<BR>\n" );
document.write( "then<BR>\n" );
document.write( "(x-4) = actual no. of members that paid<BR>\n" );
document.write( ":<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3120%2Fx ALIGN=MIDDLE  ALT=\"3120%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" > = original cost for each member<BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3120%2F%28%28x-4%29%29 ALIGN=MIDDLE  ALT=\"3120%2F%28%28x-4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = actual amt each had to pay<BR>\n" );
document.write( ":<BR>\n" );
document.write( "The equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3120%2F%28%28x-4%29%29 ALIGN=MIDDLE  ALT=\"3120%2F%28%28x-4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3120%2Fx ALIGN=MIDDLE  ALT=\"3120%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 26<BR>\n" );
document.write( "multiply by x(x-4) resulting in<BR>\n" );
document.write( "3120x - 3120(x-4) = 26x(x-4)<BR>\n" );
document.write( "3120x - 3120x + 12480 = 26x^2 - 104x<BR>\n" );
document.write( "A quadratic equation<BR>\n" );
document.write( "0 = 26x^2 - 104x - 12480 = 0<BR>\n" );
document.write( "Simplify, divide by 26<BR>\n" );
document.write( "x^2 - 4x - 480 = 0<BR>\n" );
document.write( "Factors to<BR>\n" );
document.write( "(x-24)(x+20) = 0<BR>\n" );
document.write( "The positive solution is all we want here<BR>\n" );
document.write( "x = 24 original members<BR>\n" );
document.write( ":<BR>\n" );
document.write( ":<BR>\n" );
document.write( "See if that checks out, find the actual cost for each scenario<BR>\n" );
document.write( "3120/20 = $156<BR>\n" );
document.write( "3120/24 = $130 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );