document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=575297>Question 575297</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A restaurant bill that comes to £200 is to be divided equally among a group of people. However, three people leave before the bill is settled and the remainder of the group has to pay an extra £15 each.<BR>\n" );
document.write( "How many people were orginally in the group? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #369466 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=369466\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A restaurant bill that comes to £200 is to be divided equally among a group of people.<BR>\n" );
document.write( " However, three people leave before the bill is settled and the remainder of the group has to pay an extra £15 each.<BR>\n" );
document.write( "How many people were originally in the group?<BR>\n" );
document.write( ":<BR>\n" );
document.write( "let x = no. originally in the group<BR>\n" );
document.write( "then<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=200%2Fx ALIGN=MIDDLE  ALT=\"200%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" > = amt each should have paid<BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=200%2F%28%28x-3%29%29 ALIGN=MIDDLE  ALT=\"200%2F%28%28x-3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = amt that was paid<BR>\n" );
document.write( ":<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=200%2F%28%28x-3%29%29 ALIGN=MIDDLE  ALT=\"200%2F%28%28x-3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=200%2Fx ALIGN=MIDDLE  ALT=\"200%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 15<BR>\n" );
document.write( "multiply by x(x-3)<BR>\n" );
document.write( "x(x-3)*<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=200%2F%28%28x-3%29%29 ALIGN=MIDDLE  ALT=\"200%2F%28%28x-3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > - x(x-3)*<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=200%2Fx ALIGN=MIDDLE  ALT=\"200%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 15x(x-3)<BR>\n" );
document.write( "Cancel the denominators and you have<BR>\n" );
document.write( "200x - 200(x-3) = 15x^2 - 45x<BR>\n" );
document.write( "200x - 200x + 600 = 15x^2 - 45x<BR>\n" );
document.write( "Combine on the right to form a quadratic equation<BR>\n" );
document.write( "0 = 15x^2 - 45x - 600<BR>\n" );
document.write( "Simplify, divide by 15<BR>\n" );
document.write( "x^2 - 3x - 40 = 0<BR>\n" );
document.write( "factors to<BR>\n" );
document.write( "(x-8)(x+5) = 0<BR>\n" );
document.write( "positive solution<BR>\n" );
document.write( "x = 8 people in the original group<BR>\n" );
document.write( ";<BR>\n" );
document.write( ":<BR>\n" );
document.write( "see if this checks, find out how much should be paid and was paid<BR>\n" );
document.write( "200/8 = 25<BR>\n" );
document.write( "200/5 = 40<BR>\n" );
document.write( "------------<BR>\n" );
document.write( "differs by $15  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );