document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=784955>Question 784955</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A bus company carries about 40 000 riders per day for a fee of $1.00. A survey indicates that if the fare is decreased , the number of riders will increase by 2500 for every 5 cents  decrease. What fare will result in the greatest reverse?\r<BR>\n" );
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document.write( "Can you please help me out and can you show all the steps it would really help me understand. Thanks so much in advance:) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #477305 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=477305\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A bus company carries about 40 000 riders per day for a fee of $1.00.<BR>\n" );
document.write( " A survey indicates that if the fare is decreased, the number of riders will increase by 2500 for every 5 cents decrease.<BR>\n" );
document.write( "What fare will result in the greatest reverse? <BR>\n" );
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document.write( "I'm not sure what \"reverse\" means here. Perhaps you mean \"revenue\".<BR>\n" );
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document.write( "Let x = number of 5 cent decreases and no. of 2500 passenger increases<BR>\n" );
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document.write( "Find the fare that gives maximum revenue<BR>\n" );
document.write( "Revenue = fare * no. of passengers<BR>\n" );
document.write( "R(x) = (1-.05x)(40000+2500x)<BR>\n" );
document.write( "FOIL<BR>\n" );
document.write( "R(x) = 40000 + 2500x - 2000x - 125x^2<BR>\n" );
document.write( "Write as a quadratic equation<BR>\n" );
document.write( "y = -125x^2 + 500x + 40000<BR>\n" );
document.write( "Max y occurs at the axis of symmetry, find that using x = -b/(2a)<BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-500%29%2F%282%2A-125%29 ALIGN=MIDDLE  ALT=\"%28-500%29%2F%282%2A-125%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-500%29%2F%28-250%29 ALIGN=MIDDLE  ALT=\"%28-500%29%2F%28-250%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = +2 fare decreases $.90 fare<BR>\n" );
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document.write( "That would give a increase in passengers of 5000<BR>\n" );
document.write( "Max revenue: .90 *(40000+5000) = $40,500 max revenue<BR>\n" );
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document.write( "You can prove this to yourself, find the revenue using $.85 and $.95 </SPAN>\n" );
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