document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1054799>Question 1054799</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An airline sells all the tickets for a certain route at the same price. If it charges 200 dollars per ticket it sells 10,000 tickets. For every 20 dollars the ticket price is reduced, an extra thousand tickets are sold. Thus if the tickets are sold for 180 dollars each then 11,000 tickets sell. It costs the airline 100 dollars to fly a person. <BR>\n" );
document.write( "(a) Express the total profit P in terms of the number n of tickets sold. <BR>\n" );
document.write( "(b) Express the total profit P in terms of the price p of one ticket.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #669984 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39618)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=669984\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Look first at how revenue relates to price.<BR>\n" );
document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "price      Count Sold Tickets\r\n" );
document.write( " 200         10000\r\n" );
document.write( " 180         11000            ---- here, i=1\r\n" );
document.write( " 160         12000\r\n" );
document.write( "200-20i      10000+1000i\r\n" );
document.write( "\r\n" );
document.write( "i is used to count increments of $20.\r\n" );
document.write( "</PRE>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "You may want to express that price <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=200-20i ALIGN=MIDDLE  ALT=\"p=200-20i\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "COST for flying 1 person was given as $100, for ONE PERSON.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "KEY IDEA:  P=r-c, PROFIT is revenue minus cost, but understand cost will be for all ticket buyers who are to fly.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "As your description gives, P is for profit and p is for price of a ticket.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "(a) profit in terms of number of tickets sold;<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=r-c ALIGN=MIDDLE  ALT=\"P=r-c\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "n for count of tickets<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=r-c%2An ALIGN=MIDDLE  ALT=\"P=r-c%2An\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28P=%28200-20i%29n-100n%29 ALIGN=MIDDLE  ALT=\"highlight%28P=%28200-20i%29n-100n%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >---------No way getting away from the unknown ticket price.  Otherwise you could simply say  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28P=pn-100n%29 ALIGN=MIDDLE  ALT=\"highlight%28P=pn-100n%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );