document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1108140>Question 1108140</A>: <I><SPAN STYLE=\"word-break: break-all;\"> At the local ball park, the team charges $5 for each ticket and expects to make 1,400 in concessions. The team must pay its players $2,000 and pay all other workers $1,600. Each fan gets a free bat that cost the team $3 per bat. How many tickets must be sold to break even? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #723159 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=723159\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> profit = revenue minus cost.\r<BR>\n" );
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document.write( "revenue is 5 dollars a ticket plus 1400 dollars in concessions.\r<BR>\n" );
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document.write( "the cost for the players is 2000 dollars and the cost for the other workers is 1600.\r<BR>\n" );
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document.write( "each person who buys a tickets gets a free bat that costs 3 dollars each.\r<BR>\n" );
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document.write( "let x equal the number of people who buy a ticket.\r<BR>\n" );
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document.write( "revenue = 1400 + 5x.\r<BR>\n" );
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document.write( "that's the revenue from the concessions plus 5 dollars for each ticket sold.\r<BR>\n" );
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document.write( "cost = 3600 + 3x\r<BR>\n" );
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document.write( "that's 2000 for the players and 1600 for the workers and 3 dollars for each bat given away.\r<BR>\n" );
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document.write( "profit = revenue minus cost.\r<BR>\n" );
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document.write( "profit = 1400 + 5x - (3600 + 3x)\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( "profit = 1400 + 5x - 3600 - 3x.\r<BR>\n" );
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document.write( "combine like terms to get:\r<BR>\n" );
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document.write( "profit = -2200 + 2x.\r<BR>\n" );
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document.write( "to find the break even point, set profit equal to 0.\r<BR>\n" );
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document.write( "set p = 0 and the profit equation becomes:\r<BR>\n" );
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document.write( "0 = -2200 + 2x.\r<BR>\n" );
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document.write( "add 2200 to both sides of this equation to get:\r<BR>\n" );
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document.write( "2200 = 2x\r<BR>\n" );
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document.write( "divide both sides of this equation by 2 to get:\r<BR>\n" );
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document.write( "1100 = x\r<BR>\n" );
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document.write( "they will  break even when the number of tickets sold is 1100.<BR>\n" );
document.write( "to make a profit, they have to sell more than 1100.<BR>\n" );
document.write( "to take a loss, they have to sell less than 1100.\r<BR>\n" );
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document.write( "profit equation is, once again:\r<BR>\n" );
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document.write( "p = -2200 + 2x\r<BR>\n" );
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document.write( "when x = 1100, the equation becomes:\r<BR>\n" );
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document.write( "p = -2200 + 2*1100 which becomes p = -2200 + 2200 which becomes p = 0.\r<BR>\n" );
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document.write( "they didn't take a loss, but they didn't make a profit either.\r<BR>\n" );
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document.write( "when x > 1100, like say 1200, the equation becomes:\r<BR>\n" );
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document.write( "p = -2200 + 2 * 1200 which becomes p = -2200 + 2400 which becomes p = 200.\r<BR>\n" );
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document.write( "now they've made a profit of 200 dollars if they sold 1200 tickets.\r<BR>\n" );
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document.write( "make x < 1100, like say 800, the equation becomes:\r<BR>\n" );
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document.write( "p = -2200 + 2 * 800 which becomes p = -2200 + 1600 which becomes p = -600.\r<BR>\n" );
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document.write( "negative profit is a positive loss, therefore they took a loss of 600 if they only sold 800 tickets.\r<BR>\n" );
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document.write( "let's look at the profit equation when they sold 1200 tickets and break it down into its revenue and cost components.\r<BR>\n" );
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document.write( "p = -2200 + 2 * x becomes p = -2200 + 2400 which becomes p = 200.\r<BR>\n" );
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document.write( "revenue is 1400 + 5*1200 = 1400 + 6000 = 7400.<BR>\n" );
document.write( "cost is 3600 + 3*1200 = 3600 + 3600 = 7200.<BR>\n" );
document.write( "profit is revenue minus cost = 7400 - 7200 = 200.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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