document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1118566>Question 1118566</A>: <I><SPAN STYLE=\"word-break: break-all;\"> For an upcoming event, a 2500 seat arena is selling tickets for $25 and $15. At least 1000 tickets must be priced at $15 and total sales need to exceed $10,000 to make a profit. Let x represent the number of tickets priced at $25 and y represent the number of tickets priced at $15. Write a system of inequalities that shows the possible combinations of ticket sales in order to make a profit. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #733924 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=733924\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> number of seats is 2500 which means that a total of 2500 tickets can be sold.\r<BR>\n" );
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document.write( "let x equal the number of tickets sold at 25 dollars.<BR>\n" );
document.write( "let y equal the number of tickets sold at 15 dollars.\r<BR>\n" );
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document.write( "25x equals the amount of money made from selling 25 dollar tickets.<BR>\n" );
document.write( "15y equals the amount of money made from selling 15 dollar tickets.\r<BR>\n" );
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document.write( "total sales must be greater than 10,000, so 25x + 15y >= 10,000.\r<BR>\n" );
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document.write( "maximum number of tickets that could be sold is 2500, so x + y <= 2500.\r<BR>\n" );
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document.write( "at least 1000 tickets must be priced at 15 dollars, so y >= 1000.\r<BR>\n" );
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document.write( "your system of requirements would be:\r<BR>\n" );
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document.write( "y >= 1000<BR>\n" );
document.write( "25x + 15y >= 10,000<BR>\n" );
document.write( "x >= 0 (unstated but necessary since number of tickets can't be negative).<BR>\n" );
document.write( "x + y <= 2500\r<BR>\n" );
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document.write( "note that, if you only sold 1000 tickets at 15 dollars apiece, you would automatically make a profit because 15 * 1000 = 15,000 which is greater than 10,000.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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