document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1137125>Question 1137125</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A baseball team plays in a stadium that holds 50000 spectators. When the ticket price is $10, the average attendance is 27000. When the price is lowered to $6, the average attendance rose to 39000. \r<BR>\n" );
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document.write( "Find a demand function, D(q), where q is the quantity or number of spectators and D(q) is linear.\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #754962 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=754962\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> looks like the demand is based on the price.\r<BR>\n" );
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document.write( "you have two points to consider.\r<BR>\n" );
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document.write( "let x equal the price and y equal the average attendance.\r<BR>\n" );
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document.write( "the two points are (x1,y1) = (10,27000)and (x2,y2) = (6,39000)\r<BR>\n" );
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document.write( "the slope of a straight line is equal to (y2-y1) / (x2-x1) = (39000 - 27000) / (6 - 10) which is equal to 12000 / -4 which is equal to -3000.\r<BR>\n" );
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document.write( "the slope intercept form of the equation of a straight line is y = mx + b.\r<BR>\n" );
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document.write( "m is the slope and b is the y-intercept.\r<BR>\n" );
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document.write( "replace m with -3000 and the equation becomes y = -3000 * x + b.\r<BR>\n" );
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document.write( "to solve for b, replace x and y with the value of one the points on the line.\r<BR>\n" );
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document.write( "i chose (6,39000).\r<BR>\n" );
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document.write( "y = -3000 * x + b becomes 39000 = -3000 * 6 + b\r<BR>\n" );
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document.write( "simplify to get 39000 = -18000 + b.\r<BR>\n" );
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document.write( "add 18000 to both sides of this equation to get 39000 + 18000 = b.\r<BR>\n" );
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document.write( "solve for b to get b = 57000.\r<BR>\n" );
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document.write( "the equation becomes y = -3000 * x + 57000.\r<BR>\n" );
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document.write( "y is the demand and x is the price.\r<BR>\n" );
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document.write( "let t = d(x) and the equation becomes d(x) = -3000 * x + 57000.\r<BR>\n" );
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document.write( "this can also be shown as d(x) = 57000 - 3000 * x.\r<BR>\n" );
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document.write( "based on this equation , .....\r<BR>\n" );
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document.write( "when x = 0, the price is 0 and the demand will be 57000 which will be more than the stadium can hold because the stadium can only hold 50,000.\r<BR>\n" );
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document.write( "when x = 6, the price is 6 and the demand is 57000 - 18000 = 39000.\r<BR>\n" );
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document.write( "when x = 10, the price is 10 and the demand is 57000 - 30000 = 27000.\r<BR>\n" );
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