document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=564173>Question 564173</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi, I am having a problem forming the equation from a worded problem. I am struggling to understand what the terms mean in this equation and how they worked them out. I understand how to solve and can write quadratic motion equations. I have a good understanding. \r<BR>\n" );
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document.write( "The problem is: A school concert usually attracts 600 people at a cost of $10 per person. On avaerage for every $1 rise in admission price, 50 less people attend the concert. If T is the total amount of takings and n is the number of $1 increases write a rule for the function which gives T in terms of n.\r<BR>\n" );
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document.write( "The answer is: T = 6000 + 100n -50n^2\r<BR>\n" );
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document.write( "My thinking is that the 6000 represents the miinmum of the independant variable 600 people at $10 each which totals $6000. So this is where the parabola will start from the y-axis (i.e at zero). But how did they get the 100n? What does this mean in the context of the problem and why n^2?\r<BR>\n" );
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document.write( "Why isn't it linear? Like T = 6000 - 50(n)\r<BR>\n" );
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document.write( "Your help would be appreciated. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #365281 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=365281\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A school concert usually attracts 600 people at a cost of $10 per person.<BR>\n" );
document.write( " On average for every $1 rise in admission price, 50 less people attend the concert.<BR>\n" );
document.write( " If T is the total amount of takings and n is the number of $1 increases write a rule for the function which gives T in terms of n. <BR>\n" );
document.write( "The equation:<BR>\n" );
document.write( "Total = no. of people * cost for each ticket<BR>\n" );
document.write( "Which is<BR>\n" );
document.write( "T(n) = (600-50n)*(10+n)<BR>\n" );
document.write( "FOIL<BR>\n" );
document.write( "T(n) = 6000 + 600n - 500n - 50n^2<BR>\n" );
document.write( "The quadratic equation which has max value for some value of n<BR>\n" );
document.write( "T(n) = -50n^2 + 100n + 6000<BR>\n" );
document.write( ":<BR>\n" );
document.write( "The parabola will look like this<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-6%2C+15%2C+-1000%2C+7000%2C+-50x%5E2%2B100x%2B6000%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-6%2C+15%2C+-1000%2C+7000%2C+-50x%5E2%2B100x%2B6000%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Looks like max revenue will occur when n=1, 550 people and $11 ticket $6050 </SPAN>\n" );
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