document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1113247>Question 1113247</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).<BR>\n" );
document.write( "John hosts an art workshop on the weekends. He has an average of 14 students in each session and charges a fee of $12 per session. He estimates that for every $2 increases in the fee, the average number of students reduces by 1.\r<BR>\n" );
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document.write( "Complete the equation that models this scenario, where c(x) is the revenue generated and x is the number of $2 fee increases.\r<BR>\n" );
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document.write( "c(x) = x2 + x +  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #728240 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=728240\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "The way you posed this question was confusing.  <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE c(x)\ =\ x^2\ +\ x\ +\ \"> implies that the coefficients on the high order and first-degree terms must be one, which, of course, is impossible.  Had you said \"find the coefficients for <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE c(x)\ =\ ax^2\ +\ bx\ +\ d\">\" then it would make sense.  And that is the only way that I can make sense of your question so that's what I'm going to show here.\r<BR>\n" );
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document.write( "We know that he gets 14 students @ $12 each, so if <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\ =\ 0\"> then his revenue is $168.  If <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\ =\ 1\"> he gets 13 students @ $14 each, so his revenue is $182.  And if <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\ =\ 2\"> we have 12 @ $16 for $192.  Symbolically:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ c(0)\ =\ a(0)^2\ +\ b(0)\ +\ d\ =\ 168\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ c(1)\ =\ a(1)^2\ +\ b(1)\ +\ d\ =\ 182\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ c(2)\ =\ a(2)^2\ +\ b(2)\ +\ d\ =\ 192\">\r<BR>\n" );
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document.write( "Since the first equation reduces to <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE d\ =\ 168\"> we can reduce the other two equations to:\r<BR>\n" );
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document.write( "(1)  <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ a\ +\ b\ =\ 14\">\r<BR>\n" );
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document.write( "(2)  <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 4a\ +\ 2b\ =\ 24\">\r<BR>\n" );
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document.write( "From (1):\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ b\ =\ 14\ -\ a\">\r<BR>\n" );
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document.write( "Substituting into (2)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 4a\ +\ 2(14\ -\ a)\ =\ 24\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 2a\ =\ 24\ -\ 28\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ a\ =\ -2\">\r<BR>\n" );
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document.write( "Substituting back into (1)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ -2\ +\ b\ =\ 14\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ b\ =\ 16\">\r<BR>\n" );
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document.write( "And the desired function becomes:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ c(x)\ =\ -2x^2\ +\ 16x\ +\ 168\">\r<BR>\n" );
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document.write( "Extra credit:  What is the price point to maximize revenue?  Hint:  What is the <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\">-coordinate of the vertex of this concave-down parabola?\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \\r\"> </SPAN>\n" );
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