document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=121757>Question 121757</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The demand equation for a certain printer is given by <BR>\n" );
document.write( "D = -200p +35,000\r<BR>\n" );
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document.write( "The supply equation is predicted to be<BR>\n" );
document.write( "S = -p^2+ 400p - 20,000\r<BR>\n" );
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document.write( "Find the equilibrium price?\r<BR>\n" );
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document.write( "I just need some help on how to start this problem. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #89401 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=89401\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The equilibrium price occurs when the demand (D) equals the supply (S). In other words, when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S=D ALIGN=MIDDLE  ALT=\"S=D\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-p%5E2%2B+400p+-+20000=+-200p+%2B35000 ALIGN=MIDDLE  ALT=\"-p%5E2%2B+400p+-+20000=+-200p+%2B35000\"   DISABLED_style= \"max-width:90%; height:auto;\" > Set the two equations equal to each other. Now let's solve for p\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-p%5E2%2B400p-20000%2B200p-35000=0 ALIGN=MIDDLE  ALT=\"-p%5E2%2B400p-20000%2B200p-35000=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Add 200p to both sides.  Subtract 35000 from both sides. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-p%5E2%2B600p-55000=0 ALIGN=MIDDLE  ALT=\"-p%5E2%2B600p-55000=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms\r<BR>\n" );
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document.write( "Let's use the quadratic formula to solve for p:\r<BR>\n" );
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document.write( "Starting with the general quadratic\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ap%5E2%2Bbp%2Bc=0 ALIGN=MIDDLE  ALT=\"ap%5E2%2Bbp%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "the general solution using the quadratic equation is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29 ALIGN=MIDDLE  ALT=\"p+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So lets solve <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-p%5E2%2B600%2Ap-55000=0 ALIGN=MIDDLE  ALT=\"-p%5E2%2B600%2Ap-55000=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > ( notice <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=-1 ALIGN=MIDDLE  ALT=\"a=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=600 ALIGN=MIDDLE  ALT=\"b=600\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=-55000 ALIGN=MIDDLE  ALT=\"c=-55000\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p+=+%28-600+%2B-+sqrt%28+%28600%29%5E2-4%2A-1%2A-55000+%29%29%2F%282%2A-1%29 ALIGN=MIDDLE  ALT=\"p+=+%28-600+%2B-+sqrt%28+%28600%29%5E2-4%2A-1%2A-55000+%29%29%2F%282%2A-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in a=-1, b=600, and c=-55000\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p+=+%28-600+%2B-+sqrt%28+360000-4%2A-1%2A-55000+%29%29%2F%282%2A-1%29 ALIGN=MIDDLE  ALT=\"p+=+%28-600+%2B-+sqrt%28+360000-4%2A-1%2A-55000+%29%29%2F%282%2A-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square 600 to get 360000  \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p+=+%28-600+%2B-+sqrt%28+360000%2B-220000+%29%29%2F%282%2A-1%29 ALIGN=MIDDLE  ALT=\"p+=+%28-600+%2B-+sqrt%28+360000%2B-220000+%29%29%2F%282%2A-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%2A-55000%2A-1 ALIGN=MIDDLE  ALT=\"-4%2A-55000%2A-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-220000 ALIGN=MIDDLE  ALT=\"-220000\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p+=+%28-600+%2B-+sqrt%28+140000+%29%29%2F%282%2A-1%29 ALIGN=MIDDLE  ALT=\"p+=+%28-600+%2B-+sqrt%28+140000+%29%29%2F%282%2A-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms in the radicand (everything under the square root)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p+=+%28-600+%2B-+100%2Asqrt%2814%29%29%2F%282%2A-1%29 ALIGN=MIDDLE  ALT=\"p+=+%28-600+%2B-+100%2Asqrt%2814%29%29%2F%282%2A-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify the square root (note: If you need help with simplifying the square root, check out this <a  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Radicals/simplifying-square-roots.solver> solver</a>)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p+=+%28-600+%2B-+100%2Asqrt%2814%29%29%2F-2 ALIGN=MIDDLE  ALT=\"p+=+%28-600+%2B-+100%2Asqrt%2814%29%29%2F-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 2 and -1 to get -2\r<BR>\n" );
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document.write( "So now the expression breaks down into two parts\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p+=+%28-600+%2B+100%2Asqrt%2814%29%29%2F-2 ALIGN=MIDDLE  ALT=\"p+=+%28-600+%2B+100%2Asqrt%2814%29%29%2F-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p+=+%28-600+-+100%2Asqrt%2814%29%29%2F-2 ALIGN=MIDDLE  ALT=\"p+=+%28-600+-+100%2Asqrt%2814%29%29%2F-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now break up the fraction\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=-600%2F-2%2B100%2Asqrt%2814%29%2F-2 ALIGN=MIDDLE  ALT=\"p=-600%2F-2%2B100%2Asqrt%2814%29%2F-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=-600%2F-2-100%2Asqrt%2814%29%2F-2 ALIGN=MIDDLE  ALT=\"p=-600%2F-2-100%2Asqrt%2814%29%2F-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Simplify\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=300-50%2Asqrt%2814%29 ALIGN=MIDDLE  ALT=\"p=300-50%2Asqrt%2814%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=300%2B50%2Asqrt%2814%29 ALIGN=MIDDLE  ALT=\"p=300%2B50%2Asqrt%2814%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So these expressions approximate to\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=112.917130661303 ALIGN=MIDDLE  ALT=\"p=112.917130661303\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=487.082869338697 ALIGN=MIDDLE  ALT=\"p=487.082869338697\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the possible solutions are:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=112.917130661303 ALIGN=MIDDLE  ALT=\"p=112.917130661303\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=487.082869338697 ALIGN=MIDDLE  ALT=\"p=487.082869338697\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "However, when you plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=487.082869338697 ALIGN=MIDDLE  ALT=\"p=487.082869338697\"   DISABLED_style= \"max-width:90%; height:auto;\" > into the equations, you get a negative number (which does not make sense). So our only solution is \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=112.917130661303 ALIGN=MIDDLE  ALT=\"p=112.917130661303\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "Now round to the nearest hundredth\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=112.92 ALIGN=MIDDLE  ALT=\"p=112.92\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the equilibrium price is $112.92<BR>\n" );
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