document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=42476>Question 42476</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help with this word problem.\r<BR>\n" );
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document.write( "The demand equation for a certain type of printer is given by<BR>\n" );
document.write( "D = -200p + 35000<BR>\n" );
document.write( "The supply equation is predicted to be<BR>\n" );
document.write( "S = -p^2 + 400p - 20000\r<BR>\n" );
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document.write( "Find the equilibrium price.\r<BR>\n" );
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document.write( "Thanks!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #27594 by </B><A HREF=/tutors/aboutme.mpl?userid=Nate><B>Nate(3500)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Nate><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=27594\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The demand equation for a certain type of printer is given by<BR>\n" );
document.write( "D = -200p + 35000 or y = -200p + 35000<BR>\n" );
document.write( "The supply equation is predicted to be<BR>\n" );
document.write( "S = -p^2 + 400p - 20000 or y = -p^2 + 400p - 20000<BR>\n" );
document.write( "So ....<BR>\n" );
document.write( "y = -p^2 + 400p - 20000<BR>\n" );
document.write( "-200p + 35000 = -p^2 + 400p - 20000<BR>\n" );
document.write( "0 = -p^2 + 600p - 55000<BR>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=quadratic.solver>SOLVE quadratic equation with variable</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Quadratic equation <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;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1p%5E2%2B600p%2B-55000+=+0 ALIGN=MIDDLE  ALT=\"-1p%5E2%2B600p%2B-55000+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >) has the following solutons:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"p%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  For these solutions to exist, the <U>discriminant</U> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" > should not be a negative number.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  First, we need to compute the discriminant <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" >: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac=%28600%29%5E2-4%2A-1%2A-55000=140000 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28600%29%5E2-4%2A-1%2A-55000=140000\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=140000 is greater than zero. That means that there are two solutions: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5B12%5D+=+%28-600%2B-sqrt%28+140000+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-600%2B-sqrt%28+140000+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%5B1%5D+=+%28-%28600%29%2Bsqrt%28+140000+%29%29%2F2%5C-1+=+112.917130661303 ALIGN=MIDDLE  ALT=\"p%5B1%5D+=+%28-%28600%29%2Bsqrt%28+140000+%29%29%2F2%5C-1+=+112.917130661303\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%5B2%5D+=+%28-%28600%29-sqrt%28+140000+%29%29%2F2%5C-1+=+487.082869338697 ALIGN=MIDDLE  ALT=\"p%5B2%5D+=+%28-%28600%29-sqrt%28+140000+%29%29%2F2%5C-1+=+487.082869338697\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <BR>\n" );
document.write( "    Quadratic expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1p%5E2%2B600p%2B-55000 ALIGN=MIDDLE  ALT=\"-1p%5E2%2B600p%2B-55000\"   DISABLED_style= \"max-width:90%; height:auto;\" > can be factored:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1p%5E2%2B600p%2B-55000+=+-1%28p-112.917130661303%29%2A%28p-487.082869338697%29 ALIGN=MIDDLE  ALT=\"-1p%5E2%2B600p%2B-55000+=+-1%28p-112.917130661303%29%2A%28p-487.082869338697%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 112.917130661303, 487.082869338697.\n" );
document.write( "Here's your graph:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-1%2Ax%5E2%2B600%2Ax%2B-55000+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-1%2Ax%5E2%2B600%2Ax%2B-55000+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+1000%2C+1000%2C+100%2C+500%2C+-10%2C+10%2C+-x%5E2+%2B+600x+-+55000%29+ ALIGN=MIDDLE  ALT=\"+graph%28+1000%2C+1000%2C+100%2C+500%2C+-10%2C+10%2C+-x%5E2+%2B+600x+-+55000%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );