document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=109996>Question 109996</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The demand and supply equations for a certain item are given by<BR>\n" );
document.write( "D= -5p+40<BR>\n" );
document.write( "S=-p^2+30p-8<BR>\n" );
document.write( "Find the equilibrium price.\r<BR>\n" );
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document.write( "What does that mean and can you help me?  Thank you! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #80141 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=80141\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The demand and supply equations for a certain item are given by<BR>\n" );
document.write( "D= -5p+40<BR>\n" );
document.write( "S=-p^2+30p-8<BR>\n" );
document.write( "Find the equilibrium price. <BR>\n" );
document.write( "What does that mean and can you help me? Thank you!<BR>\n" );
document.write( "-------------------------------------------------<BR>\n" );
document.write( "Equilibrium occurs when demand equals supply.<BR>\n" );
document.write( "EQUATION:<BR>\n" );
document.write( "D = S<BR>\n" );
document.write( "-5p+40 = -p^2+30p-8<BR>\n" );
document.write( "p^2-35p+48=0<BR>\n" );
document.write( "p = [35 +- sqrt(1225-4*48)]/2\r<BR>\n" );
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document.write( "p = [35 +- sqrt(1033)]/2\r<BR>\n" );
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document.write( "p = [35 +- 32.14...]/2\r<BR>\n" );
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document.write( "p = (35+32.14)/2 = 33.57 or p = (35-32.14)/2 = 1.43\r<BR>\n" );
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document.write( "---------------<BR>\n" );
document.write( "Which is the correct answer?<BR>\n" );
document.write( "Check p = 33.57<BR>\n" );
document.write( "Using p=33.57, D and S both have negative values<BR>\n" );
document.write( "-------------------<BR>\n" );
document.write( "Check p = 1.43<BR>\n" );
document.write( "Using p = 1.43 D and S both equal 32.85<BR>\n" );
document.write( "Therefore p= $1.43 is the price that coincides with equilibrium.<BR>\n" );
document.write( "====================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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