document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=84863>Question 84863</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 = –p2 + 30p – 8<BR>\n" );
document.write( "Find the equilibrium price.\r<BR>\n" );
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document.write( "I get sooooooo Lost on these type of problems! Help! Thanks In advance. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #61185 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=61185\">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 = –p2 + 30p – 8<BR>\n" );
document.write( "Find the equilibrium price.<BR>\n" );
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document.write( "Equilibrium price occurs when demand = supply<BR>\n" );
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document.write( "Which means D = S<BR>\n" );
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document.write( "Which means:<BR>\n" );
document.write( "-5p + 40 = -p^2 + 30p - 8<BR>\n" );
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document.write( "Arrange all terms on the left:<BR>\n" );
document.write( "+p^2 - 30p - 5p + 40 + 8 = 0<BR>\n" );
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document.write( "p^2 - 35p + 48 = 0; a not-so-friendly quadratic equation<BR>\n" );
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document.write( "Requires the quadratic formula to solve: a=1; b=-35; c=48<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p+=+%28-%28-35%29+%2B-+sqrt%28+-35%5E2+-+4+%2A+1+%2A+48+%29%29%2F%282%2A1%29+ ALIGN=MIDDLE  ALT=\"p+=+%28-%28-35%29+%2B-+sqrt%28+-35%5E2+-+4+%2A+1+%2A+48+%29%29%2F%282%2A1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p+=+%28%2B35+%2B-+sqrt%281033+%29%29%2F%282%29+ ALIGN=MIDDLE  ALT=\"p+=+%28%2B35+%2B-+sqrt%281033+%29%29%2F%282%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p+=+%28%2B35+%2B+32.14%29%2F%282%29+ ALIGN=MIDDLE  ALT=\"p+=+%28%2B35+%2B+32.14%29%2F%282%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p+=+67.14%2F2 ALIGN=MIDDLE  ALT=\"p+=+67.14%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "p = 33.57, 1st solution<BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p+=+%28%2B35+-+32.14%29%2F%282%29+ ALIGN=MIDDLE  ALT=\"p+=+%28%2B35+-+32.14%29%2F%282%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p+=+2.86%2F2 ALIGN=MIDDLE  ALT=\"p+=+2.86%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "p = 1.43; 2nd solution<BR>\n" );
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document.write( "The 1st solution does not make sense, substitute in the demand equation,<BR>\n" );
document.write( "-5(33.57) + 40  gives a negative value<BR>\n" );
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