document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1045240>Question 1045240</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me with this. Detailed workings are very much appreciated, thanks!<BR>\n" );
document.write( "The weekly demand and supply functions for a type of watch is given by<BR>\n" );
document.write( "p=-0.1x^2-x+40  and  p=0.1x^2+2x+20  respectively, <BR>\n" );
document.write( "where p is measured in dollars and x is measured in units of a hundred. Find the equilibrium quantity and price. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #660641 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=660641\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> set the two equal to each other, for then it is in equilibrium.<BR>\n" );
document.write( "-0.1x^2-x+40 =0.1x^2+2x+20, put everything on the right.<BR>\n" );
document.write( "0=0.2x^2+3x-20<BR>\n" );
document.write( "multiply everything by 5 to make the x^2 leading coefficient 1.<BR>\n" );
document.write( "0=x^2+15x-100<BR>\n" );
document.write( "0=(x+20)(x-5)<BR>\n" );
document.write( "x=5, since x can't equal -20<BR>\n" );
document.write( "That is 500 watches since x is hundreds.<BR>\n" );
document.write( "now substitute into both, since they should be the same to check<BR>\n" );
document.write( "-2.5-5+40=$32.50<BR>\n" );
document.write( "2.5+10+20=$32.50<BR>\n" );
document.write( "That is 500 watches at $32.50 each for the equilibrium price.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-10%2C10%2C-10%2C50%2C-0.1x%5E2-x%2B40%2C0.1x%5E2%2B2x%2B20%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-10%2C10%2C-10%2C50%2C-0.1x%5E2-x%2B40%2C0.1x%5E2%2B2x%2B20%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );