document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=55054>Question 55054</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi, I have the following question and I don't know what to do.<BR>\n" );
document.write( "It is the demand for goods is p^2 + q^2 = 169 where p is price and q is quantity.  The supply equation is p = q + 7.<BR>\n" );
document.write( "What are the equilibrium price and quantity?\r<BR>\n" );
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document.write( "I'm unsure but i'm assuming that equilibrium is where supply equals demand<BR>\n" );
document.write( "but the demand equation has roots, so would it be p+q= square root of 169<BR>\n" );
document.write( "then that equals p-q-7.<BR>\n" );
document.write( "But i still from that cannot get a price for p and a price for q.<BR>\n" );
document.write( "I'm extremely stuck and any help would be greatly appreciated. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #37400 by </B><A HREF=/tutors/aboutme.mpl?userid=Hook><B>Hook(36)</B></A><img src=\"/images/stars/stars-07.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Hook><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=37400\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You have one equation that defines demand<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%5E2+%2B+q%5E2+=+169 ALIGN=MIDDLE  ALT=\"p%5E2+%2B+q%5E2+=+169\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "and one that defines supply<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p+=+q%2B7 ALIGN=MIDDLE  ALT=\"p+=+q%2B7\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "You are right that equilibrium happens when supply equals demand. <BR>\n" );
document.write( "However, what you want to do is substitute the second equation into the first one.\r<BR>\n" );
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document.write( "If we do that, we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28q%2B7%29%5E2+%2B+q%5E2+=+169 ALIGN=MIDDLE  ALT=\"%28q%2B7%29%5E2+%2B+q%5E2+=+169\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "I'll FOIL that first term<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=q%5E2%2B14q%2B49%2Bq%5E2+=+169 ALIGN=MIDDLE  ALT=\"q%5E2%2B14q%2B49%2Bq%5E2+=+169\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Combine like terms<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2q%5E2+%2B+14q+%2B+49+=+169 ALIGN=MIDDLE  ALT=\"2q%5E2+%2B+14q+%2B+49+=+169\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Moving the 169 to the left<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2q%5E2+%2B14q+-120+=+0 ALIGN=MIDDLE  ALT=\"2q%5E2+%2B14q+-120+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Divide both sides by 2<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=q%5E2+%2B+7q+-+60+=+0 ALIGN=MIDDLE  ALT=\"q%5E2+%2B+7q+-+60+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "I can solve this quadratic equation by any number of ways. I'll use factoring<BR>\n" );
document.write( "Factoring it out, I get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28q%2B12%29%28q-5%29=0 ALIGN=MIDDLE  ALT=\"%28q%2B12%29%28q-5%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Solving, I get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=q++=+-12 ALIGN=MIDDLE  ALT=\"q++=+-12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=q+=+5 ALIGN=MIDDLE  ALT=\"q+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "We can toss -12 out because a negative quantity is nonsense for this problem. \r<BR>\n" );
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document.write( "I can then put <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=q+=+5 ALIGN=MIDDLE  ALT=\"q+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" > into our supply equation\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p+=+q+%2B+7+ ALIGN=MIDDLE  ALT=\"p+=+q+%2B+7+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p+=+5%2B7 ALIGN=MIDDLE  ALT=\"p+=+5%2B7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p+=+12 ALIGN=MIDDLE  ALT=\"p+=+12\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Ok, equilibrium price is 7 at a quantity of 5.  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );