document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1092513>Question 1092513</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The income in dollars for a charity fundraiser can be expressed by 360p-12p^2 where p is the ticket price. What ticket price(s) will result in an income of $0?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #707136 by </B><A HREF=/tutors/aboutme.mpl?userid=DrSteve><B>DrSteve(7)</B></A><img src=\"/images/stars/stars-05.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=DrSteve><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=DrSteve><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=707136\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This one is a bit more difficult than it looks, but it's totally do-able with the knowledge that you have!\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=360%2Ap+-+12%2Ap%5E2+=+0 ALIGN=MIDDLE  ALT=\"360%2Ap+-+12%2Ap%5E2+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "in other words, the income is expressed as the equation, and setting the whole thing to zero and solving for \"p\" will give the price (p)<BR>\n" );
document.write( " you'd have to charge to make zero money on this fundraiser (a really, really bad idea!)  \r<BR>\n" );
document.write( "\n" );
document.write( "So let's do this!\r<BR>\n" );
document.write( "\n" );
document.write( "First, notice that 360 is divisible by 12 and there is a \"p\" in all parts of the left hand of the equation.  So we can factor out  -12p to get:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-12%2Ap+%2A+%28-30%2Bp%29+=+0+ ALIGN=MIDDLE  ALT=\"-12%2Ap+%2A+%28-30%2Bp%29+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "or\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-12%2Ap+%2A+%28p-30%29+=+0 ALIGN=MIDDLE  ALT=\"-12%2Ap+%2A+%28p-30%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "this is where having a zero on one side of the equation makes things easy!\r<BR>\n" );
document.write( "\n" );
document.write( "divide both sides by -12 to get\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p+%2A+%28p-30%29+=+0 ALIGN=MIDDLE  ALT=\"p+%2A+%28p-30%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "there are two ways that that equation can equal zero.\r<BR>\n" );
document.write( "\n" );
document.write( "One is if p = 0, as can be seen in:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+%2A+%280-30%29+=+0 ALIGN=MIDDLE  ALT=\"0+%2A+%280-30%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "or if P =30  as in:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30+%2A+%2830-30%29+=+0 ALIGN=MIDDLE  ALT=\"30+%2A+%2830-30%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "so if you charge 0 dollars, it'll result in an income of 0 dollars (which makes sense, when you think about it).  \r<BR>\n" );
document.write( "\n" );
document.write( "Also if you charge $30 it will result in an income that is exactly zero.\r<BR>\n" );
document.write( "\n" );
document.write( "And that is the answer, both 0, and 30!\r<BR>\n" );
document.write( "\n" );
document.write( "YAY!\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );