document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=991202>Question 991202</A>: <I><SPAN STYLE=\"word-break: break-all;\">  Your class is selling boxes of flower seeds as a fundraiser the total profit P depends on the amount X that your class charges for each box of seeds the Quetion P = -0.5 X^2+36x-103 models the profit  of the fundraiser what's the smallest amount in dollars that you can charge and make a profit of at least $419? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #611141 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=611141\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> your answer appears to be:<BR>\n" );
document.write( "20.125492133612454<BR>\n" );
document.write( "you can solve it by use of the quadratic formula, or by graphing.<BR>\n" );
document.write( "use of the quadratic formula requires the following transformation.<BR>\n" );
document.write( "let y = profit<BR>\n" );
document.write( "your equation is y = -.5x^2 + 36x - 103<BR>\n" );
document.write( "set y = 419 to get:\<BR>\n" );
document.write( "419 = -.5x^2 + 36x - 103<BR>\n" );
document.write( "subtract 419 from both sides of the equation to get:<BR>\n" );
document.write( "0 = -.5x^2 + 36x - 522<BR>\n" );
document.write( "that in standard quadratic form of 0 = ax^2 + bx + c, where:<BR>\n" );
document.write( "a = -.5<BR>\n" );
document.write( "b = 36<BR>\n" );
document.write( "c = -522<BR>\n" );
document.write( "you just plug those numbers in the quadratic formula and  you will get your answer.<BR>\n" );
document.write( "you can also solve it graphically.<BR>\n" );
document.write( "two ways to do it.<BR>\n" );
document.write( "one way is to use the transformed equation and look for the zero crossing points.<BR>\n" );
document.write( "that equation would be y = -.5x^2 + 36x - 522<BR>\n" );
document.write( "the other way is to graph two equations and look for the intersection points.<BR>\n" );
document.write( "those equations are:<BR>\n" );
document.write( "y = -.5x^2 + 36x - 103<BR>\n" );
document.write( "y = 419<BR>\n" );
document.write( "the following graphs show you the results of both methods.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2015/092201.jpg\" alt = \"$$$\" </>\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2015/092202.jpg\" alt = \"$$$\" </>\r<BR>\n" );
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document.write( "if you need to learn how to use the quadratic formula, it can be found here:\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"http://www.regentsprep.org/regents/math/algtrig/ate3/quadformula.htm\" target = \"_blank\">http://www.regentsprep.org/regents/math/algtrig/ate3/quadformula.htm</a><BR>\n" );
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