document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=76658>Question 76658</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The profit on a watch is given by P = x^2 - 13x -80, where x is the number of watches sold per day. How many watches were sold on a day when there was a $50 loss?\r<BR>\n" );
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document.write( "Thanks so much for you help this one has me stummped. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #54982 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=54982\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P+=+x%5E2+-+13x+-80 ALIGN=MIDDLE  ALT=\"P+=+x%5E2+-+13x+-80\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Where P = profit and x = the number of watches sold in a day.<BR>\n" );
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document.write( "If there was a $50 loss for the day, the profit was -50.  Substitute this amount of profit<BR>\n" );
document.write( "into the equation and you get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-50+=+x%5E2+-13x+-+80 ALIGN=MIDDLE  ALT=\"-50+=+x%5E2+-13x+-+80\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Eliminate the -50 on the left side by adding +50 to both sides to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+x%5E2+-+13x+-+30 ALIGN=MIDDLE  ALT=\"0+=+x%5E2+-+13x+-+30\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "and reverse sides so that you have the equation in the standard quadratic form:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+13x+-+30+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+-+13x+-+30+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The left side of this equation can be factored to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+-+15%29%2A%28x+%2B+2%29+=+0 ALIGN=MIDDLE  ALT=\"%28x+-+15%29%2A%28x+%2B+2%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "and this equation will be true if either of the factors are zero because multiplying<BR>\n" );
document.write( "anything by zero results in zero.<BR>\n" );
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document.write( "So solve for values of x that will make the left side zero by setting each factor, one<BR>\n" );
document.write( "at a time equal to zero.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+-+15+=+0 ALIGN=MIDDLE  ALT=\"x+-+15+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > can be solved by adding 15 to both sides to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+15 ALIGN=MIDDLE  ALT=\"x+=+15\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "and<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%2B+2+=+0 ALIGN=MIDDLE  ALT=\"x+%2B+2+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > can be solved by subtracting 2 from both sides to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-2 ALIGN=MIDDLE  ALT=\"x=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "We can reject the second solution because what does it mean to sell -2 watches ... buy 2 watches?<BR>\n" );
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document.write( "So the answer is that if you only sell 15 watches in a day, you lose $50.<BR>\n" );
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document.write( "And just for fun, let's get an idea of how many watches you need to sell daily to break even.<BR>\n" );
document.write( "You break even if your profit is zero, so we can write the equation:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+13x+-+80+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+-+13x+-+80+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "If you solve this using the quadratic formula (if you don't know this method yet, you<BR>\n" );
document.write( "probably will soon) you will find that the left side of this equation will be zero if <BR>\n" );
document.write( "x is equal to approximately 17.56 or if x = -4.56.  Again we can ignore the negative <BR>\n" );
document.write( "solution.  So this tells us that if 17 watches are sold in a day, you lose a little money<BR>\n" );
document.write( "and if 18 watches are sold, you make a little money.<BR>\n" );
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document.write( "Hope this analysis of the watch business gives you some insight into solving quadratic<BR>\n" );
document.write( "equations. A tricky part was to recognize that a negative profit is a loss, so you needed<BR>\n" );
document.write( "to substitute minus 50 dollars for the profit and then solve the equation for x.  <BR>\n" );
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