document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=465504>Question 465504</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Could you please help me by providing a step-by-step answer to the following equation:<BR>\n" );
document.write( "A museum offers excursions at $12.00 per ticket if 100 or fewer tickets are purchased.  For each ticket over 100, the price is reduced by 10 cents.  How many tickets will lead to a maximum income? (Solve using a quadratic formula.)\r<BR>\n" );
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document.write( "I'm familiar with the quadratic formula and how to use it, but I'm not quite sure how to approach this particular word problem. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #319000 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=319000\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let x = number of tickets over 100.<BR>\n" );
document.write( "==> price of ticket is 12 - 0.10x<BR>\n" );
document.write( "==> number of tickets is 100 + x\r<BR>\n" );
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document.write( "==> Income, or revenue, is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28100+%2B+x%29%2812+-+0.10x%29+=+1200+%2B+2x+-+0.10x%5E2 ALIGN=MIDDLE  ALT=\"%28100+%2B+x%29%2812+-+0.10x%29+=+1200+%2B+2x+-+0.10x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Since the the coefficient of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > is negative (-0.10), there is an absolute maximum (parabola faces downward).  The x-value that gives the maximum income is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-b%2F%282a%29+=+-2%2F%282%2A-0.10%29+=+2%2F0.20+=+10 ALIGN=MIDDLE  ALT=\"-b%2F%282a%29+=+-2%2F%282%2A-0.10%29+=+2%2F0.20+=+10\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Hence 100 + 10 = 110 tickets must be sold to get maximum income. </SPAN>\n" );
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