document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=221208>Question 221208</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In planning for a school dance, you find that one band will play for $250, plus 50% of the total ticket sales. Another band will play for a flat fee of $550. In order for the first band to produce more profit for the school than the other band, what is the highest price you can charge per ticket, assuming 300 people attend?\r<BR>\n" );
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document.write( "i tried setting it up something like .50(250-x)+250>550  x= the price of tickets<BR>\n" );
document.write( "but I am not getting the correct answer. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #166049 by </B><A HREF=/tutors/aboutme.mpl?userid=MathTherapy><B>MathTherapy(10552)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathTherapy><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=MathTherapy><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=166049\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let price of ticket be P\r<BR>\n" );
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document.write( "Then proceeds from sale of 300 tickets = 300P\r<BR>\n" );
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document.write( "Since the 1st band wants $250, plus 50% of ticket sales, then the school would have to pay the 1st band 250 + .5(300P), or 250 + 150P, and the profit from using the 1st band = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=300P+-+%28250+%2B+150P%29 ALIGN=MIDDLE  ALT=\"300P+-+%28250+%2B+150P%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since the 2nd band wants a flat fee of $550, then the school would have to pay the 2nd band $550, and the profit from using the 2nd band = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=300P+-+550 ALIGN=MIDDLE  ALT=\"300P+-+550\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since we're looking for the 1st band to make more profit for the school than the 2nd band, then we'll have: \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=300P+-+%28250+%2B+150P%29+%3E+300P+-+550 ALIGN=MIDDLE  ALT=\"300P+-+%28250+%2B+150P%29+%3E+300P+-+550\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "300P - 250 - 150P > 300P - 550\r<BR>\n" );
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document.write( "300P - 150P - 300P > - 550 + 250\r<BR>\n" );
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document.write( "- 150P > - 300\r<BR>\n" );
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document.write( "P < <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-300%29%2F-150 ALIGN=MIDDLE  ALT=\"%28-300%29%2F-150\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or P < <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > ----- Take note that the inequality changes from > to < when dividing by a negative value\r<BR>\n" );
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document.write( "Therefore, in order for the 1st band to make more profit for the school than the 2nd band, the price of 300 tickets should be < $<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%282%29 ALIGN=MIDDLE  ALT=\"highlight_green%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > each. </SPAN>\n" );
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