document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=305372>Question 305372</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A marketing group developing online ad space is offering two payment options: <BR>\n" );
document.write( "Option 1: $210 set up fee plus $10/inch of the ad.<BR>\n" );
document.write( "Option 2: No set up fee but $25/inch of the ad. <BR>\n" );
document.write( "Let x = inches of the proposed ad, for example x=2 for a colum ad that is 2 <BR>\n" );
document.write( "a) Write a mathematical model representin the total ad cost, c, in terms of x for the following: <BR>\n" );
document.write( "Option 1: C=<BR>\n" );
document.write( "Option 2: C=\r<BR>\n" );
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document.write( "b) How many inches of ad space would need to be purchased for option 1 to be less than option 2? Set up an inewuality and show work algebraically usint the information in part a. Summarize the findings in a brief sentence. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #218626 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=218626\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Option 1: $210 set up fee plus $10/inch of the ad.<BR>\n" );
document.write( "Option 2: No set up fee but $25/inch of the ad.\r<BR>\n" );
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document.write( "Let x equal number of inches of ad space.\r<BR>\n" );
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document.write( "Equation for option 1:\r<BR>\n" );
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document.write( "C = 210 + 10*x\r<BR>\n" );
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document.write( "Equation for option 2:\r<BR>\n" );
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document.write( "C = 25*x\r<BR>\n" );
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document.write( "b) How many inches of ad space would need to be purchased for option 1 to be less than option 2?\r<BR>\n" );
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document.write( "Equation you want to solve is:\r<BR>\n" );
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document.write( "210 + 10*x < 25*x\r<BR>\n" );
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document.write( "Subtract 10*x from both sides of this equation to get:\r<BR>\n" );
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document.write( "210 < 15*x\r<BR>\n" );
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document.write( "Divide both sides of this equation by 15 to get:\r<BR>\n" );
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document.write( "14 < x\r<BR>\n" );
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document.write( "This would be the same as:\r<BR>\n" );
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document.write( "x > 14\r<BR>\n" );
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document.write( "If the inches of ad space were greater than 14, then option 1 would be cheaper than option 2.\r<BR>\n" );
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document.write( "To confirm if this is true, we need to test at x = 13, 14, and 15.\r<BR>\n" );
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document.write( "When x = 13, option 1 will cost 210 + 10*13 = 210 + 130 = 340<BR>\n" );
document.write( "When x = 14, option 1 will cost 210 + 10*14 = 210 + 140 = 350<BR>\n" );
document.write( "When x = 15, option 1 will cost 210 + 10*15 = 210 + 150 = 360\r<BR>\n" );
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document.write( "When x = 13, option 2 will cost 25*13 = 325<BR>\n" );
document.write( "When x = 14, option 2 will cost 25*14 = 350<BR>\n" );
document.write( "When x = 15, option 2 will cost 25*15 = 375 \r<BR>\n" );
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document.write( "The results are:\r<BR>\n" );
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document.write( "When x = 13, option 1 costs 340 and option 2 costs 325 so option 1 is more expensive than option 2.<BR>\n" );
document.write( "When x = 14, option 1 costs 350 and option 2 costs 350 so option 1 and option 2 cost the same.<BR>\n" );
document.write( "When x = 15, option 1 costs 360 and option 2 costs 375 so option 1 is cheaper than option 2.\r<BR>\n" );
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document.write( "Break even point is when x = 14.\r<BR>\n" );
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document.write( "When x > 14, option 1 becomes less than option 2 and stays less than option 2.\r<BR>\n" );
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document.write( "Answer to the question is that more than 14 inches of ad space would have to be purchased for option 1 to cost less than option 2.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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