document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1198749>Question 1198749</A>: <I><SPAN STYLE=\"word-break: break-all;\"> ) A builder must decide whether to rent or buy an excavating machine. If he were to rent the machine, the rental fee would be €600 per month, and the daily cost (gas, oil, and driver) would be €60 per day it is used. If he were to buy it, his fixed annual cost would be €4,000, and the daily operating and maintenance costs would be €80 per day the machine is used. What is the least number of days each year that he would have to use the machine to justify renting rather than buying it?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #832387 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=832387\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> rent = 600 per month plus 60 for each day it is used.<BR>\n" );
document.write( "buy = 4,000 per year plus 80 for each day it is used.\r<BR>\n" );
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document.write( "the yearly cost for renting is equal to 600 * 12 = 7200 plus 60 for each day it is used.\r<BR>\n" );
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document.write( "the yearly cost for buying is 4,000 plus 80 for each day it is ued.\r<BR>\n" );
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document.write( "your inequality is 7200 + 60x < 4000 + 80x<BR>\n" );
document.write( "x is the  number of days.<BR>\n" );
document.write( "subtract 4000 from both sides of the equation and subtract 60x from both sides of the equation to get:<BR>\n" );
document.write( "3200 < 20x<BR>\n" );
document.write( "divide both sides of the equation by 20 to get:<BR>\n" );
document.write( "160 < x\r<BR>\n" );
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document.write( "the machine would have to be used more than 160 days for the rental option to be cheaper than the buy option.\r<BR>\n" );
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document.write( "at 160 days, the rental option is 7200 + 60 * 160 = 16800<BR>\n" );
document.write( "at 160 days, the buy option is 4000 _+ 80 * 160 = 16800\r<BR>\n" );
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document.write( "that'a the break even point.\r<BR>\n" );
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document.write( "at 161 days, the rental option is 7200 + 60 * 161 = 16860<BR>\n" );
document.write( "at 161 days, the buy option is 4000 + 80 * 161 = 16880<BR>\n" );
document.write( "the rental option is cheaper than the buy option by 20.\r<BR>\n" );
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document.write( "at 300 days, the rental option is 7200 + 60 * 300 = 25200<BR>\n" );
document.write( "at 300 days, the buy option is 4000 + 80 * 300 = 28000.<BR>\n" );
document.write( "the rental option is cheaper than the buy option by 2800.\r<BR>\n" );
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document.write( "2800 / (300 - 160) = 2800 / 140 = 20.<BR>\n" );
document.write( "the rental option is cheaper than the buy option by 20 dollars for each day over 160.\r<BR>\n" );
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document.write( "the equations can be graphed as shown below:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2022/113004.jpg\">\r<BR>\n" );
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