document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=151689>Question 151689</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A car rental compan has two rental rates. rate 1 is $72 per day plus $0.16 per mile. Rate 2 is $144 per day plus $0.08 per mile. If you plan to rent for one week, how many miles would you need to drive to pay less by taking rate 2? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #111502 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><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=111502\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First, we'll express the two rates as equations:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%5B1%5D+=+72%2Fd+%2B+0.16%2Fm ALIGN=MIDDLE  ALT=\"R%5B1%5D+=+72%2Fd+%2B+0.16%2Fm\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rate 1 is $72 per day + $0.16 per mile.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%5B2%5D+=+144%2Fd+%2B+0.08%2Fm ALIGN=MIDDLE  ALT=\"R%5B2%5D+=+144%2Fd+%2B+0.08%2Fm\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rate 2 is $144 per day + $0.08 per mile.<BR>\n" );
document.write( "Since you are renting for one week (7 days) and letting x = the number of miles, we can refine the equations a bit:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%5B1%5D+=+72%287%29%2B0.16x ALIGN=MIDDLE  ALT=\"R%5B1%5D+=+72%287%29%2B0.16x\"   DISABLED_style= \"max-width:90%; height:auto;\" >=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=504%2B0.16x ALIGN=MIDDLE  ALT=\"504%2B0.16x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%5B2%5D+=+144%287%29%2B0.08x ALIGN=MIDDLE  ALT=\"R%5B2%5D+=+144%287%29%2B0.08x\"   DISABLED_style= \"max-width:90%; height:auto;\" >=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1008%2B0.08x ALIGN=MIDDLE  ALT=\"1008%2B0.08x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now the question is, what value of x (number of miles) will make <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%5B2%5D%3CR%5B1%5D ALIGN=MIDDLE  ALT=\"R%5B2%5D%3CR%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so we need to write the inequality:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1008%2B0.08x+%3C+504%2B0.16x ALIGN=MIDDLE  ALT=\"1008%2B0.08x+%3C+504%2B0.16x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now we solve this inequality for x. Subtract 0.08x from both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1008+%3C+504%2B0.08x ALIGN=MIDDLE  ALT=\"1008+%3C+504%2B0.08x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now subtract 504 from both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=504+%3C+0.08x ALIGN=MIDDLE  ALT=\"504+%3C+0.08x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Finally, divide both sides by 0.08<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6300+%3C+x ALIGN=MIDDLE  ALT=\"6300+%3C+x\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%3E+6300 ALIGN=MIDDLE  ALT=\"x+%3E+6300\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So, you would need to drive more than 6300 miles to pay less with rate 2.<BR>\n" );
document.write( "Let's check the answer by driving 6301 miles (6301 > 6300):<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%5B1%5D+=+504%2B0.16%286301%29 ALIGN=MIDDLE  ALT=\"R%5B1%5D+=+504%2B0.16%286301%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%5B1%5D+=+504%2B1008.16 ALIGN=MIDDLE  ALT=\"R%5B1%5D+=+504%2B1008.16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%5B1%5D+=+1512.16 ALIGN=MIDDLE  ALT=\"R%5B1%5D+=+1512.16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Rate 1 would be $1512.16 for one week's rental driven 6301 miles.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%5B2%5D+=+1008%2B0.08%286301%29 ALIGN=MIDDLE  ALT=\"R%5B2%5D+=+1008%2B0.08%286301%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%5B2%5D+=+1008%2B504.08 ALIGN=MIDDLE  ALT=\"R%5B2%5D+=+1008%2B504.08\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%5B2%5D+=+1512.08 ALIGN=MIDDLE  ALT=\"R%5B2%5D+=+1512.08\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Rate 2 would be $1512.08 for one week's rental driven 6301 miles.<BR>\n" );
document.write( "So you can see that if you were to drive more than 6300 miles for the week, rate 2 would cost you less than rate 1.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );