document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=277289>Question 277289</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A car rental company has two rental rates. Rate 1 is $63 per day plus $0.18 per mile. Rate 2 is $126 per day plus $0.09 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 #201921 by </B><A HREF=/tutors/aboutme.mpl?userid=oberobic><B>oberobic(2304)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=oberobic><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=201921\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> y = mx + b is the standard slope-intercept formula for a line<BR>\n" );
document.write( "we can put the information given into two equations in slope-intercept format<BR>\n" );
document.write( "R1 = .18x + 63, where x= miles driven<BR>\n" );
document.write( "R2 = .09x + 126<BR>\n" );
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document.write( "we can graph the two lines to see where they cross<BR>\n" );
document.write( "R1 = red line, which has a steeper slope<BR>\n" );
document.write( "R2 = green line, which has a lower slope<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28500%2C500%2C-100%2C1000%2C-100%2C500%2C0.18%2Ax%2B63%2C+0.09%2Ax%2B126%29 ALIGN=MIDDLE  ALT=\"graph%28500%2C500%2C-100%2C1000%2C-100%2C500%2C0.18%2Ax%2B63%2C+0.09%2Ax%2B126%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "it appears the lines cross at about x=700 (or 700 miles driven)<BR>\n" );
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document.write( "of course, we know R1 and R2 really are just other names for 'y'<BR>\n" );
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document.write( "y = .18x + 63<BR>\n" );
document.write( "y = .09x + 126<BR>\n" );
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document.write( "multiplying both equations by 100 to remove decimals<BR>\n" );
document.write( "100y = 18x + 6300<BR>\n" );
document.write( "100y = 9x + 12600<BR>\n" );
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document.write( "rearranging to put into simultaneous equation format<BR>\n" );
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document.write( "-18x + 100y = 6300<BR>\n" );
document.write( "-9x + 100y = 12600<BR>\n" );
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document.write( "subtracting the second equation from the first<BR>\n" );
document.write( "-9x = -6300<BR>\n" );
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document.write( "dividing both sides by -9<BR>\n" );
document.write( "x = 700<BR>\n" );
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document.write( "so we confirm that the two lines cross at x=700.<BR>\n" );
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document.write( "that means that at a distance driven 'x' of 700, the cost of the two rental plans is the same.<BR>\n" );
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document.write( "but after that point, the line with lower slope rises more slowly, which means the other plan (the one with the steeper slope) is more expensive and getting more expensive for every mile driven > 700.<BR>\n" );
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document.write( "Answer:<BR>\n" );
document.write( "You need to drive more than 700 miles for Rate 2 to be less expensive than Rate 1.<BR>\n" );
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