document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=101040>Question 101040</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A rental car agency charges $29 per day plus 8 cents per mile to rent a certain car. ANother agency charges &18 per day plus 15 cents per mile to rent the same car. If the car is rented for one day in how many miles will the charge from both agencies be equal? Round your answer to two decimal places.\r<BR>\n" );
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document.write( "I can't figure out how to form the equations. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #73546 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=73546\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's recognize that in terms of dollars, 8 cents is 0.08 dollars and 15 cents is 0.15 dollars.<BR>\n" );
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document.write( "If you rent a car from the first car agency your cost for the rental will be $29 times the<BR>\n" );
document.write( "number of days you rent it plus $0.08 for each mile you drive. Therefore, you will pay a<BR>\n" );
document.write( "total of $29*D + 0.08*M where D is the number of days and M is the total number of miles you<BR>\n" );
document.write( "drive.<BR>\n" );
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document.write( "If you rent a car from the second car agency your cost for the rental will be $18 times the<BR>\n" );
document.write( "number of days you rent it plus $0.15 times the number of miles you drive. Therefore,<BR>\n" );
document.write( "you will pay a total of $18*D + 0.15*M.<BR>\n" );
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document.write( "The problem says that you plan on renting for just 1 Day. This being the case, you can<BR>\n" );
document.write( "substitute 1 for D and you get that the two rental costs will be:<BR>\n" );
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document.write( "First agency = $29*1 + 0.08*M = $29 + 0.08*M<BR>\n" );
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document.write( "Second agency = $18*1 + 0.15*M = $18 + 0.15M<BR>\n" );
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document.write( "At some number of miles driven the two costs will be the same. We can find that number of miles<BR>\n" );
document.write( "by setting the two equations equal to get:<BR>\n" );
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document.write( "29 + 0.08*M = 18 + 0.15*M<BR>\n" );
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document.write( "Get rid of the decimals by multiplying both sides of the equation (all terms) by 100 to get:<BR>\n" );
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document.write( "2900 + 8*M = 1800 + 15*M<BR>\n" );
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document.write( "Get rid of the 15*M on the right side by subtracting 15*M from both sides to get:<BR>\n" );
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document.write( "2900 - 7*M = 1800<BR>\n" );
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document.write( "Next get rid of the 2900 on the left side by subtracting 2900 from both sides to reduce the<BR>\n" );
document.write( "equation to:<BR>\n" );
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document.write( "-7*M = -1100<BR>\n" );
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document.write( "Solve for M by dividing both sides by -7 and the result is:<BR>\n" );
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document.write( "M = -1100/-7 = 157.1429 miles<BR>\n" );
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document.write( "Up until you drive 157 miles you would save money by going with the second company ...<BR>\n" );
document.write( "the one that charges $18 per day plus 15 cents per mile. But if you drive 158 miles or<BR>\n" );
document.write( "more you will save money by going with the company that charges $29 per day but less in<BR>\n" );
document.write( "the per mile charge.<BR>\n" );
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document.write( "If you think in terms of the graphs of these two equations, it might help you to visualize the<BR>\n" );
document.write( "problem. The red graph below shows the cost of renting a car from the first company that<BR>\n" );
document.write( "charges $29.00 per day + 8 cents per mile. The green graph shows the cost of renting a car from <BR>\n" );
document.write( "the second company that charges $18 per day + 15 cents per mile. The y-axis is the cost<BR>\n" );
document.write( "and the x axis is the number of miles driven:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28600%2C600%2C-10%2C200%2C-1%2C50%2C29%2B.08x%2C18%2B.15x%29 ALIGN=MIDDLE  ALT=\"graph%28600%2C600%2C-10%2C200%2C-1%2C50%2C29%2B.08x%2C18%2B.15x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "You can see that the two graphs cross at about 157 miles on the x-axis. As the miles increase<BR>\n" );
document.write( "above 157 the green graph for the second company is above the red graph which means that<BR>\n" );
document.write( "it has a higher cost. So beyond 157 miles of driving the red graph is not as high in cost<BR>\n" );
document.write( "meaning that the company charging 8 cents per mile will have a cheaper cost.<BR>\n" );
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document.write( "Hope this helps you to see the problem a little better.<BR>\n" );
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