document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=169697>Question 169697</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need help. I have been trying to work this problem for several days and I am confused.  This is the problem:  The Johnson family is planning a weeklong vacation in California and needs to rent a car. They don't know exactly how far they will drive, but they estimate between 400 and 800 miles. Here are the options:<BR>\n" );
document.write( "Weekly Rates: $329 per week, unlimited mileage or $219 per week, plus 12 cents per mile.  <BR>\n" );
document.write( "Daily Rates: $50 per day, unlimited mileage or $40 per day, plus 3 cents per mile.\r<BR>\n" );
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document.write( "Write the total week's rental car cost as a function of the number of miles driven in a week for each of the options.  The costs of each option must also be represented on a data table and then graphed to show the cost of each option.<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 #125084 by </B><A HREF=/tutors/aboutme.mpl?userid=gonzo><B>gonzo(654)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=gonzo><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=125084\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> you have 4 options.<BR>\n" );
document.write( "you need to outline how much each option will cost per week.<BR>\n" );
document.write( "assume a week is 7 days without any other information to go on.<BR>\n" );
document.write( "they will travel between 400 and 800 miles (given).<BR>\n" );
document.write( "option 1:<BR>\n" );
document.write( "$329 + $0.0 per mile<BR>\n" );
document.write( "option 2:<BR>\n" );
document.write( "$219 + $.12 per mile<BR>\n" );
document.write( "option 3:<BR>\n" );
document.write( "7*$50 = $350 + $0.0 per mile<BR>\n" );
document.write( "option 4:<BR>\n" );
document.write( "7*$40 = $280 + $.03 per mile<BR>\n" );
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document.write( "easiest way to do this is to create a function and graph it.<BR>\n" );
document.write( "i'll make the functions a,b,c,d<BR>\n" );
document.write( "a(x) = 329 + 0*x<BR>\n" );
document.write( "b(x) = 219 + .12*x<BR>\n" );
document.write( "c(x) = 350 + 0*x<BR>\n" );
document.write( "d(x) = 280 + .03*x<BR>\n" );
document.write( "graph of all 4 equations follows:<BR>\n" );
document.write( "look below the graph for further comments.<BR>\n" );
document.write( "negative numbers on the graph are only there so the x and y axis will show up.  it won't otherwise.<BR>\n" );
document.write( "you can figure out which line is which by looking at the starting values.<BR>\n" );
document.write( "on this graph, the x axis is the number of miles traveled and the y axis is the cost.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph+%28800%2C800%2C-100%2C1000%2C-50%2C500%2C329%2C219%2B.12%2Ax%2C350%2C280%2B.03%2Ax%29 ALIGN=MIDDLE  ALT=\"graph+%28800%2C800%2C-100%2C1000%2C-50%2C500%2C329%2C219%2B.12%2Ax%2C350%2C280%2B.03%2Ax%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "assuming you will not travel more than 800 miles, the two plans with 0 cost per mile are too expensive relative to the other plans.  they only become competitive over 800 miles traveled.<BR>\n" );
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document.write( "the cheapest plan in the beginning is the one that start off at $219.  it's the best up to about 600 miles when the plan that starts off at $280 becomes cheaper.<BR>\n" );
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document.write( "you could actually solve for the crossover points.<BR>\n" );
document.write( "take the plans that start off at $219 and $280.<BR>\n" );
document.write( "those are:<BR>\n" );
document.write( "b(x) = 219 + .12x<BR>\n" );
document.write( "d(x) = 280 + .03x<BR>\n" );
document.write( "just make them equal to each other and solve for x.<BR>\n" );
document.write( "219 + .12x = 280 + .03x<BR>\n" );
document.write( "subtract .03x from both sides:<BR>\n" );
document.write( "219 + .12x - .03x = 280<BR>\n" );
document.write( "subtract 219 from both sides:<BR>\n" );
document.write( ".12x - .03x = 280 - 219<BR>\n" );
document.write( "combine like terms:<BR>\n" );
document.write( ".09x = 61<BR>\n" );
document.write( "divide both sides by .09:<BR>\n" );
document.write( "x = 61 / .09 = 677.777777...... miles.<BR>\n" );
document.write( "that's the crossover point when both these plans are equal.<BR>\n" );
document.write( "it's hard to see on the graph but it's in the general vicinity of 679 miles on the graph.<BR>\n" );
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document.write( "if you want to plot data points, you may.<BR>\n" );
document.write( "takes miles from 400 to 800 in 50 mile chunks and solve for each equation at each of those points.<BR>\n" );
document.write( "for example:<BR>\n" );
document.write( "1 point is 400 miles<BR>\n" );
document.write( "at 400 miles you'll get these numbers:<BR>\n" );
document.write( "a(x) = 329 + 0*400 = 329<BR>\n" );
document.write( "b(x) = 219 + .12*400 = 219 + 48 = 267<BR>\n" );
document.write( "c(x) = 350 + 0*400 = 350<BR>\n" );
document.write( "d(x) = 280 + .03*400 = 280 + 12 = 292<BR>\n" );
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document.write( "you would need to do this every 50 or 100 miles, whichever you prefer.  since it's less work, do it every 100 miles.<BR>\n" );
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document.write( "looking at the graph is easier.<BR>\n" );
document.write( "since they're all straight lines, you can actually plot at 400 miles and at 800 miles and draw a straight line in between.<BR>\n" );
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