document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1190430>Question 1190430</A>: <I><SPAN STYLE=\"word-break: break-all;\"> OMG I need help! I cannot solve this problem for the life of me. Please explain so I can understand. I think the unlimited miles is what's messing me up. Thanks in advance!\r<BR>\n" );
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document.write( "A car rental company offers 2 plans for renting a car <BR>\n" );
document.write( "Plan A: $40 per day and $0.19 per mile<BR>\n" );
document.write( "Plan B: $60 per day with unlimited miles\r<BR>\n" );
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document.write( "For what range of miles will Plan B save you money for a 1 day rental?<BR>\n" );
document.write( "For what range of miles will Plan A save you money for a 1 day rental?<BR>\n" );
document.write( "Give your answer accurate to at least one decimal place. </SPAN>\n" );
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document.write( "The \"unlimited\" miles means that the company doesn't charge per mile in this scenario. All they get is the $60 per day.<BR>\n" );
document.write( "If you only rent for one day, then all they get is the $60. This applies to plan B only of course.\r<BR>\n" );
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document.write( "x = number of miles<BR>\n" );
document.write( "y = total cost\r<BR>\n" );
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document.write( "If you only plan to do a 1 day rental, then,<BR>\n" );
document.write( "Plan A has the equation y = 0.19x+40<BR>\n" );
document.write( "The 0.19x is the extra 19 cents (aka $0.19) per mile on top of the $40 initially paid\r<BR>\n" );
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document.write( "Plan B has the equation y = 60 for 1 day rentals.<BR>\n" );
document.write( "The x is not involved because again they don't charge per mile. The cost is simply 60 dollars.\r<BR>\n" );
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document.write( "Both cost equations involve y<BR>\n" );
document.write( "Let's apply substitution to find x<BR>\n" );
document.write( "y = 60<BR>\n" );
document.write( "0.19x+40 = 60 ... y replaced with 0.19x+40<BR>\n" );
document.write( "0.19x = 60-40<BR>\n" );
document.write( "0.19x = 20<BR>\n" );
document.write( "x = 20/0.19<BR>\n" );
document.write( "x = 105.263 approximately<BR>\n" );
document.write( "This rounds to 105.3 when rounding to one decimal place.<BR>\n" );
document.write( "The two costs are roughly the same when driving 105.3 miles for 1 day rentals.\r<BR>\n" );
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document.write( "If you traveled 105 miles in one day, then plan A costs you<BR>\n" );
document.write( "y = 0.19x+40<BR>\n" );
document.write( "y = 0.19*105+40<BR>\n" );
document.write( "y = 19.95+40<BR>\n" );
document.write( "y = 59.95<BR>\n" );
document.write( "which is just barely under the $60 mark. This shows that plan A is the better choice for this mileage.\r<BR>\n" );
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document.write( "If you traveled 106 miles in one day, then plan A costs you<BR>\n" );
document.write( "y = 0.19x+40<BR>\n" );
document.write( "y = 0.19*106+40<BR>\n" );
document.write( "y = 20.14+40<BR>\n" );
document.write( "y = 60.14<BR>\n" );
document.write( "You are paying 14 cents more than if you went with plan B.<BR>\n" );
document.write( "For any larger x values, plan A will get more expensive and it's better to go for plan B.<BR>\n" );
document.write( "Intuitively this is what we'd expect because plan A's cost grows based on the number of miles driven, while B has a fixed cost.\r<BR>\n" );
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document.write( "Those are two examples to show that the boundary is 105.3<BR>\n" );
document.write( "I'll let you play with other x values. I recommend making a table to compare costs.\r<BR>\n" );
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document.write( "Answers:\r<BR>\n" );
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document.write( "For what range of miles will Plan B save you money for a 1 day rental? <font color=red>Anything larger than 105.3 miles</font> <BR>\n" );
document.write( "For what range of miles will Plan A save you money for a 1 day rental? <font color=red>Anything between 0 and 105.3 miles</font>\r<BR>\n" );
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document.write( "In terms of inequalities, the first statement in red is the same as saying <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%3E+105.3 ALIGN=MIDDLE  ALT=\"x+%3E+105.3\"   DISABLED_style= \"max-width:90%; height:auto;\" > while the second statement would translate to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+%3C=+x+%3C=+105.3 ALIGN=MIDDLE  ALT=\"0+%3C=+x+%3C=+105.3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, where x is the number of miles driven. Also, this all applies to one day rentals only.\r<BR>\n" );
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document.write( "If you require more accuracy, then change the 105.3 to something like 105.26 or perhaps 105.263 or whatever you prefer to round to; there are infinitely many ways to write this value because we're dealing with a rounded approximation. <BR>\n" );
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document.write( " </SPAN>\n" );
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