Question 101040
Let's recognize that in terms of dollars, 8 cents is 0.08 dollars and 15 cents is 0.15 dollars.
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If you rent a car from the first car agency your cost for the rental will be $29 times the
number of days you rent it plus $0.08 for each mile you drive. Therefore, you will pay a
total of $29*D + 0.08*M where D is the number of days and M is the total number of miles you
drive.
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If you rent a car from the second car agency your cost for the rental will be $18 times the
number of days you rent it plus $0.15 times the number of miles you drive. Therefore,
you will pay a total of $18*D + 0.15*M.
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The problem says that you plan on renting for just 1 Day. This being the case, you can
substitute 1 for D and you get that the two rental costs will be:
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First agency = $29*1 + 0.08*M = $29 + 0.08*M
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Second agency = $18*1 + 0.15*M = $18 + 0.15M
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At some number of miles driven the two costs will be the same. We can find that number of miles
by setting the two equations equal to get:
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29 + 0.08*M = 18 + 0.15*M
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Get rid of the decimals by multiplying both sides of the equation (all terms) by 100 to get:
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2900 + 8*M = 1800 + 15*M
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Get rid of the 15*M on the right side by subtracting 15*M from both sides to get:
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2900 - 7*M = 1800
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Next get rid of the 2900 on the left side by subtracting 2900 from both sides to reduce the
equation to:
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-7*M = -1100
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Solve for M by dividing both sides by -7 and the result is:
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M = -1100/-7 = 157.1429 miles
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Up until you drive 157 miles you would save money by going with the second company ...
the one that charges $18 per day plus 15 cents per mile. But if you drive 158 miles or
more you will save money by going with the company that charges $29 per day but less in
the per mile charge.
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If you think in terms of the graphs of these two equations, it might help you to visualize the
problem. The red graph below shows the cost of renting a car from the first company that
charges $29.00 per day + 8 cents per mile. The green graph shows the cost of renting a car from 
the second company that charges $18 per day + 15 cents per mile. The y-axis is the cost
and the x axis is the number of miles driven:
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{{{graph(600,600,-10,200,-1,50,29+.08x,18+.15x)}}}
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You can see that the two graphs cross at about 157 miles on the x-axis. As the miles increase
above 157 the green graph for the second company is above the red graph which means that
it has a higher cost. So beyond 157 miles of driving the red graph is not as high in cost
meaning that the company charging 8 cents per mile will have a cheaper cost.
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Hope this helps you to see the problem a little better.
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