One rental car agency charges $40 per day plus 13 cents per mile for a midsize car. Another agency charges $43 per day plus 9 cents per mile for a midsize car. Write a system of equations you could solve to determine the number of miles (m) for which the daily rental cost (c) is the same for both agencies.
Answers
Enterprise, for example, allows 100 miles per day for all weekend rentals. Each additional mile is typically charged at a small fee, but those can really add up. Hertz charges $0.25 per extra mile, which means drivers should be super careful to calculate the distance they plan to travel on the rental
Step-by-step explanation:
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.
.
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.
.
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:
.
First agency = $29*1 + 0.08*M = $29 + 0.08*M
.
Second agency = $18*1 + 0.15*M = $18 + 0.15M
.
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:
.
29 + 0.08*M = 18 + 0.15*M
.
Get rid of the decimals by multiplying both sides of the equation (all terms) by 100 to get:
.
2900 + 8*M = 1800 + 15*M
.
Get rid of the 15*M on the right side by subtracting 15*M from both sides to get:
.
2900 - 7*M = 1800
.
Next get rid of the 2900 on the left side by subtracting 2900 from both sides to reduce the
equation to:
.
-7*M = -1100
.
Solve for M by dividing both sides by -7 and the result is:
.
M = -1100/-7 = 157.1429 miles
.
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.
.
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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