SOLUTION: 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 r

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Question 101040: 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.
I can't figure out how to form the equations.
Found 2 solutions by bucky, stanbon:
Answer by bucky(2189) (Show Source):
You can put this solution on YOUR website!
Let's recognize that in terms of dollars, 8 cents is 0.08 dollars and 15 cents is 0.15 dollars.
.
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:
.

.
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.
.
Hope this helps you to see the problem a little better.
.

Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
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.
------------------
1st agency cost = 29+0.08x for x miles of driving.
2nd agency cost = 18+0.15x for x miles of driving.
--------------------
When are the costs equal?
EQUATION:
29+0.08x=18+0.15x
11 = 0.07x
x = 157.143 miles
Costs will be equal when the driver drives 157.143 miles
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Cheers,
Stan H.