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Rent-Me Rent-A-Car charges $25.00 per day plus $0.14 per mile to rent an economy car. Better Deal Rental Car charges $23.00 per day plus $0.
Question
Rent-Me Rent-A-Car charges $25.00 per day plus $0.14 per mile to rent an economy car. Better Deal Rental Car charges $23.00 per day plus $0.18 per mile for the same type of car. For how many miles will a car rented from either company cost the same amount?
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Mathematics
3 years
2021-09-03T14:41:21+00:00
2021-09-03T14:41:21+00:00 1 Answers
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Answer:
The number of miles at which a car rented from either company cost the same amount is 50 miles.
Step-by-step explanation:
Let x represents the number of miles at which a car rented from either company cost the same amount. Therefore, we can have the following equation:
RC = 25 + 0.14x ………………….. (1)
BC = 23 + 0.18x …………………. (2)
Where;
RC = Total cost of Rent-Me Rent-A-Car
BC = Total cost of Better Deal Rental Car
The the cost of the two companies equal where RC = BC. Therefore, we equate equations (1) and (2) and solve for x as follows:
25 + 0.14x = 23 + 0.18x
25 – 23 = 0.18x – 0.14x
2 = 0.04x
x = 2 / 0.04
x = 50
Therefore, the number of miles at which a car rented from either company cost the same amount is 50 miles.
Note:
This can be confirmed for equations (1) and (2) individually by substituting for x = 50 as follows:
For equation (1):
RC = 25 + 0.14(50)
RC = 25 + 7
RC = 32
For equation (2):
BC = 23 + 0.18(50)
BC = 23 + 9
BC = 32
Therefore, RC = BC = 32 confirms the answer.