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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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## Answers ( )

Answer:The number of miles at which a car rented from either company cost the same amount is

.50 milesStep-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 milesNote: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.