Question

Amina wants to rent a car for a trip to the Serengeti park for one week.

She calls two car rental companies to get prices. Mr. Asani’s Rentals rents a Cadillac
Escalade for $99 for one week plus $0.11 per km over 100 km.

Mr. Hatari’s Rentals has the same vehicle for $75 per week and $0.15 per km over 150
km. If it is 432 kilometers to the Serengeti park, which company has the better deal?
How many kilometers would Amina drive before she would be spending the same amount
at either company?

Answer 1

Answer:

Mr. Hatari’s Rentals gives her a better deal.

There is no distance to travel for equal expenditure in both the options.

Step-by-step explanation:

Anima has to travel 432 km. to the Serengeti park.

In  Mr. Asani’s Rentals, she has to pay 99+(432-100)0.11 = 135.52$

And in Mr. Hatari’s Rentals, she has to pay 75+(432-150)0.15 = 117.3$.

So, Mr. Hatari’s Rentals gives her a better deal. (Answer)

Now, let us assume that, for traveling x Km. (x> 150 km.) she has to pay equally for both the companies. Then x is given by  

99+(x-100)0.11 = 75+(x-150)0.15

⇒0.04x+99-11=75-22.5

⇒0.04x = -35.5

⇒ x = -887.5 ( x can not be negative)

Hence, there is no distance to travel (>150 km.) for equal price in both the deals.

Now again, let us assume that, for traveling x Km. (100 km. <x< 150 km.) she has to pay equally for both the companies. Then x is given by  

99+(x-100)0.11 = 75

⇒0.11x+99-11=75

⇒0.11x = -13

⇒ x = -118.18 km. ( x can not be negative)

Hence, there is no distance to travel (100 km.<x<150 km.) for equal price in both the deals.

Again for x<100 km. she has to pay $99 and $75 for both the companies respectively.

Therefore, there is no distance to travel for equal expenditure in both the options. (Answer)