Question

Joseph is going on a trip and he needs to rent a car. He looks online and finds two companies that offer different pricing options for car rentals. Company A charges $0.25 per mile plus a $50 rental fee. Company B charges $0.45 per mile plus a $20 rental fee. What is the minimum number of miles that Joseph must drive in order for Company A to be a better buy? The company charges only for whole number mileage (not fractional increments of miles driven). A) 125 miles B) 149 miles C) 150 miles D) 151 miles

Answer 1

Answer: The answer is B.

Step-by-step explanation:

I choose D and got it wrong so don't listen to them . It's B.

Answer 2

Answer:

if Joseph travels minimum 151 miles , then Company A will be better buy.

Step-by-step explanation:

lets create equation for both that is company A and Company B

Lets assume number of miles be represented by x

Company A charges = (0.25 × x ) + 50 = 0.25x + 50

Company B charges = (0.45 × x ) + 20 = 0.45x + 20

lets first find out number of miles when Company A charges = Company B charges

⇒0.25x + 50 =  0.45x + 20

⇒ 50 - 20 = 0.20x

⇒x = 30÷0.20 = 150

so At x = 150 miles  , charges for both the company will be same.

Need to observe that for company A to be better buy ,it should be travelling more as its rental fee is more but charges per mile is less. and since company charges only for whole number mileage , next whole number after 150 is 151 . hence if Joseph travels minimum 151 miles , then Company A will be better buy.

we can check by keeping x = 151 in equation formed

Company A charges = (0.25 × 151 ) + 50 = 87.75

Company B charges = (0.45 × 151) + 20 = 87.95

hence for 151 miles travel  Company A is better buy than Company B