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

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

151 miles travel

Step-by-step explanation:

hope this helps