Question

Ralna is going to rent a truck for one day. There are two companies she can choose from, and they have the following prices.Company A charges an initial fee of $40 and an additional 60 cents for every mile driven.Company B charges an initial fee of $49.50 and an additional 50 cents for every mile driven.For what mileages will Company A charge less than Company B?Write your answer as an inequality, using m for the number of miles driven.

Answer 1

First, lets find the general equation for Cost(C) as function of mile driven (m) for each company.

Company A:

Fixed value (initial fee): $40

Variable value (function of mile driven): $0.60

The cost for a truck in company A (Ca) will be:

Ca = 40+0.6m

Company B:

Fixed value (initial fee): $49.50

Variable value (function of mile driven): $0.50

Cb = 49.50+0.5m

The questions asks the value of m in which company A will charge less than company B. Then:

Ca40+0.6m<49.50+0.5m

0.6m-0.5m<49.50-40

0.1m<9.50

m<9.50/0.1

m<95

Answer: m < 95 mile driven.