Question

Yoko 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 90 cents for every mile driven.

Company B charges an initial fee of $75 and an additional 40 cents for every mile driven.

For what mileages will Company A charge less than Company B?

A) m > 35 miles
B) m > 25 miles
C) m > 15 miles
D) m > 5 miles
E) m > 45 miles

Answer 1

Company A charges less than Company B for mileages greater than 5 miles.

Step-by-step explanation:

To determine the mileages for which Company A charges less than Company B, we need to compare the total cost for each company for a given mileage. Let's assume the mileage is represented by the variable 'm'.

For Company A, the total cost can be calculated using the formula: cost = $40 + $0.90 * m

For Company B, the total cost can be calculated using the formula: cost = $75 + $0.40 * m

To find the mileages for which Company A charges less than Company B, we need to solve the inequality: $40 + $0.90 * m < $75 + $0.40 * m

Simplifying the inequality, we get: $0.50 * m < $35

Dividing both sides of the inequality by $0.50, we get: m < 70

Therefore, the correct answer is option D) m > 5 miles.