Question

A truck can be rented from Company A for $70 a day plus $0.20 per mile. Company B charges $40 a day plus $0.50 per mile to rent the same truck. Find the number of miles in a day at which the rental costs for Company A and Company B are the same.

Answer 1

You have the following costs for the rent of a truck:

Cost of company A: $70 a day plus $0.20 per mile

Cost of company B: $40 a day plus $0.50 per mile

The previous cost can be written in the following algebraic form:

70 + 0.20x

40 + 0.50x

where x is the number of miles. In order to calculate the number of milles that makes the costs of both companies equal, you equal the two previous algebraic expression, just as follow:

70 + 0.20x = 40 + 0.50x you subtract 0.20x and 40 both sides

70 - 40 + 0.20x - 0.20x = 40 - 40 + 0.50x - 0.20x simplify

30 = 0.30x divide by 0.30 both sides

30/0.30 = 0.30x/0.30

100 = x

Hence, for 100 miles at day the costs of both companies are equal.