Question

A truck can be rented from Company A for ​$130 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

Using simultaneous equations, the rental costs for Company A and Company B will be equal when the truck is taken for 300 hours a day.

Simultaneous equations are equations solved concurrently.

Company A Company B

Fixed rental charge per day $130 $40

The charge per mile $0.20 $0.50

Let the number of miles in a day = x

Let the total cost = y

Total Costs:

Equation 1 for Company A: y = 130 + 0.2x

Equation 2 for Company B: y = 40 + 0.5x

For the rental costs for Company A and Company B to be the same, Equation 1 must equal Equation 2:

130 + 0.2x = 40 + 0.5x

90 = 0.3x

x = 300

Thus, for the two companies' rental costs to be the same, the number of miles must be 300 miles for both companies.