Question

Jane wants to rent a truck for one day, so she contacted two companies. Company 1 charges 20 dollars plus 2 dollar per mile and Company 2 charges 3 dollar per mile. Find the number of miles at which both the companies charge the same amount of total cost.

Answer 1

Let x be the miles driven.

Company 1: cost = 20 + 2x
Company 2: cost = 3x

Set equal: 20 + 2x = 3x
=> 20 = x

So at 20 miles the total costs are equal (both $60). For fewer than 20 miles Company 2 is cheaper; for more than 20 miles Company 1 is cheaper.