Question

A transponder for a toll bridge costs $71.50. With the​ transponder, the toll is $4 each time you cross the bridge. The only other option is​ toll-by-plate, for which the toll is $7.25 each time you cross the bridge with an additional administrative fee of $2.25 for each crossing. How many times would you need to cross the bridge for the costs of the two toll options to be the​ same?

Answer 1

The answer is n = 15. Please use the explanation below to help you remember the steps.

Explanation:

Let's denote the number of times you cross the bridge as n.

The cost of using the transponder is the cost of the transponder plus the cost per crossing, which is $71.50 + 4n.

The cost of toll-by-plate is the cost per crossing plus the administrative fee, which is ($7.25 + $2.25)n

We can set these two equations equal to each other to find the number of times you would need to cross the bridge for the costs to be the same:

71.50 + 4n = ($7.25 + $2.25)n

71.50 = ($7.25 + $2.25 - 4)n

n = 71.50 / ($7.25 + $2.25 - 4)

The Final answer is n = 15.