Question

a transponder for a toll bridge costs $67.50. 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 $6.25 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? you need to cross the bridge \square times.

Explanation:

Step1: Define variable for crossings

Let $x$ = number of bridge crossings.

Step2: Cost equation for transponder

Total transponder cost: $67.50 + 4x$

Step3: Cost equation for toll-by-plate

Total toll-by-plate cost: $(6.25 + 2.25)x = 8.5x$

Step4: Set costs equal, solve for $x$

$$67.50 + 4x = 8.5x$$
$$67.50 = 8.5x - 4x$$
$$67.50 = 4.5x$$
$$x = \frac{67.50}{4.5}$$

Answer:

15