Question

Entrance ponder for a toll bridge cost $38.50 what is a transponder the troll is four dollars each time you cross the bridge the only other option is toll by plate which the tall is $5.25 each Time across the bridge with an additional administrative fee of two dollars and 25 for each crossing how many times would you need to cross the bridge for the cost of the two tall options to be the same

Answer 1

Explanation:

To find out how many times you would need to cross the bridge for the cost of the two toll options to be the same, we can set up an equation.

Let's denote the number of crossings as "x".

For the transponder option:

- The entrance ponder for a toll bridge costs $38.50, which is a one-time fee.

- Each time you cross the bridge with a transponder, it costs $4.

So the total cost for the transponder option would be:

Total cost = $38.50 + ($4 * x)

For the toll by plate option:

- Each time you cross the bridge with toll by plate, it costs $5.25.

- There is also an additional administrative fee of $2.25 for each crossing.

So the total cost for the toll by plate option would be:

Total cost = ($5.25 * x) + ($2.25 * x)

To find when the cost of both options is the same, we can set up an equation and solve for x:

$38.50 + ($4 * x) = ($5.25 * x) + ($2.25 * x)

Let's simplify the equation:

$38.50 + $4x = $5.25x + $2.25x

Combine like terms:

$38.50 + $4x = $7.50x

Subtract $4x from both sides:

$38.50 = $7.50x - $4x

Simplify the right side:

$38.50 = $3.50x

Now, divide both sides by $3.50:

$38.50 / $3.50 = x

Approximately,

11 = x

So you would need to cross the bridge approximately 11 times for the cost of the two toll options to be the same.

Please note that the approximation is necessary since the actual solution is not a whole number.