Question

A toll bridge charges $1.00 for passenger cars and $2.50 for other vehicles. Suppose that during daytime hours, 55% of all vehicles are passenger cars. If 20 vehicles cross the bridge during a particular daytime period, what is the resulting expected toll revenue? [Hint: Let X = the number of passenger cars; then the toll revenue h(X) is a linear function of X.]

Answer 1

$33.50

Explanation:

The number of vehicles cross the bridge during daytime hours = 20

55% of all vehicles are passenger cars.

The toll bridge charges $1.00 for passenger cars and $2.50 for other vehicles.

The number of passenger cars = 55% of 20

= 0.55 × 20

= 11

Then the toll revenue for passenger cars = 11($1.00)

The number of other vehicles = 20 - 11 = 9

Then the toll revenue for other vehicles = 9($2.50)

The expected toll revenue = 11(1) + 9(2.50)

= 11 + 22.50

= $33.50

The resulting expected toll revenue would be $33.50

Answer 2

The number of passenger cars that crossed the bridge is the product of 20 and 0.55 which is equal to 11. Hence, the number of other vehicles is 9. The revenue is calculated below,
11($1) + 9($2.50) = $33.5
Thus, the total revenue of the toll bridge is $33.5.