Calculating Expected Income Using Passenger Car Ratio
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.]
Let X be the number of passenger cars crossing the bridge during the daytime period. Then the number of other vehicles crossing the bridge is (20 - X).
Since 55% of all vehicles are passenger cars, we have:
X = 0.55(20) = 11 passenger cars
Thus, the number of other vehicles crossing the bridge is:
20 - X = 20 - 11 = 9 other vehicles
The expected toll revenue can be calculated as follows:
h(X) = 1.00(X) + 2.50(20 - X) = 1.00X + 50 - 2.50X = -1.50X + 50
So the total revenue can be found by plugging X = 11 into the equation:
h(11) = -1.50(11) + 50 = -16.50 + 50 = $33.50
Therefore, the resulting expected toll revenue during the daytime period is $33.50.