Name: Jacky Lam

Who is asking: Student
Level: Secondary

Question: I am having this problem in my math homework.

The city transit system carries an average of 9450 bus riders a day, for a fare of $1.75 each. The city wants to reduce car pollution by increasing ridership and to maximize the transit system's revenue at the same time. A survey indicates that the number of riders will increase by 150 for every $0.05 decrease in fare.

Now, I have to write an equation to represent the total daily revenue, using 'f' to represent the fare for one passenger, in dollars. The hint is revenue = fare x number of passengers.

The answer is R = -3000f^2 + 14700f but I have no clue as to what this came from.

Hi Jacky,

If the fare is $f then you need to find the number of passangers, P, and then the revenue will be $f x P. To do this you need to know how many 5 cent decreases there have been. $1.75 - f is the price decrease from the original price of $1.75, and hence  ($1.75 - f)/0.05 is the number of 5 cent decreases.

Each time there is a 5 cent decrease in the fare the number of passengers increases by 150. Thus the number of new passengers is 150 x ($1.75 - f)/0.05 and the total number of passengers is P = 9450 + 150 x ($1.75 - f)/0.05

To find the total revenue calculate f x P.

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