word problem...plz help

snow123

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Sep 25, 2010
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I don't know how to do this word problem...please help me, i would really appreciate it
Thank you

The city transit system carries 24800 bus riders per day for a fare of $1.85. The city hopes to reduce car pollution by getting more people to ride the bus, while maximizing the transit system's revenue at the same time. A survey indicates that the number of riders will increase by 800 for every $0.05 decrease in the fare. What fare will produce the greatest revenue?

Thank you for your time.
 
24800 @ 1.85 = $45,880
25600 @ 1.80 = $46,060 ; keep going until a drop occurs :wink:
 


Here's an algebraic approach. To understand it, you would need to be familiar with 2nd-degree polynomials (i.e., quadratic polynomials) and their graphs.

Revenue equals Riders times Fare.

The number of riders is given (24800), and so is the fare (1.85).

The given information tells us that both these numbers will change, according to some survey.

24800 increases, depending upon the number of nickel reductions in the fare.

1.85 decreases to become a new fare, also dependent upon the number of nickel reductions.

In other words, the new revenue is a function of this unknown number of nickel reductions in the fare.

Therefore, you need to pick a symbol to represent this unknown. (Write down your symbol definition.)

Next, we look at how the number of riders and the fare change, with respect to the unknown.

The information says that 24800 goes up by 800 for each nickel reduction. It also says that 1.85 goes down by 0.05 for each reduction.

New Revenue = New Riders * New Fare

Can you write expressions for the New Fare and the New Riders, using your symbol that represents the number of nickel fare reductions?

New Riders is going to be 24800 plus [800 times the number of fare reductions]

New Fare is going to be 1.85 minus [0.05 times the number of fare reductions]

Multiply these two expressions together, and you'll have a quadratic polynomial for New Revenue, in terms of the unknown.

Do you know how to find the vertex point of the parabolic graph? The y-coordinate of that point is the maximum revenue.

The value of the unknown at the vertex point is what you use to calculate the actual value of the new fare (i.e., the number of nickel reductions of 1.85). 8-)

 
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