# Math Question: Quadratic Equations?

Could someone please answer this question: A ferry operator takes tourists to an island. The operator carries an average of 500 people per day for a round trip fare of $20. The operator estimates that for each $1 increase in fare, 20 fewer people will take the trip. What fare will maximize the number of people taking the ferry

Please show your work, thank you!

### 1 Answer

- Anonymous7 years agoFavorite Answer
Let P be the number of people that will take the trip. Let F be the fare in dollars. We are told:

P(20) = 500

ΔP/ΔF = -20/1 = -20

And so we have the point (20,500) and the slope -20, thus the point-slope formula gives us:

P - 500 = -20(F - 20)

P = -20F + 900

I suspect you are to maximize the revenue R, rather than the number of passengers. The revenue is the product of the number of people and the fare per person:

R = PF = -20F² + 900F = 20F(18 - F)

The vertex of this parabolic revenue function will be on the axis of symmetry with is midway between the roots, hence the fare that maximizes revenue is $9.

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