How Many Empty Seats Maximize Profit on a Ski Trip Minibus?

[hallowon]

Homework Statement

It Costs a bus company $225 to run a minibus on a ski trip, plus $30 per passenger. the bus has seating for 22 passengers, and the company charges $60 per fare if the bus is full. For each empty seat, the company has to increase ticket price by $5. How many empty seats should the bus run with to maximize profit from this trip?

Homework Equations

vertex form
factored form
standardform
cost function
revenue function
profit function

The back of the book says 8 empty seats

The Attempt at a Solution

my equations
C(x)=(225+30x)
R(x)=(60-5x)
P(x)=R(x)-C(x)
So far I've tried doing the equations numerus ways, I've tried multiplying the terms together, doesn't work I think it gave me 3 empty seats. Tried using the profit functions above, still doesn't give me 8 empty seats. I'm guessing it is either one of my functions that is incorrect but I am not sure which

 

[symbolipoint]

You formulated the Rate ( R(x) ) incorrectly. View the passenger rate as Dollars Per Passenger. The company charges 60 dollars per fare if bus is full, or bus takes 22 passengers. How much money is that? 60 dollars per fare multiplied by 22 fares. Now, what happens for each decrement of 1 passenger? This is where you became stuck(?).
Why did you subtract instead of add? Best I could tell, you want R(x)=60+5x, because "increase ticket price by $5 for each empty seat". x=[count of passengers]