SOLUTION: # A Vancouver travel agency advertises all-expenses-paid trips to the Grey Cup Game for special groups. Transportation is by bus which seats 48 passengers, and the charge per perso

Question 167742: # A Vancouver travel agency advertises all-expenses-paid trips to the Grey Cup Game for special groups. Transportation is by bus which seats 48 passengers, and the charge per person is $80, plus an additional $2 for each empty seat.
1. If there are X empty seats, find the equations for:
1. How many passengers are on the bus and
2. How much does each pay?
2. What are the travel agency's total revenue when there are X empty seats?
3. Find the maximum revenue.
I have come up with the following solutions but I believe they want some or all of these answers to be in the form of quadratic equations. 1i)80-x ii)80+2x/(48-x) 2.Total revenue=80*(48-x)+2x 3. Maximum revenue=80*48
If anyone can show me how to create quadratic equations for these questions, I would appreciate it very much.

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A Vancouver travel agency advertises all-expenses-paid trips to the Grey Cup Game for special groups. Transportation is by bus which seats 48 passengers, and the charge per person is $80, plus an additional $2 for each empty seat.
1. If there are X empty seats, find the equations for:
1. How many passengers are on the bus: 48-x
------------------
2. How much does each pay? 80 + 2x
--------------------
2. What are the travel agency's total revenue when there are X empty seats?
(80+2x)(48-x) = 3840 - 80x + 96x -2x^2 = -2x^2+16x+3840
------------------------
3. Find the maximum revenue.
Max occurs when x = -16/-4 = 4
Maximum revenue is (80+8)(48-4) = 88*44 = 3872
--------------------------
Cheers,
Stan H.

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