Step 1 :

From the given data :

The girls softball team is sponsoring a fund-raising trip to see a professional baseball game.

They charter a 60-passenger bus for $525.

In order to make a profit, they will charge $15 per person if all seats on the bus are sold, but for each empty seat, they will increase the price by $1.50 per person.

Step 2 :

Let be the number of empty seats on the bus and also,

be the number of $1.50 increases for each empty seat.

Profit of the softball team is .

Step 3 :

a)

Revenue and expense =$525

Hence the quadratic function is

Step 4 :

b).

Break even points :.

Solve the equation .

is a is a quadratic equation, use quadratic formula to find the solution of the related quadratic equation.

Solution .

Compare the equation with standard form of the quadratic equation .

Solution

The positive solution =  .

The minimum number of passengers needed in order for the soft ball team  not to lose money are 54.

54 empty seats, only 6 paying passengers the minimum to not lose money.

Step 5 :

c)

Confirm that, 54 empty seats means the cost for the remaining 6 will be :

 .

.

The cost per passenger if the minimum number take the trip and the team does not lose money is $576.