math help !!

Question

The girls’ softball team is sponsoring a fundraising 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.

a) Write a quadratic function giving the softball team’s profit, P(n), from this fundraiser as a function 

of the number of empty seats, n.

b) What is the minimum number of passengers needed in order for the softball team not to lose 

money?

c) What is the cost per passenger if the minimum number take the trip and the team does not lose 

money?

 

Answer 1

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 .

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

Step 2 :

Let be the number of increases for each empty seat.

Profit of the softball team is .

Step 3 :

a)

.

Revenue and expense =.

Hence the quadratic function is

Step 4 :

b)

Break even points : .

Solve the equation .

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 .

.

Step 5 :

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.

Comments

Step 6 :

c)

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

 .

.

They would gain about .

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

Solution :

a) The quadratic function is

b) The minimum number of passengers needed in order for the soft ball team lose money are 54.

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