word problem

Question

A teacher is planning a trip to France.  A plane that will hold up to 75 people has been chartered for $100,000 and admission tickets to events in Paris are $250 each.  If the cost of the trip is set at $1,500 per person, what is the minimum number of students needed to commit for the trip to "make"? Teachers and chaperones travel for free. 

Answer 1

The cost of the plane charter is $100,000.  If the cost of the trip is $1,500 per person, and the admission tickets will be also charged to the students, only $1,250 per student is available to pay for the plane charter.

 

If S is the amount of students needed to pay for the plane,

 

S * $1,250 = $100,000

 

S = $100,000 / $1,250

 

S = 80, which is in excess of the plane capacity.  And there wouldn't be any room for the teachers and chaperones either.

 

So the trip won't "make".  It's a badly-worded question because the admission ticket information is a red herring and the number of teachers/ chaperones is not given.  If we assume the students are charged extra for the admission tickets, and the teachers/ chaperones pay for their admission tickets,

 

S = $100,000 / $1,500 = 66 2/3, and the trip would work with no more than 8 teachers/ chaperones.

Answer 2

The number of students times $1,500 has to be greater than or equal to $100,000 plus the number of students times $250

If the number of students is S:

 

1500S >(or=) 100,000 + 250S

 

Solve for S.

 

If S is > 75, they cannot go on the trip