A teacher has decided to take her fifth grade class to a play. The manager of the theater agreed to discount the regular $35 price of the ticket by $0.30 for each ticket sold. The cost of the bus, $480 , will be split equally among each of the students. How many students must attend to keep the cost per student at or below $35 ?

40 students

Explanation:

The cost of the bus is $480

For x students, the cost of each ticket will be 35 - 0.30x

The total cost of the tickets for x students will be x (35 - 0.30x)

To find the number of students that will make the cost per student equal to $33, we solve for x:

480 + x (35 - 0.30x) = 35

x

480 + x (35 - 0.30x) = 35x

480 + 35x - 0.30x² = 35x

480 = 0.30x²

1,600 = x²

40 = x

The cost per student will be $35 if the number of students is 40; it will be less than $35 if the number of students is greater than 40.