Question

Field Trip Mrs. West has decided to take her fifth grade class to a play. The manager of the theater agreed to discount the regular \( 40 price of the ticket by \) 0.20 for each ticket sold. The cost of the bus, \( 500, will be split equally among each of the students. How many students must attend to keep the cost per student at or below \) 40?

Short answer

The number of students that should attend should be at least is 50.

Step-by-step solution

Given information

The manager of the theater agreed to discount the regular $40 price of the ticket by $0.20 for each ticket sold. The cost of the bus, $500, will be split equally among each of the students.

Determine the number of students must attend to keep the cost per student at or below $ 40. 

The expression for cost of theater ticket for each student if $x$is the number of students is:

$40-0.20x$

Step 2

The expression for the bus cost for each student with $x$students is:

$\frac{500}{x}$

Therefore, the total cost for each student is:

$40-0.20x+\frac{500}{x}$

Since the total cost for each students should be less than 40 , the expression is:

$\begin{array}{rcl}40-0.20x+\frac{500}{x}& \le & 40\\ -0.20x+\frac{500}{x}& \le & 0\\ \frac{500}{x}& \le & 0.20x\\ \frac{500}{0.20}& \le & x^2\\ 2500& \le & x^2\\ x& \ge & 50\end{array}$

Write the conclusion

the number of students must attend to keep the cost per student at or below $ 40 is 50.