SOLUTION: A teacher has decided to take her fifth grade class to a play. The manager of the theater agreed to discount the regular ​$33 price of the ticket by ​$0.50 for each tic

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: A teacher has decided to take her fifth grade class to a play. The manager of the theater agreed to discount the regular ​$33 price of the ticket by ​$0.50 for each tic      Log On


   



Question 1127380: A teacher has decided to take her fifth grade class to a play. The manager of the theater agreed to discount the regular ​$33 price of the ticket by ​$0.50 for each ticket sold. The cost of the​ bus, ​$450​, will be split equally among each of the students. How many students must attend to keep the cost per student at or below $33?
Answer by greenestamps(13216) About Me  (Show Source):
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The cost of the bus is a fixed $450.

For x students, the cost of each ticket will be 33-0.5x; the total cost of the tickets for the x students will be x%2833-0.5x%29.

We want the cost per student to be $33 or less. Instead of solving an inequality, we can solve an equation to find the number of students that will make the cost per student equal to $33.

%28450%2Bx%2833-0.5x%29%29%2Fx+=+33
450%2B33x-0.5x%5E2+=+33x
450-0.5x%5E2+=+0
0.5x%5E2+=+450
x%5E2+=+900
x+=+30

ANSWER: The cost per student will be $33 if the number of students is 30; it will be less than $33 if the number of students is greater than 30.