Question

A theater has a seating capacity of 900 and charges $2.50 for children, $4 for students, and $5.50 for adults. At a certain screening with full attendance, there were half as many adults as children and students combined. The total money brought in was $3825. Fill in the blank constants or variables to create a system that models this scenario. You do NOT need to put the "$" sign. Use lower case letters for variables.

Answer 1

To solve the problem, we need to create a system of equations based on the given information. This system will help us find the values of the variables representing the number of children, students, and adults attending the screening.

Step-by-step explanation:

Let's start by defining variables for the number of children, students, and adults attending the screening. Let c be the number of children, s be the number of students, and a be the number of adults.

According to the problem, there were half as many adults as children and students combined, so we can write the equation a = (c + s)/2.

Since the theater has a seating capacity of 900, we can write another equation for the total number of people attending the screening, which is c + s + a = 900.

Now, let's assign the prices to the tickets. The total money brought in from ticket sales is given as $3825, so we can write the equation 2.50c + 4s + 5.50a = 3825.

We now have a system of equations:

a = (c + s)/2,

c + s + a = 900,

2.50c + 4s + 5.50a = 3825.

Solving this system of equations will give us the values of c, s, and a.