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The problem asks for a system of linear equations based on the given situation. Let’s define the variables as instructed:

- Let $ x $ represent the cost of an adult ticket.
- Let $ y $ represent the cost of a student ticket.

### Key Information:
- The drama club earns $1040 in total from ticket sales.
- It sells 64 adult tickets and 132 student tickets.
- The cost of an adult ticket is twice the cost of a student ticket.

### Step 1: Create Equations Based on Total Earnings
From the ticket sales and the total revenue:
- The total amount of money earned from adult tickets is $ 64x $.
- The total amount of money earned from student tickets is $ 132y $.
- Together, they add up to $1040, so:
\[
64x + 132y = 1040
\]

### Step 2: Relate the Cost of Adult and Student Tickets
The problem states that an adult ticket costs twice as much as a student ticket, so:
\[
x = 2y
\]

### System of Linear Equations:
\[
\begin{cases}
64x + 132y = 1040 \\
x = 2y
\end{cases}
\]

Would you like a detailed solution for solving this system of equations or any further questions about this setup?

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Here are 5 related questions to explore further:

1. How do you solve this system of equations using substitution or elimination methods?
2. What happens to the ticket sales total if the number of tickets sold changes?
3. How would the system change if an adult ticket were three times the cost of a student ticket?
4. How can this problem be represented graphically?
5. How would you solve the system if you were only given the total number of tickets sold and not the breakdown?

**Tip:** Always identify your variables clearly and extract equations directly from the problem's conditions to set up a solid foundation for solving.

A drama club earns $1040 from a production. It sells a total of 64 adult tickets and 132 student tickets. An adult ticket costs twice as much as a student ticket. Write a system of linear equations that represents this situation. Let x represent the cost of an adult ticket and y represent the cost of a student ticket.

Learn how to set up a system of linear equations based on a real-life scenario where a drama club earns $1040 by selling adult and student tickets. The problem includes key algebraic concepts such as linear equations and the substitution method. Suitable for students in Grades 8-10.

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