Questions: Determine the cost of one adult ticket: Last week, the theater sold 35 adult tickets and 25 student tickets for a total of 420. This week, they sold 2 adult tickets and 40 student tickets for a total of 330. Find the cost of one adult ticket and one student ticket.

Solution Steps

To find the cost of one adult ticket and one student ticket, we can set up a system of linear equations based on the information given. Let \( x \) be the cost of an adult ticket and \( y \) be the cost of a student ticket. From the problem, we have two equations:

1. \( 35x + 25y = 420 \) (from last week's sales)
2. \( 2x + 40y = 330 \) (from this week's sales)

We can solve this system of equations using Python to find the values of \( x \) and \( y \).

We start by defining the variables:

• Let \( x \) be the cost of one adult ticket.
• Let \( y \) be the cost of one student ticket.

From the problem, we can set up the following system of equations based on the sales data:

1. \( 35x + 25y = 420 \) (from last week's sales)
2. \( 2x + 40y = 330 \) (from this week's sales)

We solve the system of equations to find the values of \( x \) and \( y \). The solution yields:

• \( x = \frac{19}{3} \)
• \( y = \frac{119}{15} \)

The values obtained represent the costs of the tickets:

• The cost of one adult ticket is \( \frac{19}{3} \) dollars.
• The cost of one student ticket is \( \frac{119}{15} \) dollars.

Final Answer