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The problem given involves a theater selling three types of tickets: general admission, senior citizen, and child tickets. We have three transactions with different quantities and total payments:

1. **Mark** bought 9 general admission, 2 senior citizen, and 3 child tickets and paid $170.
2. **Sarah** bought 5 general admission, 4 senior citizen, and 7 child tickets and paid $173.
3. **Kyle** bought 4 general admission, 1 senior citizen, and 6 child tickets and paid $116.50.

We need to find the cost of each type of ticket. Let's denote:
- $ x $ as the cost of one general admission ticket,
- $ y $ as the cost of one senior citizen ticket, and
- $ z $ as the cost of one child ticket.

The problem gives us three equations based on the given information:

1. $ 9x + 2y + 3z = 170 $
2. $ 5x + 4y + 7z = 173 $
3. $ 4x + 1y + 6z = 116.50 $

We can solve this system of equations using methods such as substitution or elimination. Let me solve it step-by-step.The cost of each type of ticket is:

- General admission ticket ($ x $): $13.50
- Senior citizen ticket ($ y $): $11.50
- Child ticket ($ z $): $8.50

Would you like more details or have any questions? Here are 5 related questions to consider:

1. How would the total cost change if the number of tickets purchased in each category increased proportionally?
2. Can you find the total amount paid if someone bought 3 of each type of ticket?
3. What method can be used to verify the solution to this problem?
4. How would the problem change if there was a discount applied to child tickets?
5. What if we only knew the total number of tickets purchased, could we still solve for the ticket prices?

**Tip:** In problems involving multiple variables and equations, organizing information clearly and using algebraic methods like elimination or substitution can simplify finding solutions.

The theater sells three types of tickets: general admission, senior citizen, and child. Mark bought 9 general admission, 2 senior citizen, and 3 child tickets and paid $170. Sarah bought 5 general admission, 4 senior citizen, and 7 child tickets and paid $173. Kyle bought 4 general admission, 1 senior citizen, and 6 child tickets and paid $116.50. Find the cost of each type of ticket.

Learn how to solve a system of linear equations involving three different types of theater tickets: general admission, senior citizen, and child. The problem includes three purchases and asks you to find the individual price of each ticket type. Suitable for students in Grades 9-12.

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