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Let's analyze the problem step by step:

We are given a table that shows the relationship between the number of tickets and the total cost. To check if the relationship is proportional, we need to verify whether the ratio of the total cost to the number of tickets is constant.

### Step 1: Check if the relationship is proportional
We calculate the ratio of the total cost to the number of tickets for each data point:
- For 2 tickets: \( \frac{54}{2} = 27 \)
- For 3 tickets: \( \frac{81}{3} = 27 \)
- For 4 tickets: \( \frac{108}{4} = 27 \)
- For 5 tickets: \( \frac{135}{5} = 27 \)

Since the ratio is the same for each pair, the relationship is proportional.

### Step 2: Write the equation
Since the relationship is proportional, the total cost \( C \) is directly proportional to the number of tickets \( n \), and the constant of proportionality is 27. Therefore, the equation is:
\[ C = 27n \]

### Step 3: Number of tickets for a given total cost
If you need the number of tickets for a specific total cost, you can use the equation \( n = \frac{C}{27} \).

### Step 4: Calculate total cost for a given number of tickets
If you're given a specific number of tickets, use the equation \( C = 27n \) to calculate the total cost.

### Answers:
a. **Proportional?** Yes  
b. **Equation:** \( C = 27n \)  
c. **Number of tickets:** Use \( n = \frac{C}{27} \)  
d. **Total cost:** Use \( C = 27n \)

Would you like to explore these steps in more detail or have any other questions?

### Related Questions:
1. What happens to the total cost if the number of tickets doubles?
2. How would you determine the cost of 10 tickets using the equation?
3. What is the cost per ticket, and how does it relate to the constant of proportionality?
4. How can you verify the proportional relationship using a graph?
5. What would the total cost be if the number of tickets is a non-integer value (e.g., 2.5)?

### Tip:
In a proportional relationship, the graph of the equation will always pass through the origin and form a straight line.

Use the table to determine whether the relationship is proportional. If so, write an equation for the relationship it represents.

Analyze the relationship between the number of tickets and total cost to determine if the relationship is proportional. Learn how to calculate the constant of proportionality and write the equation C = 27n based on the given data.

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