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The problem asks for the constant of proportionality that relates the total cost (\( y \)) in dollars to the number of tickets (\( x \)).

To find the constant of proportionality \( k \), we can use the relationship:

\[
y = kx
\]

Where:
- \( y \) is the total cost,
- \( x \) is the number of tickets,
- \( k \) is the constant of proportionality.

The constant of proportionality \( k \) is the ratio of \( y \) to \( x \), calculated as:

\[
k = \frac{y}{x}
\]

Let's calculate \( k \) using different values from the table:

- When \( x = 8 \), \( y = 2.00 \):
  \[
  k = \frac{2.00}{8} = 0.25
  \]

- When \( x = 12 \), \( y = 3.00 \):
  \[
  k = \frac{3.00}{12} = 0.25
  \]

- When \( x = 20 \), \( y = 5.00 \):
  \[
  k = \frac{5.00}{20} = 0.25
  \]

- When \( x = 30 \), \( y = 7.50 \):
  \[
  k = \frac{7.50}{30} = 0.25
  \]

- When \( x = 50 \), \( y = 12.50 \):
  \[
  k = \frac{12.50}{50} = 0.25
  \]

Thus, the constant of proportionality is \( k = 0.25 \).

The correct answer is \( 0.25 \). If you selected \( 4.00 \), it seems there may have been a mistake. Would you like further clarification on this?

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Here are 5 related questions to expand your understanding:
1. What happens to the total cost if you buy 100 tickets?
2. How would you calculate the total cost for 15 tickets?
3. If the cost per ticket increased, how would that affect the constant of proportionality?
4. What other real-life scenarios might follow a proportional relationship like this one?
5. How would you explain the concept of proportionality to someone learning it for the first time?

**Tip:** When working with tables and proportionality, always double-check by dividing each \( y \) value by its corresponding \( x \) value to ensure consistency.

What is the constant of proportionality that relates the total cost (y) in dollars to the number of tickets (x) purchased?

Find the constant of proportionality relating the total cost to the number of tickets purchased in this school carnival example. This problem uses key proportionality concepts and is suitable for students in Grades 6-8.

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