Cleo paid $9.50 for 19 ride tokens. Leona paid $19 for 38 ride tokens. What is the constant of proportionality?

To find the constant of proportionality, we first need to determine whether the ratio of dollars to tokens is the same for both Cleo and Leona. The constant of proportionality represents the cost per token.

### Step 1: Find the cost per token for Cleo

Cleo paid $9.50 for 19 tokens.

\[
\text{Cost per token for Cleo} = \frac{\text{Total Cost}}{\text{Number of Tokens}} = \frac{9.50}{19}
\]

Calculating this:

\[
\frac{9.50}{19} = 0.50
\]

### Step 2: Find the cost per token for Leona

Leona paid $19 for 38 tokens.

\[
\text{Cost per token for Leona} = \frac{\text{Total Cost}}{\text{Number of Tokens}} = \frac{19}{38}
\]

Calculating this:

\[
\frac{19}{38} = 0.50
\]

### Step 3: Determine the constant of proportionality

Both Cleo and Leona have the same cost per token of $0.50. Thus, the constant of proportionality is:

\[
\boxed{0.50}
\]

This means that the cost per token is 50 cents for both Cleo and Leona, showing a consistent proportional relationship.

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Would you like more details, or do you have any questions?

Here are 5 related questions you might find interesting:

1. How do you determine if two quantities are directly proportional?
2. What is a constant of proportionality in the context of unit rates?
3. How would the constant of proportionality change if Cleo or Leona received a discount?
4. How can you represent this proportional relationship graphically?
5. What are other real-life examples of proportional relationships?

**Tip:** Always check if the ratios are equal when determining if quantities are proportional!

Learn how to find the constant of proportionality in a real-life example where Cleo paid $9.50 for 19 ride tokens, and Leona paid $19 for 38 ride tokens. Understand how to calculate the unit rate and identify proportional relationships. Suitable for students in Grades 6-8.

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