Josiah and Tillery have jobs at an ice cream shop.  
Josiah gets paid $14 per hour. 
Tillery gets paid $7 per hour. 
Every year, they will be given a raise of $2 per hour.  Is the relationship between Josiah’s pay and Tillery’s pay proportional?
Use a table to help you explain your reasoning. 



Use this space to make a table.

The relationship between Josiah’ pay and Tillery’s pay     ______    proportional.
  [IS or IS NOT]


Explain your answer. 



### Table: Josiah's and Tillery's Pay Over the Years

| Year | Josiah's Pay ($/hr) | Tillery's Pay ($/hr) | Ratio (Josiah's Pay / Tillery's Pay) |
|------|---------------------|---------------------|-------------------------------------|
| 0    | 14                  | 7                   | 14/7 = 2                           |
| 1    | 16                  | 9                   | 16/9 ≈ 1.78                        |
| 2    | 18                  | 11                  | 18/11 ≈ 1.64                       |
| 3    | 20                  | 13                  | 20/13 ≈ 1.54                       |
| 4    | 22                  | 15                  | 22/15 ≈ 1.47                       |

### Conclusion:
The relationship between Josiah’s pay and Tillery’s pay **IS NOT** proportional.

### Explanation:
A relationship is proportional if the ratio between two quantities remains constant. In this case, the ratio of Josiah's pay to Tillery's pay decreases over time, as seen in the table. Initially, the ratio is 2, but as the years progress, the ratio continues to drop. Therefore, the relationship is not proportional.

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

1. What does it mean for two quantities to have a proportional relationship?
2. How would the situation change if both got equal percentage raises instead of fixed raises?
3. Can you think of an example where two quantities have a proportional relationship?
4. If Josiah and Tillery received the same dollar increase in pay every year, would the difference in their pay ever close?
5. What other factors can affect whether two relationships are proportional?

**Tip**: Always check the ratio between two values over time to see if it's constant when determining proportionality.

Josiah and Tillery have jobs at an ice cream shop. Josiah gets paid $14 per hour. Tillery gets paid $7 per hour. Every year, they will be given a raise of $2 per hour. Is the relationship between Josiah’s pay and Tillery’s pay proportional? Use a table to help you explain your reasoning.

Explore the concept of proportional relationships through a real-world example involving pay raises. Learn how the ratio of Josiah’s pay to Tillery’s pay changes over time and why the relationship is not proportional. Suitable for students in Grades 6-8.

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