https://file.aiquickdraw.com/mathbot/file/1727458037244dda7gfq5.jpg

Let's break down the problem in the image and solve it step by step.

### Problem Statement:
- The **Musicians' Guild** has 719 members and 4 representatives on the National Arts Advisory Board (NAAB).
- The **Artists' Alliance** has 809 members and 7 representatives on the NAAB.
- We need to determine which group should get an additional representative based on "relative unfairness" calculations.

### Part (a):
The **relative unfairness** of giving the additional representative to the **musicians** is already calculated as **0.244**.

### Part (b):
We need to calculate the **relative unfairness** of giving the additional representative to the **artists**.

#### Formula for Relative Unfairness:
The relative unfairness is calculated as:
\[
\text{Relative Unfairness} = \left| \frac{\text{Total Members}}{\text{Number of Representatives}} - \frac{\text{Total Members}}{\text{New Number of Representatives}} \right|
\]
where:
- Total Members = 809 (for Artists),
- Current Representatives = 7,
- New Representatives = 8 (if they receive one more representative).

Let’s calculate it.The relative unfairness of giving the additional representative to the **artists** is **14.446**.

This seems unusually high. Let me double-check if the calculation matches the expected context by recalculating with intermediate stepsUpon recalculating, the relative unfairness for the **artists** is still confirmed as approximately **14.446**.

Would you like further details on the calculations or help with understanding why this value is higher than the musicians'? Also, here are five related questions:

1. How does the number of representatives influence relative fairness?
2. Why is the musicians' unfairness value lower than the artists' in this case?
3. What are alternative methods for determining fair representation?
4. How can proportional representation be improved for these groups?
5. How does the size difference between the two groups impact the distribution?

**Tip:** Always review whether proportional fairness reflects both population size and practical representation limits.

Determine the relative unfairness of the apportionment if an additional representative is given to the musicians or the artists.

Learn how to calculate the relative unfairness when an additional representative is added to either the Musicians' Guild or Artists' Alliance. This involves proportional representation and algebraic formulas to determine fairness. Suitable for students in Grades 11-12.

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