https://file.aiquickdraw.com/mathbot/file/1725571539776qxedvrjg.jpg

The image shows a problem involving the allocation of promotions for faculty members at three different campuses of a community college. 

To solve the problem, let's break down the information:

1. The total number of faculty members at each campus is given in the table:
   - Central Campus: 22 faculty members
   - East Campus: 34 faculty members
   - West Campus: 44 faculty members

2. The total number of promotions available is 10.

The goal is to allocate these 10 promotions proportionally to the number of faculty members at each campus.

### Solution

To distribute the promotions proportionally, we calculate the fraction of the total faculty members at each campus and multiply it by the total number of promotions.

1. **Calculate the total number of faculty members:**

\[
\text{Total Faculty Members} = 22 + 34 + 44 = 100
\]

2. **Determine the proportion of faculty members at each campus:**

- Central Campus: \(\frac{22}{100} = 0.22\)
- East Campus: \(\frac{34}{100} = 0.34\)
- West Campus: \(\frac{44}{100} = 0.44\)

3. **Allocate the promotions accordingly:**

- Promotions for Central Campus: \(0.22 \times 10 = 2.2\) (round to 2)
- Promotions for East Campus: \(0.34 \times 10 = 3.4\) (round to 3)
- Promotions for West Campus: \(0.44 \times 10 = 4.4\) (round to 5)

### Final Allocation:

- **Central Campus:** 2 promotions
- **East Campus:** 3 promotions
- **West Campus:** 5 promotions

Would you like a more detailed explanation or have any questions? 

Here are some additional related questions you might consider:

1. How would the allocation change if the total number of promotions were different?
2. What if the proportions were rounded differently?
3. How can the method of proportional allocation be used in other resource distribution scenarios?
4. How would the solution change if there were a minimum or maximum number of promotions per campus?
5. Could a different mathematical approach be used to solve this problem?

**Tip:** Always check the total number of promotions after rounding to ensure it matches the original total available!

This year, 10 faculty members are to receive promotions at a community college with three campuses. The number of promotions will be apportioned according to the number of full-time faculty members at each campus.

Learn how to allocate 10 promotions proportionally among faculty members at three different campuses. The solution involves proportional allocation concepts and basic arithmetic calculations, making it suitable for students in Grades 8-10.

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