The graph below shows the number of notepads that each location of a business used last year. The number of departments per location are presented in the table below. Four of the locations used the same number of notepads per department, but the Northwest and Central offices used less notepads per department. The graph shows that the Northwest location used the same number of notepads as the  Southeast location overall. If the Northwest location used less notepads per department, which of the following could be the number of departments for the Northwest location?

To solve this, we can follow these steps logically:

### Key Information:
- Four locations used the same number of notepads **per department**.
- The **Northwest** and **Central** locations used fewer notepads per department.
- The **Northwest** location used the same total number of notepads as the **Southeast** location.
- We need to determine a possible number of departments for the Northwest location, which used fewer notepads per department.

### Step-by-Step Approach:

1. **Let’s Define Variables:**
   - Let \( N_{NW} \) be the number of notepads used by the Northwest location.
   - Let \( D_{NW} \) be the number of departments in the Northwest location.
   - Let \( N_{SE} \) be the number of notepads used by the Southeast location.
   - Let \( D_{SE} \) be the number of departments in the Southeast location.

   From the problem, we know:
   \[
   N_{NW} = N_{SE}
   \]
   (The Northwest and Southeast locations used the same total number of notepads.)

2. **Same Number of Notepads:**
   Since the Northwest used fewer notepads per department than the Southeast, it must have more departments to match the total number of notepads. This means:
   \[
   \frac{N_{NW}}{D_{NW}} < \frac{N_{SE}}{D_{SE}}
   \]
   Therefore, \( D_{NW} > D_{SE} \).

3. **Conclusion:**
   The number of departments in the Northwest location must be larger than the number of departments in the Southeast location.

### Now, let’s assume you are given a list of possible department numbers. The correct choice would be any number greater than the number of departments in the Southeast location.

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Do you have any specific numbers from the table or choices you can provide? It would help in determining the exact number of departments for the Northwest location.

### Follow-up questions:
1. How many departments are there in the Southeast location?
2. How many departments are listed for each location in the table?
3. What are the possible department numbers for the Northwest location?
4. How many notepads did each location use in total?
5. What were the notepad usage rates for the Central and Southeast locations?

### Tip:
To solve these types of problems, always look for proportional relationships (e.g., total items vs. per-department usage).

The graph below shows the number of notepads that each location of a business used last year. The number of departments per location are presented in the table below. Four of the locations used the same number of notepads per department, but the Northwest and Central offices used less notepads per department. The graph shows that the Northwest location used the same number of notepads as the Southeast location overall. If the Northwest location used less notepads per department, which of the following could be the number of departments for the Northwest location?

Analyze notepad usage at different business locations to determine the number of departments in the Northwest office. Understand proportional relationships and solve inequalities to identify the correct department count.

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