At her hot dog stand, Juile sells hot dogs for $2 each Purchasing hot dogs and other supplies costs $200 per month. The solution of which of the following inequalities models the numbers of hot dogs, h, Julie can sell per month and make a profit?

Options

A. `h - 200 gt 0`
B. `h - 200 lt 0`
C. `h + 200 gt 0`
D. `2h - 200 gt 0`

Answer

To determine the number of hot dogs, \( h \), that Julie can sell per month to make a profit, we need to set up an inequality based on her selling price and costs.

### Step-by-Step Solution:

1. **Identify the Selling Price and Costs:**
- Julie sells each hot dog for $2.
- The total cost for purchasing hot dogs and other supplies is $200 per month.

2. **Define the Total Selling Price:**
- If Julie sells \( h \) hot dogs, the total selling price (SP) can be calculated as:
\[ SP = 2h \]

3. **Set Up the Profit Condition:**
- To make a profit, the total selling price must be greater than the total costs. Thus, we need:
\[ SP > \text{Cost} \]
- Substituting the values we have:
\[ 2h > 200 \]

4. **Rearranging the Inequality:**
- To isolate \( h \), we divide both sides of the inequality by 2:
\[ h > 100 \]

5. **Formulate the Inequality:**
- The inequality \( 2h - 200 > 0 \) can also be derived from the previous step:
\[ 2h - 200 > 0 \]
- This indicates that the total selling price minus the total cost must be greater than zero for Julie to make a profit.

6. **Conclusion:**
- The correct inequality that models the number of hot dogs Julie can sell to make a profit is:
\[ 2h - 200 > 0 \]

### Answer:
The correct option is D: \( 2h - 200 > 0 \).