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### Problem Summary:
- Malcolm has a lemonade business called **Tropical Treats**.
- He charges **$5.50** per cup of lemonade.
- He incurs a fixed cost of **$50** to account for supplies.
- His profit is determined as the revenue minus the costs.
  
### Objective:
Determine the minimum number of cups Malcolm needs to sell to make **at least $45.50** in profits.

### Steps to Solve:

1. **Revenue Calculation**:
   Let $ x $ be the number of cups sold.
   - Revenue from selling $ x $ cups of lemonade is given by:
     \[
     \text{Revenue} = 5.50 \times x
     \]

2. **Profit Calculation**:
   - Profit is calculated as:
     \[
     \text{Profit} = \text{Revenue} - \text{Costs}
     \]
   - Here, the profit equation is:
     \[
     \text{Profit} = 5.50x - 50
     \]
   - We are given that the profit must be at least $45.50:
     \[
     5.50x - 50 \geq 45.50
     \]

3. **Solve the Inequality**:
   \[
   5.50x - 50 \geq 45.50
   \]
   \[
   5.50x \geq 95.50
   \]
   \[
   x \geq \frac{95.50}{5.50}
   \]
   \[
   x \geq 17.36
   \]
   Since $ x $ represents the number of cups, which must be a whole number, Malcolm must sell at least **18** cups of lemonade to make at least $45.50 in profits.

### Conclusion:
Malcolm needs to sell **18** cups of lemonade.

---

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### Related Questions:
1. How would the result change if the cost increased to $60?
2. What would be the minimum number of cups sold if Malcolm reduced the price to $4.50 per cup?
3. How much profit would Malcolm make if he sold exactly 20 cups?
4. What if Malcolm had a different fixed cost for supplies? How would that affect the break-even point?
5. Can you create a graph of profit versus the number of cups sold?

### Tip:
When solving inequalities involving money or quantities in business contexts, remember to round up to the nearest whole number where appropriate.

Malcolm has a lemonade business called Tropical Treats. He charges $5.50 for each cup of lemonade, C. that he sells. He deducts $50 from his profits to account for supplies. Malcolm is interested in his weekly profits. If Malcolm made at least $45.50 in profits at the end of this week, what is the minimum number of cups of lemonade he sold?

Determine the minimum number of cups Malcolm needs to sell to make at least $45.50 in profits. This problem involves solving an inequality with basic algebraic concepts and is suitable for students in Grades 7-9.

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