Malcolm has a lemonade business called Tropical Treats.

• Malcolm charges $5.50 for each cup of lemonade, c, that he sells.
• He deducts $50 from his profit to account for supplies.
• Malcolm is interested in his weekly profits.

If Malcolm made at least $456 in profits at the of end this week, what is minimum number of cups of lemonade he sold?

We are tasked with finding the minimum number of cups of lemonade Malcolm sold in a week, given that his profit is at least $456, and he deducts $50 from his total profit to account for supplies.

### Step 1: Write the profit equation

Let:
- $ c $ be the number of cups of lemonade Malcolm sells.
- The price of each cup of lemonade is $5.50.

The profit Malcolm earns from selling $ c $ cups of lemonade (before deducting the cost of supplies) is:

\[
\text{Total sales} = 5.50c
\]

He deducts $50 for supplies from this amount, so his net profit equation is:

\[
\text{Net profit} = 5.50c - 50
\]

### Step 2: Set up the inequality

Since we know his weekly profit is at least $456, we can set up the following inequality:

\[
5.50c - 50 \geq 456
\]

### Step 3: Solve for $ c $

First, add 50 to both sides of the inequality:

\[
5.50c \geq 506
\]

Next, divide both sides by 5.50 to isolate $ c $:

\[
c \geq \frac{506}{5.50} = 92
\]

### Step 4: Conclusion

Malcolm must sell **at least 92 cups** of lemonade to meet his goal of a profit of at least $456.

Would you like more details on the steps or have any questions?

---

Here are 5 related questions:
1. What would be Malcolm's profit if he sold exactly 100 cups?
2. How would Malcolm's profit change if the price per cup increased to $6?
3. What is the minimum profit Malcolm could make if he sold 50 cups?
4. How many cups would Malcolm need to sell to make a profit of $600?
5. If Malcolm reduces his supply cost to $30, how does that impact the required number of cups sold for $456 profit?

**Tip:** Always check for rounding errors when working with decimals to ensure accuracy!

Malcolm has a lemonade business called Tropical Treats. Malcolm charges $5.50 for each cup of lemonade, c, that he sells. He deducts $50 from his profit to account for supplies. Malcolm is interested in his weekly profits. If Malcolm made at least $456 in profits at the end of this week, what is the minimum number of cups of lemonade he sold?

Find out how to calculate the minimum number of cups Malcolm must sell to achieve a weekly profit of at least $456 in his lemonade business. This problem covers algebraic concepts like inequalities and linear equations, suitable for students in Grades 7-9.

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