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Let's break down the problem step-by-step and solve it.

### Given information:
1. Malcolm charges $5.50 per cup of lemonade, and he sells $ c $ cups.
2. He deducts $50 from his profit for supplies.
3. His total weekly profit is greater than $456.

### We can set up the equation for his total profit:
The profit from selling $ c $ cups of lemonade is:
\[
\text{Revenue} = 5.50c
\]
Then, deducting $50 for supplies:
\[
\text{Profit} = 5.50c - 50
\]
We are told that this profit is greater than $456, so:
\[
5.50c - 50 > 456
\]

### Solving the inequality:
1. Add 50 to both sides:
\[
5.50c > 506
\]
2. Divide both sides by 5.50:
\[
c > \frac{506}{5.50}
\]
Now, let's calculate $ \frac{506}{5.50} $.After solving, we get $ c > 92 $.

This means Malcolm must have sold **more than 92 cups** of lemonade to make a profit greater than $456.

Would you like further details or have any other questions?

Here are some related questions:
1. How would Malcolm's profit change if he sold fewer cups of lemonade?
2. What happens to the profit if the price per cup increases by $1?
3. How many cups would he need to sell if the supply cost increased to $75?
4. If Malcolm set a new target of $600 in profit, how many cups would he need to sell?
5. What if Malcolm offered a discount and sold each cup for $4.50 instead?

**Tip**: Always make sure to subtract fixed costs like supplies before calculating net profit.

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 more than $456 in profits this week, how many cups of lemonade did he sell?

Learn how to solve an inequality to determine how many cups of lemonade Malcolm sold to achieve a profit greater than $456. This problem involves algebraic concepts like inequalities and solving for a variable in a linear equation. Suitable for students in Grades 7-9.

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