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?

To determine the minimum number of cups of lemonade Malcolm sold to achieve at least $456 in profits, we can set up an equation.

### Step 1: Define the variables
- Let $ c $ be the number of cups of lemonade Malcolm sold.
- Each cup is sold for $5.50.
- Malcolm deducts $50 from his total earnings to account for supplies.

### Step 2: Set up the profit equation
The total earnings from selling $ c $ cups is $ 5.50c $.

After deducting $50 for supplies, the profit is given by:
\[
\text{Profit} = 5.50c - 50
\]

### Step 3: Set up the inequality for profit
We know that Malcolm's profit for the week is at least $456, so we can write the inequality:
\[
5.50c - 50 \geq 456
\]

### Step 4: Solve the inequality for $ c $
First, add 50 to both sides of the inequality:
\[
5.50c \geq 506
\]

Next, divide both sides by 5.50 to solve for $ c $:
\[
c \geq \frac{506}{5.50}
\]
\[
c \geq 92
\]

### Step 5: Conclusion
Malcolm needs to sell at least 92 cups of lemonade to make at least $456 in profit.

Would you like further details or have any questions? 

Here are five related questions that you might find helpful:
1. How would the minimum number of cups change if Malcolm deducted $100 instead of $50 for supplies?
2. If the price per cup increased to $6, how many cups would Malcolm need to sell to make $456 in profit?
3. How much profit would Malcolm make if he sold 100 cups?
4. What would happen to the profit if Malcolm reduced the price to $5 per cup?
5. How can Malcolm increase his profit margin without increasing the price per cup?

**Tip:** When solving inequalities, make sure to isolate the variable by performing operations systematically on both sides of the inequality.

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?

Discover how to calculate the minimum number of lemonade cups Malcolm needs to sell to achieve at least $456 in profit. This problem involves key algebraic concepts such as linear equations and inequalities. Ideal for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation