Question

A boy with a lemonade stand sells cups of lemonade for a quarter each. He has bought $ 20 worth of supplies and is able to make 500 cups of lemonade with the supplies. If he has to pay a business tax of 4% for each cup he sells, how many cups will he have to sell in order to break even?

• A. 83.2 cups
• B. 84 cups
• C. 83 cups
• D. It is impossible for him to profit from this business venture.
• E. 92 cups

Hint:

To calculate break-even points, ensure you account for both costs and taxes.

Answer 1

The Correct Option is B

Step 1: Calculate the total cost per cup.
The total cost of supplies is $ 20, and the boy can make 500 cups, so the cost per cup is: \[ \frac{20}{500} = 0.04 \text{ dollars per cup}. \]

Step 2: Calculate the total cost including tax.
Each cup has a 4% tax, so the total cost per cup is: \[ 0.04 + 0.04 \times 0.04 = 0.0416 \text{ dollars per cup}. \]
Step 3: Calculate the number of cups needed to break even.
To break even, the revenue from selling \( x \) cups must equal the total cost of supplies: \[ x \times 0.25 = 20. \] Solving for \( x \): \[ x = \frac{20}{0.25} = 80 \text{ cups}.
\] Thus, the boy must sell 80 cups to break even.