The Lemonade Stand Ledger: Using Math to Run a Business
Maria spent $6 on lemons, sugar, and cups. She sold 24 cups of lemonade at $1.50 each. Did she make money, and how much? If you can answer that in your head, you already know the most important math skill in business: figuring out profit. Every business, from a kid's lemonade stand to a billion-dollar company, runs on the same simple equation.
What You'll Learn
- The profit equation: Revenue minus Costs equals Profit - The difference between fixed costs and variable costs - How to calculate a break-even point - How businesses use percentages to price items and calculate discounts
Revenue, Costs, and Profit
Revenue is all the money coming IN from sales. Costs are all the money going OUT to make and sell the product. Profit is what's left over: Profit = Revenue - Costs. Back to Maria: Revenue = 24 cups x $1.50 = $36. Costs = $6. Profit = $36 - $6 = $30. Maria turned a $6 investment into $30, a profit of $30 — that's a 500% return on what she spent.
Fixed Costs vs. Variable Costs
Not all costs behave the same way. A fixed cost stays the same no matter how much you sell — like renting a table for $10 for the day, whether you sell 5 cups or 50. A variable cost changes with how much you produce — each cup of lemonade needs its own lemons and sugar, so that cost grows with every cup sold. Say Maria's fixed cost is a $10 table rental, and her variable cost is $0.25 per cup (ingredients). If she sells 40 cups at $1.50: Revenue = $60. Variable costs = 40 x $0.25 = $10. Total costs = $10 fixed + $10 variable = $20. Profit = $60 - $20 = $40.
The break-even point is how many items you must sell before you stop losing money and start making a profit. With a $10 fixed cost and $1.25 profit per cup ($1.50 price - $0.25 ingredient cost), Maria needs to sell $10 / $1.25 = 8 cups just to cover her rental fee. Cup #9 is her first cup of real profit.
Percentages in Pricing
Businesses use percentages constantly. If a shirt costs a store $8 to make and they want a 50% markup, they add 50% of $8 ($4) to get a selling price of $12. If that shirt later goes on a 25% discount sale, the customer pays $12 - (0.25 x $12) = $12 - $3 = $9 — still $1 more than it cost the store to make, so the business still profits even at a discount.
A snack stand has $15 in fixed costs and earns $0.75 profit per item after variable costs. How many items must it sell to break even?
Why might a business still make a profit even after offering a 25% discount?
Run Your Own Stand on Paper
Design a small business (a stand, a service, or a craft to sell). List: one fixed cost, one variable cost per item, and your selling price per item. Calculate your profit per item, your break-even number of sales, and your total profit if you sell 30 units. Show all four numbers with the math that produced them.
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