Digital SATMath: AlgebraEasy
A small business sells artisanal candles. The cost to produce x candles is given by C(x) = 2.5x + 50. The revenue from selling x candles is R(x) = 7.5x. How many candles must the business sell to break even?
- A5 candles
- B20 candles
- C15 candles
- D10 candles
Show answer & explanationAnswer & explanation
Correct answer: D. 10 candles
To break even, the cost must equal the revenue (C(x) = R(x)). So, set the two expressions equal to each other: 2.5x + 50 = 7.5x. Subtract 2.5x from both sides: 50 = 5x. Divide by 5: x = 10. The business must sell 10 candles to break even.
Why the other options are wrong
- A. Incorrect. At 5 candles, Revenue is 37.5, Cost is 62.5, resulting in a loss.
- B. Incorrect. At 20 candles, Revenue is 150, Cost is 100, resulting in a profit.
- C. Incorrect. At 15 candles, Revenue is 112.5, Cost is 87.5, resulting in a profit.
Break-Even Point
The point at which total cost and total revenue are equal, meaning there is no net loss or gain.
- Calculated by setting Cost Function C(x) equal to Revenue Function R(x).
- Represents the minimum number of units that must be sold to cover all expenses.
- Below this point, the business incurs a loss; above it, the business makes a profit.
Memory trick: Cost, Revenue, Profit: The business trio, where break-even balances the two.