GED Mathematical Reasoning TestAlgebraic Problem Solving with Expressions and EquationsMedium
A small business produces custom-made candles. The monthly cost (C) in dollars for producing 'x' candles is given by C(x) = 2.50x + 500. The revenue (R) in dollars from selling 'x' candles is given by R(x) = 7.50x. How many candles must the business sell to break even?
- A100 candles
- B200 candles
- C50 candles
- D500 candles
Show answer & explanationAnswer & explanation
Correct answer: A. 100 candles
To break even, revenue must equal cost: R(x) = C(x). So, 7.50x = 2.50x + 500. Subtract 2.50x from both sides: 5.00x = 500. Divide by 5.00: x = 100 candles.
Why the other options are wrong
- B. Incorrect calculation.
- C. Incorrect calculation.
- D. This is the fixed cost, not the number of candles to break even.
Break-Even Point (Linear Functions)
The point where total cost equals total revenue, resulting in zero profit. For linear functions, it's found by setting the cost function equal to the revenue function and solving for the quantity.
- Break-even occurs when Cost = Revenue.
- Set C(x) = R(x) and solve for x (the quantity).
- The fixed costs are covered, and there is no profit or loss.
Memory trick: Cost equals Revenue, then you're even!