GED Mathematical Reasoning TestAlgebraic Problem Solving with Expressions and EquationsMedium
A small business sells handmade jewelry. The cost C (in dollars) to produce 'x' pieces of jewelry is given by the function C(x) = 10x + 50. The revenue R (in dollars) from selling 'x' pieces of jewelry is given by R(x) = 25x. How many pieces of jewelry must the business sell to break even?
- A10 pieces
- B20 pieces
- C3 pieces
- D5 pieces
Show answer & explanationAnswer & explanation
Correct answer: A. 10 pieces
To break even, the cost must equal the revenue (C(x) = R(x)). Set the two equations equal: 10x + 150 = 25x. Subtract 10x from both sides: 150 = 15x. Divide by 15: x = 150 / 15 = 10. So, the business must sell 10 pieces of jewelry to break even.
Why the other options are wrong
- B. This would result in a profit (C(20)=350, R(20)=500).
- C. This would result in a significant loss (C(3)=180, R(3)=75).
- D. This would result in a loss (C(5)=200, R(5)=125).
Break-Even Point
The point at which total cost and total revenue are equal, meaning there is no net loss or gain. It is found by setting the cost function equal to the revenue function.
- Cost = Revenue.
- Profit = 0.
- Found by solving a linear equation or system.
Memory trick: Cost Meets Revenue: Find where expenses just equal income!