GED Mathematical Reasoning TestAlgebraic Problem Solving with Expressions and EquationsMedium
A financial analyst is modeling the profit (P) of a new product based on its selling price (s) in dollars. The profit is given by the equation P = -2s² + 60s - 350. At what selling price(s) will the company break even (i.e., profit is zero)?
- A$20 and $40
- B$5 and $25
- C$10 and $35
- D$15 and $30
Show answer & explanationAnswer & explanation
Correct answer: C. $10 and $35
To find the break-even points, set the profit (P) to zero and solve the quadratic equation -2s² + 60s - 350 = 0. Divide by -2 to simplify, then factor or use the quadratic formula.
Why the other options are wrong
- A. These values do not satisfy the equation when substituted.
- B. These values do not satisfy the equation when substituted.
- D. These values do not satisfy the equation when substituted.
Quadratic Equation Break-Even
The break-even point for a quadratic profit function is found by setting the profit (P) to zero and solving the resulting quadratic equation for the variable (e.g., selling price or quantity).
- Represents the points where total revenue equals total cost.
- Often yields two solutions for a quadratic equation.
- Solutions can be found by factoring, completing the square, or using the quadratic formula.
Memory trick: Zero profit means solving the quadratic puzzle.