PSAT Math Multiple-Choice Question 179: Answer and Explanation

Question: 179

A business's "break-even point" is the point at which revenue (sales) equals expenses. When a company breaks even, no profit is being made, but the company is not losing any money either. Suppose a manufacturer buys materials for producing a particular item at a cost of $4.85 per unit and has fixed monthly expenses of $11,625 related to this item. The manufacturer sells this particular item to several retailers for $9.50 per unit. How many units must the manufacturer sell per month to reach the break-even point for this item?

• A. 810
• B. 1,225
• C. 2,100
• D. 2,500

Correct Answer: D

Explanation:

D

Difficulty: Medium

Category: Heart of Algebra/Linear Equations

Getting to the Answer: Assign a variable to the unknown and then create an equation that represents the scenario. Let n be the number of units the manufacturer sells in a month. Sales must equal expenses for the manufacturer to break even (sales = expenses). The sales are equal to the selling price ($9.50) times the number of units sold (n), so write 9.5 n on one side of the equal sign. The monthly expenses are the fixed expenses ($11,625) plus the amount paid for the materials needed to produce one unit ($4.85) times the number of units (n), so write 11,625 + 4.85 n on the other side of the equal sign. Then, solve for n:

Choice (D) is correct.