SAT Math Multiple Choice Question 343: Answer and Explanation

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Question: 343

13. 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

Strategic Advice: Try not to get too bogged down in the context. Assign a variable to the unknown, and then create an equation that represents the scenario.

Getting to the Answer: 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 9.5n 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 (x), so write 11,625 + 4.85x on the other side of the equal sign. Then, solve for x.

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