SAT Math Multiple Choice Question 370: Answer and Explanation
10. An occupational health organization published a study showing an increase in the number of injuries that resulted from elderly people falling in the bathtub. In response to this increase, a medical supply company decided to drop its price on bathtub lifts from $450 to $375, hoping to still break even on the lifts. The company breaks even when its total revenue (income from selling n bathtub lifts) is equal to its total cost of producing the lifts. If the cost C, in dollars, of producing the lifts is C = 225n + 3,150, how many more of the lifts does the company need to sell at the new price to break even than at the old price?
- A. 7
- B. 12
- C. 14
- D. 21
Correct Answer: A
Category: Heart of Algebra / Systems of Linear Equations
Strategic Advice: Questions about breaking even usually involve creating a system of equations (one for cost and one for revenue), setting the equations equal to each other, and solving for the variable.
Getting to the Answer: Create a system of equations at each price point using n for the number of bathtub lifts. Then solve each system. Note that the cost equation will be the same for both systems, and it is already given to you in the question.
At the old price, the company needed to sell 14 lifts to break even. At the new price, it needs to sell 21 lifts, so it needs to sell 21 - 14 = 7 more lifts at the new price to break even.