SAT Math Multiple Choice Question 513: Answer and Explanation

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Question: 513

3. There are very few states in the United States that require public schools to pay sales tax on their purchases. For this reason, many schools pay for student portraits and then the parents reimburse the school. Parents can choose between the basic package for $29.50 and the deluxe package for $44.50. If 182 parents ordered packages and the school's total bill was $6,509, which of the following systems of equations could be used to find the number of parents who ordered a basic package, b, and the number who ordered a deluxe package, d, assuming no parent ordered more than one package?

  • A.
  • B.
  • C.
  • D.

Correct Answer: B



Difficulty: Easy

Category: Heart of Algebra / Systems of Linear Equations

Strategic Advice: Whenever a question gives you information about a total number of items and a total cost of those items, you should write one equation that represents the total number (here, the number of packages) and a second equation that represents the total cost (here, the cost of the portraits).

Getting to the Answer: The number of parents who ordered basic packages plus the number who ordered deluxe packages equals the total number of parents (182), so one equation is b + d = 182. This means you can eliminate A and C. Now write the cost equation: cost per basic package (29.5) times number ordered (b) plus cost per deluxe package (44.5) times number ordered (d) equals the total bill ($6,509). The cost equation is 29.5b + 44.5d = 6,509. Together, these two equations form the system in (B). Don't let D fool you—there are two choices of packages, but this does not impact the total amount of the school's bill.

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