SAT Math Multiple Choice Question 571: Answer and Explanation

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Question: 571

1. A home improvement store that sells carpeting charges a flat installation fee and a certain amount per square foot of carpet ordered. If the total cost for f square feet of carpet is given by the function C(f ) = 3.29f + 199, then the value 3.29 best represents which of the following?

  • A. The installation fee
  • B. The cost of one square foot of carpet
  • C. The number of square feet of carpet ordered
  • D. The total cost not including the installation fee

Correct Answer: B

Explanation:

B

Difficulty: Easy

Category: Heart of Algebra / Linear Equations

Strategic Advice: A flat fee does not depend on the variable and is, therefore, a constant. A unit rate, however, is always multiplied by the independent variable.

Getting to the Answer: The total cost consists of a flat installation fee and a price per square foot. The installation fee is a one-time fee that does not depend on the number of feet ordered and therefore should not be multiplied by f. This means that 199 is the installation fee. The other expression in the equation, 3.29f, represents the cost per square foot (the unit price) times the number of feet, f. Hence, 3.29 must represent the cost of one square foot of carpet.

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