PSAT Math Multiple-Choice Question 433: Answer and Explanation

Question: 433

To install fencing, a builder charges $15 per foot for the first 100 feet plus an additional $12 per foot thereafter. If c represents the total cost of a fence installation, in dollars, and x represents the length of the fence in feet, then which of the following functions best describes the cost of a fence that is more than 100 feet long?

• A.
• B.
• C.
• D.

Correct Answer: B

Explanation:

B

Difficulty: Medium

Category: Describing Real-Life Situations with Functions

Getting to the Answer: The cost for the first 100 feet will be $15(100) = $150. This number will be added to the cost for the remainder of the fence. Eliminate (C) and (D), which subtract the 150 instead of adding it.

Now, consider what happens after the first 100 feet. The remaining length of fencing is the total length, x, minus the first 100 feet, or x - 100. Multiply by 12 to find the cost for this section of the fence: 12(x - 100). The complete function, then, is c(x) = 150 + 12(x - 100). This matches (B).