SAT Math Multiple Choice Question 822: Answer and Explanation

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Question: 822

12.

The federal interstate weight limit for a particular four-axle transfer truck is 18,000pounds per axle. The cab (front) of the truck weighs 11,000 pounds, and the trailerof the truck, when empty, weighs 7,000 pounds. The inequality above represents thelegally permissible weight range for this truck when travelling on an interstate.What does the value 18,000 represent in the inequality?

  • A. The weight of the truck when fully loaded
  • B. The weight of the truck when the trailer is empty
  • C. The maximum weight allowed per axle
  • D. The maximum weight of the cargo being transported

Correct Answer: B

Explanation:

B

Difficulty: Medium

Category: Heart of Algebra / Inequalities

Strategic Advice: When determining the meaning of a particular number, variable, or expression that represents a real-world scenario, read the question very carefully. Here, the maximum weight per axle is 18,000 pounds, but that doesn't necessarily mean that the 18,000 in the inequality represents the same thing.

Getting to the Answer: Try writing an inequality in words to represent the scenario: The weight of the truck (cab and trailer together) plus the weight of the cargo (which varies) must be less than or equal to the maximum weight allowed per axle times the number of axles. Now, translate from English into math: (11,000 + 7,000) + x ≤ 18,000 × 4, or 18,000 + x ≤ 72,000. This means the 18,000 represents the weight of the truck before any cargo is loaded, or in other words, when the trailer is empty, which is (B).

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