7
algebra

A carbon offset program requires companies to reduce emissions to at most 500 tons per year. If a company currently emits 680 tons, which inequality represents the minimum reduction rr needed?

A

r≥180r \geq 180

B

r≤180r \leq 180

C

680−r≥500680 - r \geq 500

D

r≥500r \geq 500

Correct Answer: A

Choice A is the correct answer. Environmental constraint problems require setting up inequalities based on targets.

  1. Current situation: 680 tons currently
  2. Target: After reduction, must be ≤500\leq 500 tons
  3. Set up: 680−r≤500680 - r \leq 500 (current minus reduction)
  4. Solve: Subtract 680: −r≤−180-r \leq -180, then divide by -1: r≥180r \geq 180

?�� Strategic Tip: "Minimum reduction" means the reduction must be at least that amount, translating to ≥\geq.

Choice B is incorrect becauser≤180r \leq 180 represents a maximum reduction, not minimum. Choice C is incorrect because while this is a valid intermediate step, it's not solved for rr, and the question asks for minimum reduction, not the resulting emissions. Choice D is incorrect because it suggests reducing by at least 500 tons, which would result in 180 tons or less, overshooting the target.

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Linear Functions Set 64