4

Set 3: Linear Inequalities

Explanation

Answer: A

A car rental agency charges $30per day plus \0.15 per mile. If you rent the car for 3 days and have a budget of $150, what is the maximum number of miles $$m$ you can drive?

A.

m400m \leq 400

✓ Correct
B.

m800m \leq 800

C.

m200m \leq 200

D.

m600m \leq 600

Detailed Explanation

Choice A is correct. Choice A is the correct answer. Calculate fixed costs first. 1. Fixed Cost: 3 days ×\times $30/day = $902. Variable Cost: \0.15 per mile (0.15 m$$) 3. Total Cost: $$90+ 0.15 m$$ 4. Inequality: $$90+ 0.15 m \leq 150$$ 5. Subtract 90: $$0.15m \leq 60$$ 6. Divide by 0.15: m \leq 400$ Strategic Tip: 60÷0.15=6000÷15=40060\div 0.15 = 6000 \div 15 = 400. Choice B is incorrect because it might result from dividing 120 by 0.15 (forgetting the 3-day cost). Choice C is incorrect because it might result from dividing 30 by 0.15. Choice D is incorrect because it might result from dividing 90 by 0.15.

Key Steps:

The correct answer is m400m \leq 400

Why others are wrong:
B: Choice B is incorrect and may result from a calculation error.
C: Choice C is incorrect and may result from a calculation error.
D: Choice D is incorrect and may result from a calculation error.

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