3

Set 17: Linear Inequalities

Explanation

Answer: D

A freelance designer charges $80 per hour but pays $15 per hour in software subscriptions. If they work 8 hours and need to net at least $520, which statement is true?

A.

(8015)×8520(80-15) \times 8 \geq 520 is correct

B.

80×815×852080 \times 8 - 15 \times 8 \geq 520 is correct

C.

They will exactly meet their goal

D.

Both A and B are correct

✓ Correct

Detailed Explanation

Choice D is correct. Choice D is the correct answer. Multiple equivalent forms can represent the same constraint. 1. Choice A: Net rate is (8015)=65(80-15)=65 per hour, times 8 hours: 65×8=52065\times 8 = 520 2. Choice B: Total revenue minus total costs: 80(8)15(8)=640120=52080(8) - 15(8) = 640 - 120 = 520 3. Choice C: This is also correct since 520520520\geq 520, but D is more complete 4. Both A and B equal 520, satisfying the 520\geq 520 requirement Strategic Tip: Net earnings equal gross income minus expenses, calculated either as (rate per unit) × (quantity) or total revenue - total costs. Choice alone is incomplete because while true, choice D recognizes both forms are valid. Choice alone is incomplete because while true, choice D recognizes both forms are valid. Choice C is incomplete as the only answer because while they do meet the goal exactly, the question asks which statement is true, making D the best answer.

Key Steps:

The correct answer is Both A and B are correct

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

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