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Set 8: Linear Inequalities (Advanced)

Explanation

Answer: A

A salesperson earns a base salary of $2000plusa102000plus a 10% commission on sales. To earn at least \5000 this month, what must their sales $$s$ be?

A.

s30,000s \geq 30,000

✓ Correct
B.

s3,000s \geq 3,000

C.

s70,000s \geq 70,000

D.

s50,000s \geq 50,000

Detailed Explanation

Choice A is correct. Choice A is the correct answer. Set up the income inequality. 1. Income Equation: Base + Commission = 2000+0.10s2000+ 0.10 s 2. Target: At least $5000$$\rightarrow \geq 5000 3. Inequality: 2000+0.10s50002000+ 0.10 s \geq 5000 4. Subtract 2000: 0.10s30000.10s \geq 3000 5. Divide by 0.10: s30,000s \geq 30,000 Strategic Tip: Dividing by 0.10 is the same as multiplying by 10. Choice B is incorrect because it likely divides by 1 instead of 0.10. Choice C is incorrect because it adds 2000 to 5000 instead of subtracting. Choice D is incorrect because it ignores the base salary.

Key Steps:

The correct answer is s30,000s \geq 30,000

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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