8

Set 14: Linear Inequalities (Advanced)

Explanation

Answer: A

A concert hall has 500 seats. Tickets are $20 (regular) and $50 (VIP). Goal: at least $15,000 revenue. Which system models this?

A.

r+v≤500,20r+50v≥15000,r≥0,v≥0r + v \leq 500, 20r + 50v \geq 15000, r \geq 0, v \geq 0

✓ Correct
B.

r+v≥500,20r+50v≥15000,r≥0,v≥0r + v \geq 500, 20r + 50v \geq 15000, r \geq 0, v \geq 0

C.

r+v≤500,20r+50v≤15000,r≥0,v≥0r + v \leq 500, 20r + 50v \leq 15000, r \geq 0, v \geq 0

D.

r+v≤15000,20r+50v≤500,r≥0,v≥0r + v \leq 15000, 20r + 50v \leq 500, r \geq 0, v \geq 0

Detailed Explanation

Choice A is correct. Choice A is the correct answer. Constraints on quantity and revenue. 1. Seats: Total tickets cannot exceed capacity →r+v≤500\rightarrow r + v \leq 500 2. Revenue: Money must be at least 15000 →20r+50v≥15000\rightarrow 20 r + 50 v \geq 15000 Strategic Tip: Capacity is usually ≤\leq, Revenue goals are usually ≥\geq. Choice B is incorrect because it implies they must sell more than capacity. Choice C is incorrect because it implies revenue must be less than goal. Choice D is incorrect because it swaps quantity and money.

Key Steps:

•

The correct answer is r+v≤500,20r+50v≥15000,r≥0,v≥0r + v \leq 500, 20r + 50v \geq 15000, r \geq 0, v \geq 0

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.
← PreviousNext →

🎯 Keep Practicing!

Master all sections for your best SAT score

📚Reading & Writing→📖Vocabulary→