2

Set 6: Quadratic Equations (Advanced)

Explanation

Answer: A

A theater sells tickets for 30. For every $$1price increase, they lose 10 customers. They currently have 500 customers. Revenue $$R(x) = (30 + x)(500 - 10x). What price increase xx maximizes revenue?

A.

$10

✓ Correct
B.

$20

C.

$5

D.

$15

Detailed Explanation

Choice A is correct. Choice A is the correct answer. 1. Find Roots: 30+x=0⇒x=−3030+ x = 0 \Rightarrow x = -30. 500−10x=0⇒x=50500- 10 x = 0 \Rightarrow x = 50. 2. Find Vertex: The vertex is exactly halfway between the roots. 3. Midpoint: (−30+50)/2=20/2=10(-30 + 50) / 2 = 20 / 2 = 10. 4. So a price increase of $10 maximizes revenue. Choice B is incorrect. Choice C is incorrect. Choice D is incorrect.

Key Steps:

•

The correct answer is $10

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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