10

Set 2: Quadratic Equations (Intermediate)

Explanation

Answer: A

A photo is 8x10 inches. A frame of uniform width is placed around it. If the total area is 168 sq inches, what is the width of the frame?

A.

2 inches

✓ Correct
B.

3 inches

C.

4 inches

D.

1 inch

Detailed Explanation

Choice A is correct. Choice A is the correct answer. 1. Setup: Let width be ww. Total dimensions: (8+2w)(8+2 w) and (10+2w)(10+2 w). 2. Equation: (8+2w)(10+2w)=168(8+2 w)(10+2 w) = 168. 3. Expand: 80+16w+20w+4w2=168⇒4w2+36w−88=080+ 16 w + 20 w + 4 w^2 = 168 \Rightarrow 4 w^2 + 36 w - 88 = 0. 4. Simplify: Divide by 4: w2+9w−22=0w^2 + 9 w - 22 = 0. 5. Factor: (w+11)(w−2)=0(w + 11)(w - 2) = 0. 6. Result: w=2w = 2 inches. Choice B is incorrect. Choice C is incorrect. Choice D is incorrect.

Key Steps:

•

The correct answer is 2 inches

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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