7
advanced-math

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

B

3 inches

C

4 inches

D

1 inch

Correct Answer: A

Choice A is the correct answer.

  1. Setup: Let width be ww. Total dimensions: (8+2w)(8+2w) and (10+2w)(10+2w).
  2. Equation: (8+2w)(10+2w)=168(8+2w)(10+2w) = 168.
  3. Expand: 80+16w+20w+4w2=168⇒4w2+36w−88=080 + 16w + 20w + 4w^2 = 168 \Rightarrow 4w^2 + 36w - 88 = 0.
  4. Simplify: Divide by 4: w2+9w−22=0w^2 + 9w - 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.

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