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24 September, 05:47

A 7 by 10 inch mirror was put in a frame and hung on the wall. The mirror and frame together cover an area of 130 inches squared. How wide is the frame?

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  1. 24 September, 07:04
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    Answer: the width of the frame is 3 inches.

    Step-by-step explanation:

    Let x represent the width of the frame.

    If the length of the mirror is 10 inches, the length of the mirror and the frame would be (x + 10) inches

    If the width of the mirror is 7 inches, the width of the mirror and the frame would be (x + 7) inches

    The mirror and frame together cover an area of 130 inches squared. This means that

    (x + 10) (x + 7) = 130

    x² + 7x + 10x + 70 = 130

    x² + 17x + 70 - 130 = 0

    x² + 17x - 60 = 0

    x² + 20x - 3x - 60 = 0

    x (x + 20) - 3 (x + 20) = 0

    x - 3 = 0 or x + 20 = 0

    x = 3 or x = - 20

    Since the width cannot be negative, then x = 3
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