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Math Help - [SOLVED] Algebra word problem help

  1. #1
    antiflux
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    [SOLVED] Algebra word problem help

    Help I can't figure out an equation to solve this word problem..

    A cement walk 1 meter wide is constructed around a circular flower bed. The Area of the flower bed is 9/16 of the entire area (flower bed and walk). What is the diameter of the flower bed?
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  2. #2
    Junior Member Singular's Avatar
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    let x = radius of flowerbed
    The entire area = \pi .\left( {x + 1} \right)^2
    If you know the entire area you will know x and the diameter will be 2x
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  3. #3
    Junior Member AlvinCY's Avatar
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    Quote Originally Posted by antiflux View Post
    Help I can't figure out an equation to solve this word problem..

    A cement walk 1 meter wide is constructed around a circular flower bed. The Area of the flower bed is 9/16 of the entire area (flower bed and walk). What is the diameter of the flower bed?
    let the diameter of the flower bed be x metres, the area of the flower bed is therefore (\pi x^2) sq.m, therefore the area of the entire construction (flower bed and walk) = [\pi (x + 1)^2] sq.m

    you know that \pi x^2 is 9/16 of \pi (x + 1)^2

    Therefore x^2 = \frac{9}{16}(x + 1)^2
    16x^2 = 9x^2 + 18x + 9
    7x^2 - 18x - 9 = 0, splitting the middle term;
    7x^2 - 21x + 3x - 9 = 0
    7x(x - 3) + 3(x - 3) = 0
    (x - 3)(7x + 3) = 0

    Therefore x = 3 or x = -\frac{3}{7}

    But we said the diameter of the flower bed is x, therefore x = 3 and x \not = -\frac{3}{7} as x is a length, which must be positive.
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