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Thread: [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 = $\displaystyle \pi .\left( {x + 1} \right)^2$
    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 $\displaystyle x$ metres, the area of the flower bed is therefore $\displaystyle (\pi x^2) sq.m$, therefore the area of the entire construction (flower bed and walk) = $\displaystyle [\pi (x + 1)^2] sq.m$

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

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

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

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