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Math Help - Write A Function

  1. #1
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    Write A Function

    Marta gets paid only when she finishes tiling a room. the first rooms that Marta tiled were all square rooms. Write a function S such that S(n) expresses the number of tiles required to cover a square floor that has n tiles along the edge of the room. Include the domain of the function in your answer.

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  2. #2
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    If there are n tiles along the entire edge of a square room, then let x be the number of tiles along one width of the room. Thus there must be x-2 tiles along one length of the room (We can't count a tile twice; draw a picture to help visualize this).

    Thus we can obtain an expression for n:
    n = 2x+2(x-2) = 2(x+x-2)=4(x-1).

    Solving for x in terms of n:
    x=\dfrac{n}{4}+1.

    Since x denotes the number of tiles along the width of the room, and the room is a square, the total number of tiles is x^{2}. Hence
    x^{2} = \left(\dfrac{n}{4}+1\right)^{2}.

    Therefore, S(n) = \left(\dfrac{n}{4}+1\right)^{2}.

    Since the smallest square room possible for n tiles along the edge is n = 4 (a 2x2 tile room), then the domain of S(n) is all n \ge 4.
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  3. #3
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    ok....

    Quote Originally Posted by Pn0yS0ld13r View Post
    If there are n tiles along the entire edge of a square room, then let x be the number of tiles along one width of the room. Thus there must be x-2 tiles along one length of the room (We can't count a tile twice; draw a picture to help visualize this).

    Thus we can obtain an expression for n:
    n = 2x+2(x-2) = 2(x+x-2)=4(x-1).

    Solving for x in terms of n:
    x=\dfrac{n}{4}+1.

    Since x denotes the number of tiles along the width of the room, and the room is a square, the total number of tiles is x^{2}. Hence
    x^{2} = \left(\dfrac{n}{4}+1\right)^{2}.

    Therefore, S(n) = \left(\dfrac{n}{4}+1\right)^{2}.

    Since the smallest square room possible for n tiles along the edge is n = 4 (a 2x2 tile room), then the domain of S(n) is all n \ge 4.
    Thank you. I would have never been able to come up with the correct function.
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  4. #4
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    Quote Originally Posted by deleted post
    S(n) = the number of tiles required.
    The room is square (and assuming the tiles are square):
    n = length of room in tile lengths = width of room in tile lengths
    So Area of floor = n x n = n^2
    So S(n) = n^2
    The minimum length of the room must be 1 tile length for it to be tillable, so domain: n>=1. Sorry for the edit.
    This is my first answer I hope it's right and I hope it makes sense.
    All the best.
    You have misunderstood the question I think (although there is some ambiguity in the wording of the question). I think n is the total number of tiles around all sides of the room, not the number of tiles along one side. The correct answer is given in post #2.
    Last edited by mr fantastic; January 2nd 2009 at 03:42 AM. Reason: The username of the quoted poster was a URL to a commercial website and so has been deleted.
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  5. #5
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    Smile Thanks...

    I want to thank all who took time to help with this question.

    Happy New Year!
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