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Math Help - Patio Dimensions

  1. #1
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    Patio Dimensions

    A contractor orders 8 cubic yards of premixed cement, all of which is to be used to pour a rectangular patio that will be 4 inches thick. If the length of the patio is specified to be TWICE the width, what will be the patio dimensions?

    NOTE: 1 cubic yard = 27 cubic feet
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by symmetry View Post
    A contractor orders 8 cubic yards of premixed cement, all of which is to be used to pour a rectangular patio that will be 4 inches thick. If the length of the patio is specified to be TWICE the width, what will be the patio dimensions?

    NOTE: 1 cubic yard = 27 cubic feet
    Let the width of the patio be W (ft), then the volume will be:

    V=W*(2W)*(1/3) cubic ft,

    so:

    (2/3)W^2 = 8*27 cubic ft,

    so:

    W=sqrt(8*27*3/2)=18 ft

    so the patio is 18 by 36 ft.

    RonL
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  3. #3
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    ok

    Below is your answer followed by my reply in brackets.

    Your said:

    Let the width of the patio be W (ft), then the volume will be:

    V=W*(2W)*(1/3) cubic ft,[What part of the question indicated that we are dealing with volume?]

    so:

    (2/3)W^2 = 8*27 cubic ft,

    so:

    W=sqrt(8*27*3/2)=18 ft{Why did you take the square root?]

    so the patio is 18 by 36 ft.
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by symmetry View Post
    Below is your answer followed by my reply in brackets.

    Your said:

    Let the width of the patio be W (ft), then the volume will be:

    V=W*(2W)*(1/3) cubic ft,[What part of the question indicated that we are dealing with volume?]
    We are given the amount of cement ordered in cubic yards, which is a
    volume, and this will be the the volume of the patio when laid.

    so:

    (2/3)W^2 = 8*27 cubic ft,

    so:

    W=sqrt(8*27*3/2)=18 ft{Why did you take the square root?]
    we have from the previous equation:

    (2/3)W^2 = 8*27,

    so:

    W^2=8*27*3/2,

    the term on the left of this is W squared, so to get W we need to take
    square roots, so:

    W=sqrt(8*27*3/2)=18

    so the patio is 18 by 36 ft.
    RonL
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  5. #5
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    ok

    I can see from your reply that it's super important to pay attention to detail in terms of word problems, right? Every word leads to a clue.

    Of course, this does NOT take away the fact that there are word problems that are simply complicated in nature.

    I thank you very much.
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  6. #6
    Grand Panjandrum
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    Quote Originally Posted by symmetry View Post
    I can see from your reply that it's super important to pay attention to detail in terms of word problems, right? Every word leads to a clue.

    Of course, this does NOT take away the fact that there are word problems that are simply complicated in nature.

    I thank you very much.
    You gave to look out for problems with redundant information (information
    not needed to solve the problem, but just there to confuse things)

    RonL
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