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Thread: Word problem

  1. #1
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    Word problem

    Please help with this word problem
    A box (rectangular/no top) is to have a volume of 64 cubic meters. The width of the base must be 4 meter to insert into a vault. When trimmed to size, material cost $12.00 per square meter for the base and $6.00 per square meter for the sides. What is the cost for the box?

    Please help!
    Thanks
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by roseh
    Please help with this word problem
    A box (rectangular/no top) is to have a volume of 64 cubic meters. The width of the base must be 4 meter to insert into a vault. When trimmed to size, material cost $12.00 per square meter for the base and $6.00 per square meter for the sides. What is the cost for the box?

    Please help!
    Thanks
    The width of the box is $\displaystyle 4$m, let the height be $\displaystyle h$m and the depth be $\displaystyle d$m.

    Then to make the volume $\displaystyle 64 m^3$ we have:

    $\displaystyle
    4\times h \times d=64
    $

    The area of the base is $\displaystyle 4\times d$ so the cost of the base is:

    $\displaystyle
    6 \times 4 \times d
    $

    The area of the sides id $\displaystyle (2 \times 4+2\times d)\times h$, so the cost of the sides is:

    $\displaystyle
    12 \times (2 \times 4+2\times d)\times h =96+24\times d \times h
    $

    but $\displaystyle 4\times h \times d=64 $, so the cost of the sides is:

    $\displaystyle
    96+24\times d \times h=96+6 \times (4 \times d \times h)=\$ 480
    $.

    Hence the total cost is:

    $\displaystyle
    480+24 \times d
    $ dollars

    and you don't know enough to simplify further.

    RonL
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