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Math Help - Word problem that looks so simple!

  1. #1
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    Word problem that looks so simple!

    Hello!
    Here is the word problem:
    Three pails and 6 baskets contain 576 eggs. All the pails contain 1/3 as many eggs as all the baskets. How many eggs are there in each pail? In each basket?

    I tried to figure this one out, but the answers don't fit. I am so horrible at word problems! Could someone explain how to solve this type of problem? I would be most appreciative.
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  2. #2
    Bar0n janvdl's Avatar
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    Quote Originally Posted by jesuslover View Post
    Hello!
    Here is the word problem:
    Three pails and 6 baskets contain 576 eggs. All the pails contain 1/3 as many eggs as all the baskets. How many eggs are there in each pail? In each basket?

    I tried to figure this one out, but the answers don't fit. I am so horrible at word problems! Could someone explain how to solve this type of problem? I would be most appreciative.
    A single basket contains x eggs.
    6 baskets contain 6x eggs.

    All 3 pails contain a third the number of eggs as all the baskets.
    All 3 pails together contain \left( \frac{1}{3} \times 6x \right) = 2x eggs.

    So each pail contains \frac{2}{3}x eggs.

    Adding it all up we find we have 8x eggs.

    8x = 576
    x = 72

    Therefore each basket contains 72 eggs and each pail contains 48 eggs.
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  3. #3
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    So...(1/3)(6x) + 6x=576
    2x + 6x=576
    8x=576
    x=72
    72 eggs per basket
    72(6)=432
    432/3=144
    144/3=48
    48 eggs per pail
    I see now! Thank-you! I remember getting 48 before, but, lol, not the 72. That was a big help! Thanks again!
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  4. #4
    Bar0n janvdl's Avatar
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    Quote Originally Posted by jesuslover View Post
    I see now! Thank-you! I remember getting 48 before, but, lol, not the 72. That was a big help! Thanks again!
    You are welcome.
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  5. #5
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    Hello, Jesuslover!

    Another approach . . .


    Three pails and 6 baskets contain 576 eggs.
    All the pails contain 1/3 as many eggs as all the baskets.
    How many eggs are there in each pail? In each basket?
    \text{Let: }\;\begin{array}{ccc}P & = & \text{no. eggs in a pail} \\ B &=& \text{no. eggs in a basket} \end{array}

    Then: . \begin{array}{ccc} 3P &=& \text{total no. of eggs in pails} \\ 6B &=& \text{total no. of eggs in baskets} \end{array}

    We are told that: . 3P \:=\:\frac{1}{3}(6B)\quad\Rightarrow\quad 3P \:=\:2B

    . . .and that: . 3P + 6B \:=\:576


    Solve the system of equations.

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