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Math Help - balancing scales

  1. #1
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    balancing scales

    Imagine the letters(symbols) below to sit on scales.
    Scale 1 and 2 are perfectly balanced.

    Take D = diamonds H = Heart S = spades.

    How many diamonds are needed to balance scale 3?



    1. D H ........ S S S S


    2. S S D D H ........ H H


    3. H S S ........ ?



    I get the same answer using both logic and algebra, yet it conflicts with the answer I have been given for this.

    Please try!
    Last edited by aquajam; December 17th 2009 at 10:29 PM.
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  2. #2
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    Hello, aquajam!

    Imagine the symbols below to sit on balance scales.

    Scales 1 and 2 are perfectly balanced.


    . . [1]\quad\begin{array}{ccccc}<br />
\diamondsuit\:\heartsuit && \spadesuit\:\spadesuit\:\spadesuit\:\spadesuit\\ \hline<br />
& \Delta  \end{array}


    . . [2]\quad\begin{array}{ccccc}<br />
\spadesuit\:\spadesuit\:\diamondsuit\:\diamondsuit  \:\heartsuit && \heartsuit\:\heartsuit\<br />
 \\ \hline<br />
& \Delta \end{array}


    . . [3]\;\;\begin{array}{ccccc}<br />
\heartsuit\:\spadesuit\:\spadesuit && ?\,\diamondsuit \\ \hline<br />
& \Delta \end{array}


    How many diamonds are needed to balance [3]

    From [1], we have: . D + H \:=\:4S \quad\Rightarrow\quad H \:=\:4S - D\;\;[4]

    From [2]. we have: . 2S + 2D + H \:=\:2H \quad\Rightarrow\quad H \:=\:2S + 2D\;\;[5]

    Equate [4] and [5]: . 4S - D \:=\:2S + 2D \quad\Rightarrow\quad2S \:=\:3D \quad\Rightarrow\quad S \:=\:\tfrac{3}{2}D

    Substitute into [4]: . H \:=\:4\left(\tfrac{3}{2}D\right) - D \quad\Rightarrow\quad H \:=\:5D


    Substitute into [3]:

    . . . . . H + 2S \;=\;?\,D

    . . 5D + 2\left(\tfrac{3}{2}D\right) \;=\;?\,D

    . . . . . . . 8D \;=\;?\,D


    Therefore, 8 Diamonds are needed.

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  3. #3
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    8 is obviously the answer.
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  4. #4
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    Yeah I got 8 as well.

    The answer given in the book is 3. Must be a misprint.
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  5. #5
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    Re: balancing scales

    Hahahaha aquajam? You're the man

    Everybody did get the answer well done.


    Yeah I got 8 as well.

    The answer given in the book is 3. Must be a misprint.
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  6. #6
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    Re: balancing scales

    Bright minds can easily answer this...:-)

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  7. #7
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    Re: balancing scales

    If, like some newspaper puzzles I've seen, the force is weight multiplied by distance from the pivot, then the answer is 21, as calculated here.
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  8. #8
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    Re: balancing scales

    Hi

    This topic help me a lot in developing my project. I will contribute more when I finished it.
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  9. #9
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    Re: balancing scales

    If you want to get more materials that related to this topic, you can visit:Math teacher interview questions


    Best regards.
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