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21 January, 20:03

On a balance scale, four spools and one thimble balance twenty nine buttons. Also, one spool balances one thimble and one button. How many buttons will balance one spool

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  1. 21 January, 20:22
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    Here are the definitions I just made up:

    S = weight of 1 spool

    B = weight of 1 button

    T = weight of 1 thimble

    The question tells us that

    4S + 1T = 29B

    and

    1S = 1T + 1B

    Take the second equation, and subtract 1B from each side:

    1T = 1S - 1B

    Take this back to the first equation. In there, where it says '1T',

    substitute '1S - 1B' in place of 1T.

    4S + 1T = 29B

    4S + 1 (1S-1B) = 29B

    Eliminate the parentheses: 4S + 1S - 1B = 29B

    Add 1B to each side: 4S + 1S = 29B + 1B

    Combine like terms on the left side: 5S = 29B + 1B

    Combine like terms on the right side: 5S = 30B

    Divide each side by 5 : S = 6B

    Six (6) buttons will balance one (1) spool on the balance scale.
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