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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15-02-2015
Mathematics

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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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AL2006 AL2006 · Answer 1 · 2015-02-15T20:29:06-05:00

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.