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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

Sagot :

AL2006

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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