A carpenter used 53 ft of molding in three pieces. If long piece was 3 ft longer than three times the length of each shorter piece, how long was each piece?

Question

I don't even know where to start in solving these problems. 

Answer 1

With word (story) problems, the "place to start" is to read and re-read the problem statement until you understand it and can put it into your own words.  My statement is close to the problem statement:

  A 53-ft length has two short pieces and one long piece (3 ft longer than each short piece).  How long is each?

 

O.K.  Let's let x=length of each short piece      [algebra help us solve problems!]

   3x+3 is length of long piece

 

The total length is 53 ft:

   (x) + (x) + (3x+3) = 53

 

The math:

   5x + 3 = 53          [collect terms]

   5x = 50              [subtract 3 from both sides]

    x = 10 ft         [divide by 5 to get length of each short piece]

 

   3x+3 = 33 ft     [length of long piece]

 

Check:  Is 10 + 10 +33 = 53  ? yes