Assign x, make an equation and solve the problem.

Question

Assign x, make an equation and solve the problem.
A 56 ft cable was cut into 3 pieces.  Every next piece is twice as long as the previous piece. Find the length of smaller piece.

Answer 1

We have a choice of assigning x to be the length of any one of three pieces.  I like this problem because I can remind you to look at what the problem is asking ("Find the length of smaller piece") and advise you, if reasonable, assign x to that so you won't forget what you must report as the answer (note: if x were the length of the longer piece and we reported x, then we would have a wrong answer).

 

So, let x=length of shortest piece.

The second piece is twice as long, so it is  2x  in length.

The third piece is twice as long as the previous piece, so its length is    2(2x)

The total length is 56 ft.

 

We have    x + 2x + 2(2x) = 56

                7x = 56       (collect terms)

                  x = 8 ft       (divide both sides by 7)

 

Checking (very important):

    Is   8  + 2(8)  + 2(2(8))) = 56   ?

          8   + 16    +  32     = 56   ?    yes.

 

(note: 56 is what I call a "magic number" -- it makes the problem easy to solve so you can concentrate on solving the problem.  If a problem isn't working out very nicely, be suspicious of errors.)