a 13 foot piece of string is cut into two pieces so that the longer piece is 4 feet longer than twice the shorter piece

Question

what is the length of the shorter piece?

 

Answer 1

It often helps to assign a variable to the value that the problem asks you to find (so you won't forget to solve for it at the end).

Let x = length of the shorter piece                [eq1]

 

Translate:

    "longer piece is 4 feet longer than twice the shorter piece"    means

 <linger piece> =    4          +             2  *           x

 

"13 foot piece of string is cut into two pieces"    means

   <longer piece> +  <shorter piece>   =   13                [eq2]

 

The math:

   <longer piece> +  <shorter piece>   =   13

   <longer piece> + x = 13                                  [use the let statement]

   (4 + 2x) + x = 13                                         [substitute using eq2]

    4 + 3x = 13

      3x = 9                                      [subtract 4 from both sides]

       x = 3                                  [divide both sides by 3]

 

The shorter piece is 3 feet long.

 

To check, you may find the length of the longer piece (4+2x=10) and determine:

  Is     10 + 3 = 13   ?

             13 = 13   ?yes