3. Gloria has 2 lengths of rope. One is 6 feet longer than the other.

If the two lengths add up to 18 feet, how long are they?



We will use the steps for solving word problems


  1. Read the whole problem.
  2. Define your unknown(s).
  3. Express your information with equation(s) in your unknowns.
  4. Solve the equation(s)


The first stepis to define your unknown or unknowns. The most

efficient wayt to do this is to let your unknow be what the problem

is asking for. In this case, there are two unknowns, the two lengths of

rope. But if we let x be the one piece of rope, the fact that the other

piece is 6 feet longer allows us to express all of our unknowns with

only one equation. So we


let x = the length of one piece of rope

x + 6 - the other piece of rope.


Now the information that the two pieces of rope add up to 18

feet can be expressed as


x + (x + 6) = 18


This is an equation that can be solved. Remove parentheses and

combine like terms


2x + 6 = 18


Subtract 6 from each sied


2x = 18 - 6


2x = 12


Divide both sides by 2


x = 12/2


x = 6.


Check. If one piece is 6 feet long then the piece which is 6 eet longer

would be 12 feet, and the two pieces would total to 18 feet.


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