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 step is to define your unknown or unknowns. The most efficient way 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 ournknowns with only one variable. 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 side

2x = 18 - 6

or

2x = 12

Divide both sides by 2

x = 12/2

or

x = 6.

Check. If one piece is 6 feet long then the piece which is 6 feet longer would be 12 feet, and the two pieces would total to 18 feet.

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