A rope is 66 feet long. It is cut into two pieces such that one piece is half the length of the other. What is the length of the longer piece of rope?

L e t ' s b u i l d a n e q u a t i o n

Rope Length = 1st Piece + 2nd Piece

Where 1st Piece = 1/2 the 2nd Piece.

Therefore.

Rope Length = 1/2x + x

Now substitute and solve for x.

66 = 1/2x + x

66 = 3/2x

/1.5 / 1.5

44 = x

Therefore the longer piece is 44.

Proof.

First Piece: 1/2 x = 44 / 2 = 22

Second Piece = x = 44

22 + 44 = 66

Assume the longer piece is x feet long,

Then the other piece is 0.5x feet long

In total: x + 0.5x = 66 - > x = 44

So the longer piece is 44 feet, shorter piece is 22 feet