100 ft rope is cut in two pieces so that the larger piece is 2 less than twice the shorter piece. What is the length of the larger piece?

L = larger piece

S = shorter piece

L = 2 S - 2

L + S = 100

2 S - 2 + S = 100

3 S - 2 = 100 Add 2 to both sides

3 S - 2 + 2 = 100 + 2

3 S = 102 Divide both sides by 3

S = 102 / 3 = 34 ft

L = 2 S - 2

L = 2 * 34 - 2 = 68 - 2 = 66 ft

To solve this problem, we need to set up an equation based on the given information. Let's assume that the shorter piece of the rope has a length of "x" feet.

According to the problem, the larger piece is 2 less than twice the length of the shorter piece. Therefore, the larger piece has a length of (2x - 2) feet.

Since we know that the total length of the rope is 100 feet, we can set up the equation:

x + (2x - 2) = 100

Now we can solve for x:

3x - 2 = 100

Adding 2 to both sides:

3x = 102

Dividing both sides by 3:

x = 34

So the shorter piece of the rope is 34 feet.

To find the length of the larger piece:

2x - 2 = 2(34) - 2 = 68 - 2 = 66

Therefore, the length of the larger piece is 66 feet.