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.