The 120-foot rope is cut into 3 pieces.The first of rope is twice as long as the second piece of rope.The third piece of rope is three times as long as the second piece of rope.What is length of the longest piece of rope.
second piece - x ft
first piece - 2x feet
third piece - 3x
solve x + 2x + 3x = 12
10!! easy
To solve this problem, we'll need to set up an equation and solve for the length of each piece of rope.
Let's denote the length of the second piece of rope as x. According to the information given, the first piece of rope is twice as long as the second piece, so its length is 2x. Similarly, the third piece of rope is three times the length of the second piece, so its length is 3x.
Now, we can set up an equation to represent the total length of the rope, which is 120 feet:
x + 2x + 3x = 120
Simplifying the equation, we have:
6x = 120
To solve for x, we divide both sides of the equation by 6:
x = 120 / 6 = 20
So, the second piece of rope has a length of 20 feet. The first piece is twice as long, so it is 2 * 20 = 40 feet. The third piece is three times as long, so it is 3 * 20 = 60 feet.
Therefore, the longest piece of rope is 60 feet.
first piece is 2X
second piece is X
third piece is 3X
solve : X+2X+3X=120
once you solve for X, then just plug it in.