A length of rope is 144cm. The scout leader cut the rope into 3 pieces. One piece is twice as long as the shortest piece. The other piece is three times as long as the shortest piece.
shortest piece --- x
one piece ----- 2x
the other piece --- 3x
x + 2x + 3x = 144
solve for x
24+48+72
To solve this problem, we need to let x represent the length of the shortest piece of the rope.
According to the problem statement, the longest piece is twice as long as the shortest piece. So, the length of the longest piece is 2x.
The other piece is three times as long as the shortest piece. Therefore, the length of the third piece is 3x.
To find the lengths of the three pieces, we can set up an equation using the given information:
x + 2x + 3x = 144
Simplifying the equation, we combine like terms:
6x = 144
To solve for x, divide both sides of the equation by 6:
x = 144/6
x = 24
Therefore, the length of the shortest piece is 24 cm.
Now that we know the length of the shortest piece, we can find the lengths of the other two pieces.
The length of the longest piece is twice as long as the shortest piece, so:
Longest piece = 2 * 24 = 48 cm
The length of the third piece is three times as long as the shortest piece:
Third piece = 3 * 24 = 72 cm
Therefore, the lengths of the three pieces of the rope are 24 cm, 48 cm, and 72 cm.