a wire 54cm long is cut into three pieces. the second piece is twice the length of the first, and the third piece is three times the length of the first. Find the length of each piece?

x + 2x + 3x = 54

6x = 54

x = 9

The first piece is 9 cm long.

To find the length of each piece, let's assign a variable to the length of the first piece. Let's call it "x."

The second piece is twice the length of the first, so its length would be 2x.

The third piece is three times the length of the first, so its length would be 3x.

Since the wire was cut into three pieces, the sum of their lengths should be equal to the length of the wire, which is 54 cm.

Therefore, we can create an equation to represent the sum of the lengths of the pieces:

x + 2x + 3x = 54

Combining like terms, we get:

6x = 54

To find the value of x, we can divide both sides of the equation by 6:

x = 54/6
x = 9

Now, we can substitute the value of x back into our equations to find the lengths of each piece:

First piece: x = 9 cm
Second piece: 2x = 2 * 9 = 18 cm
Third piece: 3x = 3 * 9 = 27 cm

Therefore, the lengths of the wire pieces are 9 cm, 18 cm, and 27 cm respectively.