42 inch cut into 3 pieces. Piece 2 is twice as long as 1st and 3rd piece. Piece 3 is three times as long as piece 1. How long are the pieces

1st board
2nd board
3rd board

To find the length of each piece, let's call the length of the first piece "x".

The second piece is twice as long as the first piece, so its length is 2x.

The third piece is three times as long as the first piece, so its length is 3x.

Since we are cutting a 42-inch board into 3 pieces, the sum of the lengths of all three pieces is equal to 42:

x + 2x + 3x = 42

Combining like terms:

6x = 42

Dividing both sides of the equation by 6:

x = 7

So the length of the first piece is 7 inches.

The length of the second piece is twice as long, so it is 2 * 7 = 14 inches.

The length of the third piece is three times as long, so it is 3 * 7 = 21 inches.

Therefore, the lengths of the pieces are as follows:

1st board: 7 inches
2nd board: 14 inches
3rd board: 21 inches