A 36 inch board is cut into three pieces so that the second piece is 3 times as long as the first piece and the third piece is 5 times as long as the first piece. If X represents the length of the first piece, find the lengths of all three pieces

First piece = 4 inch, second piece = 12 inch, third piece = 20 inch

Step-by-step explanation:

Length of the board = 36 inch

Let, the length of the first piece = X

So, according to the question

Second piece = 3 times X = 3x

Third piece = 5 times X = 5X

Now, first piece + second piece + third piece = total length of the board

⇒ X + 3X + 5X = 36 inch

or, 9X = 36 inch

or, X = 36/9 = 4 inch

So, length of the : First piece = 4 inch

Second Piece = 3X = 3 x 4 = 12 inch

Third piece = 5X = 5 x 4 = 20 inch