a 27 inch board is to be 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 length of all three pieces.

To solve this problem, we need to set up an equation based on the given information.

Let's first represent the length of the first piece as x.

According to the problem, the second piece is 3 times as long as the first piece, so its length would be 3x.

Similarly, the third piece is 5 times as long as the first piece, so its length would be 5x.

Now, we can set up the equation using the sum of the lengths of the three pieces:

x + 3x + 5x = 27

Simplifying the equation, we get:

9x = 27

Dividing both sides by 9:

x = 27/9

x = 3

Therefore, the length of the first piece is 3 inches.

Using this value, we can calculate the lengths of the other two pieces:

Second piece: 3x = 3 * 3 = 9 inches
Third piece: 5x = 5 * 3 = 15 inches

So, the lengths of the three pieces are:
First piece: 3 inches
Second piece: 9 inches
Third piece: 15 inches

(X)+(3x)+(5x)=27