a 32in board is to be cut into 3 peices so that the second board is twice as long as the first piece and the third is to be 5 times longer than the first piece. if x represents the length of the first peice, find the length of all three pieces.

x + 2x + 5x = 32

x = ?

To find the lengths of the three pieces, we can use algebraic expressions. Let's assign the length of the first piece as 'x'.

According to the problem, the second piece is twice as long as the first piece. So, its length would be 2x.

Similarly, the third piece is five times longer than the first piece. Therefore, its length would be 5x.

Now, we can set up an equation based on the sum of the lengths of the three pieces:

x + 2x + 5x = 32

Combining like terms, we get:

8x = 32

Now, divide both sides of the equation by 8 to solve for x:

x = 4

Therefore, the length of the first piece is 4 units. To find the lengths of the other two pieces:

Second piece: 2x = 2 * 4 = 8 units
Third piece: 5x = 5 * 4 = 20 units

So, the lengths of the three pieces are:
First piece: 4 units
Second piece: 8 units
Third piece: 20 units.

20