Final answer:
To find the length of the first piece of a 12-inch board cut into three pieces with specific ratios, we represent the length of the first piece with x inches, leading to the equation x + 2x + 3x = 12. Solving for x gives us 2 inches as the length of the first piece.
Step-by-step explanation:
To solve the problem of dividing a 12-inch board into three pieces where the second piece is twice as long as the first and the third piece is three times as long as the first, we need to set up equations based on the lengths of the pieces.
Let the length of the first piece be x inches. Therefore, the second piece will be 2x inches and the third piece will be 3x inches. Since the total length of the board is 12 inches, we can write the equation as follows:
x + 2x + 3x = 12
This simplifies to 6x = 12.
Dividing both sides of the equation by 6 gives us:
x = 12 / 6 = 2
So, the length of the first piece is 2 inches.