Final answer:
In order to find the length of the first piece, we can set up an equation based on the given information. By solving for x, we can determine the length of the first piece. In this case, the length of the first piece is option a. 7 inches.
Step-by-step explanation:
In order to tackle this problem, let's designate the length of the first piece as x.
Following the given information, the second piece is twice the length of the first, denoted as 2x.
Similarly, the third piece measures four times the length of the first, represented as 4x.
The total length of the three pieces sums up to 35 inches, leading to the equation x + 2x + 4x = 35.
Combining like terms, the equation simplifies to 7x = 35.
Through division of both sides by 5, we determine that x equals 7.
Consequently, the length of the initial piece is 7 inches.
By adopting a variable-based approach, the solution becomes a systematic process, offering a clear and concise method for determining the lengths of the individual pieces in accordance with the given conditions.
So, the length of the first piece is option a. 7 inches.