Final answer:
The expression representing the length of the rope before it was cut is x + y. If twice the length of rope is used, the equations would be y = 5x - 2 and x + y = 200. By substitution, the lengths of the two pieces can be calculated.
Step-by-step explanation:
The question involves creating an equation to find the lengths of two pieces of rope that have been cut from a longer piece. Given that x equals the length of one piece and y equals the length of the other piece, with one piece being 2 ft less than 5 times the length of the other, we can form two equations. The first equation comes from the relationship between the pieces: y = 5x - 2. The second equation comes from the fact that the total length of the rope before cutting was 100 ft: x + y = 100.
To address the part of the question regarding what expression represents the length of the rope before it was cut, our choice would be x + y. This is because the two lengths of the pieces of rope, when added together, will give us the original length of the rope.
If we double the length of the rope to 200 ft, the equation representing the total length would simply be x + y = 200, and the relationship between the lengths of the pieces would remain the same: y = 5x - 2. By substituting one equation into the other, we could solve for either x or y to find the individual lengths of the pieces.