Jessica has a piece of rope that is 75 feet long. She cuts the rope into 2 pieces. The pieces of rope are not the same length. Which 2 lengths could be the lengths of Jessica's pieces of rope?
one could be 50 feet and the other could be 25 feet
Any answer with a pair of positive real numbers would be acceptable, as long as their sum is 75.
e.g. 13.467 and 61.533 would do, so would 2 and 73, etc
To solve this problem, we need to consider the possibilities for the lengths of the two pieces of rope that Jessica cut. Since the total length of the rope is 75 feet, we can assign a variable to one of the lengths, such as x, and then express the other length in terms of x.
Let's consider the possibilities:
1. Let's assume the first piece of rope has a length of x feet. Since the two pieces are not the same length, the second piece must have a different length, which we can represent as (75 - x) feet.
2. Now, to find the possible values of x, we consider the range of valid lengths for the pieces. The lengths of both pieces of rope must be positive numbers, and the sum of the two lengths must equal 75 feet.
3. Therefore, we set up the inequality: x + (75 - x) > 0
4. Simplifying the inequality, we have: 75 - x > 0
5. Solving for x, we get: x < 75
6. This means that the first piece of rope can have any length less than 75 feet.
7. Thus, the possible lengths of the two pieces of rope can be any positive value less than 75 feet for the first piece, and the second piece will be the remaining length.
In conclusion, the lengths of Jessica's pieces of rope can be any positive values less than 75 feet, as long as they are not the same length.