Answer :
Let's solve the problem step-by-step:
### Step-by-Step Solution:
1. Identify the Total Length:
The total length of the rope is given as 5 meters.
2. Represent the Known Part:
One part of the rope is denoted as [tex]\( y \)[/tex] meters.
3. Determine the Length of the Other Part:
When a total length is divided into two parts, the sum of the lengths of these two parts should be equal to the total length. If one part is [tex]\( y \)[/tex] meters, the length of the other part can be found by subtracting [tex]\( y \)[/tex] from the total length.
4. Set Up the Algebraic Expression:
The length of the other part of the rope can be expressed as:
[tex]\[ \text{Length of the other part} = \text{Total length} - y \][/tex]
5. Substitute the Given Total Length:
[tex]\[ \text{Length of the other part} = 5 - y \][/tex]
### Conclusion:
If one part of the 5-meter rope is [tex]\( y \)[/tex] meters, the length of the other part is [tex]\( 5 - y \)[/tex] meters.
This can be summarized in the following algebraic expression:
[tex]\[ 5 - y \][/tex]
So, given a 5-meter piece of rope and knowing that one part is [tex]\( y \)[/tex] meters, the length of the other part of the rope is [tex]\( 5 - y \)[/tex] meters.
### Step-by-Step Solution:
1. Identify the Total Length:
The total length of the rope is given as 5 meters.
2. Represent the Known Part:
One part of the rope is denoted as [tex]\( y \)[/tex] meters.
3. Determine the Length of the Other Part:
When a total length is divided into two parts, the sum of the lengths of these two parts should be equal to the total length. If one part is [tex]\( y \)[/tex] meters, the length of the other part can be found by subtracting [tex]\( y \)[/tex] from the total length.
4. Set Up the Algebraic Expression:
The length of the other part of the rope can be expressed as:
[tex]\[ \text{Length of the other part} = \text{Total length} - y \][/tex]
5. Substitute the Given Total Length:
[tex]\[ \text{Length of the other part} = 5 - y \][/tex]
### Conclusion:
If one part of the 5-meter rope is [tex]\( y \)[/tex] meters, the length of the other part is [tex]\( 5 - y \)[/tex] meters.
This can be summarized in the following algebraic expression:
[tex]\[ 5 - y \][/tex]
So, given a 5-meter piece of rope and knowing that one part is [tex]\( y \)[/tex] meters, the length of the other part of the rope is [tex]\( 5 - y \)[/tex] meters.
