Get insightful responses to your questions quickly and easily on IDNLearn.com. Ask anything and receive prompt, well-informed answers from our community of knowledgeable experts.
Sagot :
To determine the total length of the wire Rohini initially had, we can follow a step-by-step process, keeping in mind the wire usage and the remaining wire.
1. Let the total length of the wire be denoted as [tex]\( x \)[/tex].
2. Rohini used [tex]\(\frac{1}{2}\)[/tex] of the wire in wiring the room.
- This means, she has used [tex]\(\frac{1}{2} x\)[/tex] of the total wire.
- Thus, the remaining wire after wiring the room is:
[tex]\[ x - \frac{1}{2} x = \frac{1}{2} x \][/tex]
3. She gave [tex]\(\frac{1}{3}\)[/tex] of the remaining wire to her friend.
- The remaining wire after wiring the room is [tex]\(\frac{1}{2} x\)[/tex].
- The wire given to her friend is:
[tex]\[ \frac{1}{3} \times \frac{1}{2} x = \frac{1}{6} x \][/tex]
4. Wire left with Rohini after giving some to her friend:
- The wire left with her after wiring the room is [tex]\(\frac{1}{2} x\)[/tex].
- After giving [tex]\(\frac{1}{6} x\)[/tex] to her friend, the remaining wire with her is:
[tex]\[ \frac{1}{2} x - \frac{1}{6} x \][/tex]
5. Simplify this to find the remaining wire:
- Finding a common denominator for [tex]\(\frac{1}{2} x\)[/tex] and [tex]\(\frac{1}{6} x\)[/tex]:
[tex]\[ \frac{3}{6} x - \frac{1}{6} x = \frac{2}{6} x = \frac{1}{3} x \][/tex]
6. According to the problem, 30 meters of wire remained with her:
- So, we set up the equation:
[tex]\[ \frac{1}{3} x = 30 \][/tex]
7. Solve for [tex]\( x \)[/tex]:
- To isolate [tex]\( x \)[/tex], multiply both sides of the equation by 3:
[tex]\[ x = 30 \times 3 \][/tex]
[tex]\[ x = 90 \][/tex]
8. Conclusion
- Therefore, the total length of the wire Rohini initially had is 90 meters.
1. Let the total length of the wire be denoted as [tex]\( x \)[/tex].
2. Rohini used [tex]\(\frac{1}{2}\)[/tex] of the wire in wiring the room.
- This means, she has used [tex]\(\frac{1}{2} x\)[/tex] of the total wire.
- Thus, the remaining wire after wiring the room is:
[tex]\[ x - \frac{1}{2} x = \frac{1}{2} x \][/tex]
3. She gave [tex]\(\frac{1}{3}\)[/tex] of the remaining wire to her friend.
- The remaining wire after wiring the room is [tex]\(\frac{1}{2} x\)[/tex].
- The wire given to her friend is:
[tex]\[ \frac{1}{3} \times \frac{1}{2} x = \frac{1}{6} x \][/tex]
4. Wire left with Rohini after giving some to her friend:
- The wire left with her after wiring the room is [tex]\(\frac{1}{2} x\)[/tex].
- After giving [tex]\(\frac{1}{6} x\)[/tex] to her friend, the remaining wire with her is:
[tex]\[ \frac{1}{2} x - \frac{1}{6} x \][/tex]
5. Simplify this to find the remaining wire:
- Finding a common denominator for [tex]\(\frac{1}{2} x\)[/tex] and [tex]\(\frac{1}{6} x\)[/tex]:
[tex]\[ \frac{3}{6} x - \frac{1}{6} x = \frac{2}{6} x = \frac{1}{3} x \][/tex]
6. According to the problem, 30 meters of wire remained with her:
- So, we set up the equation:
[tex]\[ \frac{1}{3} x = 30 \][/tex]
7. Solve for [tex]\( x \)[/tex]:
- To isolate [tex]\( x \)[/tex], multiply both sides of the equation by 3:
[tex]\[ x = 30 \times 3 \][/tex]
[tex]\[ x = 90 \][/tex]
8. Conclusion
- Therefore, the total length of the wire Rohini initially had is 90 meters.
We are delighted to have you as part of our community. Keep asking, answering, and sharing your insights. Together, we can create a valuable knowledge resource. IDNLearn.com has the solutions you’re looking for. Thanks for visiting, and see you next time for more reliable information.