Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter7: Applying Fractions
Section7.1: Ratios
Problem 25WE
Related questions
Question
![### Question 4:
If you cut an 84 ft rope into two pieces with a ratio of 2:5, how long is the smaller piece? (SHOW WORK)
### Solution:
To determine the length of the smaller piece of the rope when divided in the ratio 2:5, follow these steps:
1. **Understand the Ratio:**
- The ratio 2:5 means for every 2 parts of the rope, there are 5 parts of the rope.
2. **Sum of the Parts:**
- Total ratio parts = 2 + 5 = 7 parts.
3. **Length of Each Part:**
- Total length of the rope = 84 feet.
- Length per part = Total Length / Total Ratio Parts = 84 feet / 7 parts = 12 feet per part.
4. **Length of Smaller Piece:**
- The smaller piece corresponds to the ‘2 parts’ from the ratio.
- Smaller Piece Length = 2 parts * Length per part = 2 * 12 feet = 24 feet.
Therefore, the length of the smaller piece of the rope is **24 feet**.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F41fb09d5-8b0e-4c41-ac4e-b73482182c8a%2Fb5e1028a-3b72-4e5e-8f51-470421d427f4%2F3a7oqtq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Question 4:
If you cut an 84 ft rope into two pieces with a ratio of 2:5, how long is the smaller piece? (SHOW WORK)
### Solution:
To determine the length of the smaller piece of the rope when divided in the ratio 2:5, follow these steps:
1. **Understand the Ratio:**
- The ratio 2:5 means for every 2 parts of the rope, there are 5 parts of the rope.
2. **Sum of the Parts:**
- Total ratio parts = 2 + 5 = 7 parts.
3. **Length of Each Part:**
- Total length of the rope = 84 feet.
- Length per part = Total Length / Total Ratio Parts = 84 feet / 7 parts = 12 feet per part.
4. **Length of Smaller Piece:**
- The smaller piece corresponds to the ‘2 parts’ from the ratio.
- Smaller Piece Length = 2 parts * Length per part = 2 * 12 feet = 24 feet.
Therefore, the length of the smaller piece of the rope is **24 feet**.
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