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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)

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)

Algebra: Structure And Method, Book 1
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
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### 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**.
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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