Question
6. Mr Makanya has a herd of 65 cattle. He wants to split the herd in the ratio \( 2: 3 \) for his two sons, the elder son getting the larger portion of the herd. Calculate how many catte each son will recelve.
Ask by Wyatt Rodriguez. in South Africa
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
Each son will receive 26 and 39 cattle respectively.
Solution
To solve this problem, we'll divide Mr. Makanya's herd of **65 cattle** between his two sons based on the given ratio of **2:3**, ensuring that the elder son receives the larger portion.
### Step-by-Step Solution:
1. **Understand the Ratio:**
- The ratio **2:3** means that for every **2 parts** the younger son receives, the elder son receives **3 parts**.
2. **Calculate the Total Number of Parts:**
- Sum of the ratio parts = **2 + 3 = 5 parts**
3. **Determine the Value of Each Part:**
- Total cattle = **65**
- Value of one part = **Total cattle ÷ Total parts**
- Value of one part = **65 ÷ 5 = 13 cattle**
4. **Allocate Cattle to Each Son:**
- **Younger Son:**
- **2 parts** × **13 cattle/part** = **26 cattle**
- **Elder Son:**
- **3 parts** × **13 cattle/part** = **39 cattle**
### **Final Distribution:**
- **Elder Son:** **39 cattle**
- **Younger Son:** **26 cattle**
This allocation maintains the desired ratio of **2:3** and ensures that the elder son receives the larger portion of the herd.
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution The Deep Dive
To split the herd of 65 cattle in the ratio \(2:3\), you first add the two parts of the ratio together: \(2 + 3 = 5\). Now, to find the value of one part, divide the total number of cattle by 5: \(65 \div 5 = 13\). Next, multiply this value by each part of the ratio to find out how many cattle each son will receive. For the elder son (larger portion), you calculate \(3 \times 13 = 39\) cattle. For the younger son, \(2 \times 13 = 26\) cattle. So, the elder son will receive 39 cattle, and the younger son will get 26 cattle!
