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.

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.