He wants to split the herd in the ratio \( 2: 3 \) for his two sons, the clder son getting the larger portion of the herd. Calculate how many cattle each son will receive. 7. Langa and Ray share R24 000 in the ratio \( 5: 3 \). How much does eac 8. Two bricklayers. Tshepo and John, work on a building. Tshepo worked for 140 hours, while John worked for 80 hours. They were paid R14 000 to do the job. They share the money in the same ratio as the hours they worked.

Sure, I'd be happy to help you solve these ratio problems. Let's tackle each one step by step. --- ### **Problem 6: Splitting the Herd** **Statement:** A father wants to split his herd in the ratio \( 2:3 \) between his two sons, with the elder son receiving the larger portion. Calculate how many cattle each son will receive. **Solution:** To determine how many cattle each son receives, we need to know the **total number of cattle** in the herd. Since the total isn't provided, I'll explain the general method to solve such problems. Once you have the total number of cattle, you can apply this method. **Steps:** 1. **Identify the Ratio Parts:** - The ratio given is \( 2:3 \), where \( 2 \) parts go to the younger son and \( 3 \) parts go to the elder son. 2. **Calculate Total Parts:** \[ \text{Total Parts} = 2 + 3 = 5 \text{ parts} \] 3. **Determine the Value of Each Part:** \[ \text{Value of One Part} = \frac{\text{Total Number of Cattle}}{5} \] 4. **Calculate Each Son's Share:** - **Younger Son:** \[ 2 \times \text{Value of One Part} \] - **Elder Son:** \[ 3 \times \text{Value of One Part} \] **Example:** If the total herd has **25 cattle**: \[ \text{Value of One Part} = \frac{25}{5} = 5 \text{ cattle per part} \] - **Younger Son:** \( 2 \times 5 = 10 \) cattle - **Elder Son:** \( 3 \times 5 = 15 \) cattle --- ### **Problem 7: Sharing Money Between Langa and Ray** **Statement:** Langa and Ray share R24,000 in the ratio \( 5:3 \). How much does each receive? **Solution:** 1. **Identify the Ratio Parts:** - Langa : Ray = \( 5 : 3 \) 2. **Calculate Total Parts:** \[ \text{Total Parts} = 5 + 3 = 8 \text{ parts} \] 3. **Determine the Value of Each Part:** \[ \text{Value of One Part} = \frac{24,000}{8} = R3,000 \text{ per part} \] 4. **Calculate Each Person's Share:** - **Langa:** \( 5 \times 3,000 = R15,000 \) - **Ray:** \( 3 \times 3,000 = R9,000 \) **Answer:** - **Langa receives R15,000** - **Ray receives R9,000** --- ### **Problem 8: Sharing Payment Between Tshepo and John** **Statement:** Two bricklayers, Tshepo and John, work on a building. Tshepo worked for 140 hours, while John worked for 80 hours. They were paid R14,000 to do the job. They share the money in the same ratio as the hours they worked. How much does each receive? **Solution:** 1. **Identify the Ratio of Hours Worked:** - Tshepo : John = \( 140 : 80 \) 2. **Simplify the Ratio:** \[ \frac{140}{80} = \frac{7}{4} \] So, the simplified ratio is \( 7:4 \) 3. **Calculate Total Parts:** \[ \text{Total Parts} = 7 + 4 = 11 \text{ parts} \] 4. **Determine the Value of Each Part:** \[ \text{Value of One Part} = \frac{14,000}{11} \approx R1,272.73 \text{ per part} \] 5. **Calculate Each Person's Share:** - **Tshepo:** \( 7 \times 1,272.73 \approx R8,909.09 \) - **John:** \( 4 \times 1,272.73 \approx R5,090.91 \) **Answer:** - **Tshepo receives approximately R8,909.09** - **John receives approximately R5,090.91** *Note:* Depending on how precise you want the amounts to be, you can round to the nearest rand or cent. --- **Summary:** - **Problem 6:** Requires the total number of cattle to provide a specific answer. Once known, divide the herd based on the ratio \( 2:3 \). - **Problem 7:** Langa gets R15,000 and Ray gets R9,000. - **Problem 8:** Tshepo receives approximately R8,909.09 and John receives approximately R5,090.91. If you have the total number of cattle for **Problem 6**, feel free to share it, and I can help you calculate the exact number each son will receive!