2. Increasing /decieasing a) Increase \( 11,47 \mathrm{~kg} \) in the ratio of \( 11: 7 \) c) Decrease \( R 2980 \) in the ratio of \( 5: 6 \) d) Decrease 153 g in the ratio of \( 5: 11 \) e) Increase \( R 90,95 \) in the ratio of \( 4: 5 \)

Sure, let's solve each of these problems step-by-step. The terms "increase" and "decrease" in the context of ratios typically involve dividing a given quantity into parts based on the specified ratio. Here's how you can approach each part: --- ### **2. Increasing / Decreasing** --- #### **a) Increase 11.47 kg in the ratio of 11:7** **Step 1: Understand the Ratio** - The ratio **11:7** means the total parts are \( 11 + 7 = 18 \) parts. **Step 2: Calculate the Value of One Part** - Total quantity = \( 11.47 \) kg - Value of one part = \( \frac{11.47 \text{ kg}}{18} \approx 0.6372 \) kg per part **Step 3: Determine Each Part** - **First Part (11 parts):** \( 11 \times 0.6372 \approx 7.0 \) kg - **Second Part (7 parts):** \( 7 \times 0.6372 \approx 4.46 \) kg **Answer:** After increasing, the quantities are **7.0 kg** and **4.46 kg**. --- #### **c) Decrease R 2980 in the ratio of 5:6** **Step 1: Understand the Ratio** - The ratio **5:6** means the total parts are \( 5 + 6 = 11 \) parts. **Step 2: Calculate the Value of One Part** - Total amount = R 2980 - Value of one part = \( \frac{2980}{11} \approx 270.91 \) R per part **Step 3: Determine Each Part** - **First Part (5 parts):** \( 5 \times 270.91 \approx 1354.55 \) R - **Second Part (6 parts):** \( 6 \times 270.91 \approx 1625.46 \) R **Answer:** After decreasing, the amounts are approximately **R 1354.55** and **R 1625.46**. --- #### **d) Decrease 153 g in the ratio of 5:11** **Step 1: Understand the Ratio** - The ratio **5:11** means the total parts are \( 5 + 11 = 16 \) parts. **Step 2: Calculate the Value of One Part** - Total weight = \( 153 \) g - Value of one part = \( \frac{153 \text{ g}}{16} = 9.5625 \) g per part **Step 3: Determine Each Part** - **First Part (5 parts):** \( 5 \times 9.5625 = 47.8125 \) g - **Second Part (11 parts):** \( 11 \times 9.5625 = 105.1875 \) g **Answer:** After decreasing, the weights are **47.81 g** and **105.19 g**. --- #### **e) Increase R 90.95 in the ratio of 4:5** **Step 1: Understand the Ratio** - The ratio **4:5** means the total parts are \( 4 + 5 = 9 \) parts. **Step 2: Calculate the Value of One Part** - Total amount = R 90.95 - Value of one part = \( \frac{90.95}{9} \approx 10.1056 \) R per part **Step 3: Determine Each Part** - **First Part (4 parts):** \( 4 \times 10.1056 \approx 40.42 \) R - **Second Part (5 parts):** \( 5 \times 10.1056 \approx 50.53 \) R **Answer:** After increasing, the amounts are approximately **R 40.42** and **R 50.53**. --- ### **Summary of Answers** - **a)** 7.0 kg and 4.46 kg - **c)** R 1354.55 and R 1625.46 - **d)** 47.81 g and 105.19 g - **e)** R 40.42 and R 50.53 --- If you have any further questions or need additional clarification on any of these steps, feel free to ask!