Increase 8 in a ratio of \( 5: 4 \) A health food company decides to increase the size of their energy bar in a ratio of \( 6: 5 \). If the old bar has a weight of 80 grams, what will the weight of the new bar be? In a disastrous year of global financial problems, the value of Thabo's retirement investment savings decreases in the ratio of \( 5: 7 \). If his savings were worth R50 000 a year ago what is their current rand value?

Sure, let's tackle each of your ratio problems step by step. --- ### 1. **Increase 8 in a Ratio of \( 5:4 \)** **Clarification Needed:** The statement "Increase 8 in a ratio of \( 5:4 \)" is a bit ambiguous. It could be interpreted in a few ways, such as: - **Adding 8 units to one part of a ratio.** - **Scaling a quantity by a ratio that includes an increase of 8.** Without additional context, it's challenging to provide a precise solution. If you can provide more details or rephrase the question, that would be helpful. However, I'll proceed with a possible interpretation below. **Possible Interpretation:** Suppose you have two quantities in the ratio \( 5:4 \), and you want to increase the smaller part by 8 units while maintaining the same ratio. **Step-by-Step Solution:** 1. **Let’s Define the Original Quantities:** - Let the original quantities be \( 5x \) and \( 4x \). 2. **Increase the Smaller Quantity by 8:** - New quantities become \( 5x \) and \( 4x + 8 \). 3. **Maintain the Ratio \( 5:4 \):** - \[ \frac{5x}{4x + 8} = \frac{5}{4} \] 4. **Solve for \( x \):** - Cross-multiply: \[ 5x \times 4 = 5 \times (4x + 8) \] \[ 20x = 20x + 40 \] - Subtract \( 20x \) from both sides: \[ 0 = 40 \] - **This results in a contradiction**, indicating that increasing the smaller part by 8 while maintaining the same ratio is impossible with the given information. **Conclusion:** The problem, as interpreted, doesn't have a feasible solution. Please provide additional details or clarify the question for a more accurate answer. --- ### 2. **Health Food Company Energy Bar Size Increase** **Problem Statement:** A health food company decides to increase the size of their energy bar in a ratio of \( 6:5 \). If the old bar weighs **80 grams**, what will the weight of the **new bar** be? **Step-by-Step Solution:** 1. **Understand the Ratio:** - The ratio \( 6:5 \) means that for every 5 parts of the old bar, the new bar has 6 parts. 2. **Define the Parts:** - Let’s denote the old size as 5 parts and the new size as 6 parts. 3. **Calculate the Value of One Part:** - Given the old bar weighs 80 grams: \[ 5 \text{ parts} = 80 \text{ grams} \] \[ 1 \text{ part} = \frac{80}{5} = 16 \text{ grams} \] 4. **Determine the New Weight:** - New bar = 6 parts: \[ 6 \times 16 = 96 \text{ grams} \] **Answer:** The new energy bar will weigh **96 grams**. --- ### 3. **Thabo's Retirement Investment Savings Decrease** **Problem Statement:** In a disastrous year of global financial problems, the value of Thabo's retirement investment savings decreases in the ratio of \( 5:7 \). If his savings were worth **R50,000** a year ago, what is their current rand value? **Understanding the Ratio:** The ratio \( 5:7 \) indicates the decrease from the original amount to the current amount. **Step-by-Step Solution:** 1. **Define the Ratio Components:** - Original value (before decrease): 7 parts - Current value (after decrease): 5 parts 2. **Total Parts:** - \( 7 \) parts (original) correspond to R50,000. 3. **Calculate the Value of One Part:** \[ 7 \text{ parts} = R50,000 \] \[ 1 \text{ part} = \frac{50,000}{7} \approx R7,142.86 \] 4. **Determine the Current Value:** \[ 5 \text{ parts} = 5 \times 7,142.86 \approx R35,714.29 \] **Answer:** Thabo's current savings are approximately **R35,714.29**. --- **Summary of Answers:** 1. **Increase 8 in a ratio of \( 5:4 \):** *Clarification needed; the problem, as interpreted, has no feasible solution.* 2. **New Energy Bar Weight:** **96 grams** 3. **Thabo's Current Savings:** **R35,714.29** If you have more details or need further assistance, feel free to ask!