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?

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Sure, let's tackle each of your ratio problems step by step.

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### 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!
**Answers:** 1. **Increase 8 in a ratio of $$ 5:4 $$:** Cannot determine with the given information. 2. **New Energy Bar Weight:** 96 grams 3. **Thabo's Current Savings:** R35,714.29

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