Decrease 72 in a ratio of $$ 7: 18 $$ Increase 8 in a ratio of $$ 5: 4 $$

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### 1. **Decrease 72 in a Ratio of $$ 7:18 $$**

**Interpretation:**  
You want to divide the total amount of 72 into two parts based on the ratio $$ 7:18 $$. This often applies when distributing a total quantity into specific proportional parts.

**Steps to Calculate:**

1. **Determine the Total Number of Parts:**
   $$
   7 + 18 = 25 \text{ parts}
   $$

2. **Calculate Each Part:**
   - **First Part (Ratio 7):**
     $$
     \frac{7}{25} \times 72 = \frac{504}{25} = 20.16
     $$
     
   - **Second Part (Ratio 18):**
     $$
     \frac{18}{25} \times 72 = \frac{1296}{25} = 51.84
     $$

**Result:**
- **First Part:** 20.16
- **Second Part:** 51.84

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### 2. **Increase 8 in a Ratio of $$ 5:4 $$**

**Interpretation:**  
Similarly, you want to split the amount of 8 into two parts based on the ratio $$ 5:4 $$. This is typically used when apportioning an increase or allocation between two categories.

**Steps to Calculate:**

1. **Determine the Total Number of Parts:**
   $$
   5 + 4 = 9 \text{ parts}
   $$

2. **Calculate Each Part:**
   - **First Part (Ratio 5):**
     $$
     \frac{5}{9} \times 8 = \frac{40}{9} \approx 4.44
     $$
     
   - **Second Part (Ratio 4):**
     $$
     \frac{4}{9} \times 8 = \frac{32}{9} \approx 3.56
     $$

**Result:**
- **First Part:** $$ \frac{40}{9} $$ (approximately 4.44)
- **Second Part:** $$ \frac{32}{9} $$ (approximately 3.56)

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### **Summary**

- **Decreasing 72 in a 7:18 Ratio:**
  - **Part 1:** 20.16
  - **Part 2:** 51.84

- **Increasing 8 in a 5:4 Ratio:**
  - **Part 1:** $$ \frac{40}{9} $$ (≈4.44)
  - **Part 2:** $$ \frac{32}{9} $$ (≈3.56)

These calculations allow you to appropriately distribute the amounts based on the specified ratios.
To decrease 72 in a ratio of $$7:18$$, divide 72 into 25 parts (7 + 18). Each part is $$ \frac{72}{25} = 2.88 $$. So, the first part is $$7 \times 2.88 = 20.16$$ and the second part is $$18 \times 2.88 = 51.84$$. To increase 8 in a ratio of $$5:4$$, divide 8 into 9 parts (5 + 4). Each part is $$ \frac{8}{9} \approx 0.8889 $$. So, the first part is $$5 \times 0.8889 \approx 4.4445$$ and the second part is $$4 \times 0.8889 \approx 3.5556$$. **Summary:** - **Decreased 72:** 20.16 and 51.84 - **Increased 8:** Approximately 4.44 and 3.56

Decrease 72 in a ratio of \( 7: 18 \) Increase 8 in a ratio of \( 5: 4 \)

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