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Solve the problem using successive percentage and Proportion table and explain 

Let's break down and solve the problem step by step using successive percentage and a proportion table.

### Problem Recap:
- **Total people:** 124
- **Vegetables needed per person (net weight):** 0.4 kg
- **Total net weight of vegetables needed:** \( 124 \times 0.4 = 49.6 \) kg
- **Peeling loss:** 11%
- **Cutting loss:** 5%

### **Step 1: Calculate Gross Weight Using Successive Percentage**
Successive percentage loss involves calculating the total loss step by step.

1. **Peeling Loss:**  
   \[
   \text{Gross weight after peeling} = \frac{\text{Net weight}}{(1 - \text{Peeling percentage})} = \frac{49.6 \, \text{kg}}{1 - 0.11} = \frac{49.6}{0.89} \approx 55.73 \, \text{kg}
   \]

2. **Cutting Loss:**  
   \[
   \text{Gross weight after cutting} = \frac{\text{Gross weight after peeling}}{(1 - \text{Cutting percentage})} = \frac{55.73 \, \text{kg}}{1 - 0.05} = \frac{55.73}{0.95} \approx 58.66 \, \text{kg}
   \]

### **Step 2: Proportion Table**

To visualize the calculation, a proportion table can be helpful:

| Step      | Net Weight | Gross Weight | Loss Percentage |
|-----------|------------|--------------|-----------------|
| Peeling   | 49.6 kg    | 55.73 kg     | 11%             |
| Cutting   | 55.73 kg   | 58.66 kg     | 5%              |

**Explanation:**
1. Start with the net weight needed for 124 people: 49.6 kg.
2. After accounting for the peeling loss of 11%, the gross weight needed to get 49.6 kg of vegetables is 55.73 kg.
3. After accounting for the additional cutting loss of 5%, the final gross weight needed is approximately 58.66 kg.

### Final Answer:
The gross weight of vegetables required for 124 people, considering 11% loss from peeling and 5% loss from cutting, is approximately **58.66 kg**.

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Do you need more details or have any questions?

Here are 8 related questions to explore further:
1. How would the calculation change if the peeling loss was 15% instead of 11%?
2. What is the impact of successive percentage losses compared to a single percentage loss?
3. How can you calculate the net weight if only the gross weight and losses are known?
4. What would be the gross weight needed for 200 people under the same conditions?
5. How does successive percentage loss differ from simply adding the percentages?
6. Can the proportion method be used for other types of food loss calculations? If so, how?
7. How would the gross weight change if the cutting loss was 10% instead of 5%?
8. What if you only had 50 kg of vegetables? How many people could you serve?

**Tip:** When working with percentages in practical situations, it's important to understand whether you should use successive percentage calculations or additive percentages, as they can yield different results.

Learn how to solve a practical problem using successive percentage and a proportion table. This problem involves calculating the gross weight of vegetables needed for 124 people, considering peeling and cutting losses. Understand the step-by-step solution and the application of successive percentage calculations in real-world scenarios.

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