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The document describes a market survey with three commodities, A, B, and C. Fixed weights are assigned to three variables for each commodity to determine their index numbers. Here's a breakdown of the content:

### Table Information:

- **Commodities:** A, B, C
- **Variables:**
  - I
  - II
  - III
- **Weights for each variable:** Different for each commodity
  - **A:** Variable I (2), Variable II (3), Variable III (5), Total weight = 10
  - **B:** Variable I (3), Variable II (2), Variable III (6), Total weight = 11
  - **C:** Variable I (1), Variable II (3), Variable III (8), Total weight = 12

### Task:
You are asked to find the weights assigned to the three variables using the "notorious method" (likely referring to weighted averages). The weights for each commodity are equal to the sum of the product of the weights assigned to the variables and the corresponding consumption of each variable for the commodity.

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### Related Questions:
1. How do we calculate the weighted sum for each commodity based on the provided weights?
2. How does the sum of products approach work in calculating index numbers?
3. Why are weights important when determining the contribution of each variable to the overall commodity score?
4. What is the significance of assigning different weights to variables for different commodities?
5. How can this method be applied to real-world data analysis scenarios?

**Tip:** Always double-check the weights and consumption values before performing calculations to ensure accuracy.

In a market survey, 3 commodities (A, B, C) were considered. Fixed weights were assigned to three variables in each of the commodities. The table provides information regarding the consumption of these commodities according to three variables and the total weight received by each commodity. You are asked to find the weights assigned to the three variables using the specified method.

Learn how to calculate the weights assigned to variables in a market survey involving three commodities (A, B, C) using the method of weighted averages. This problem covers key mathematical concepts such as index numbers, weighted sums, and algebra. Suitable for students in Grades 9-12.

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