https://file.aiquickdraw.com/mathbot/file/1726359205248kjobhzkw.jpg

Let me first analyze the problem statement to determine how to calculate the total number of food packages sent to each district. Here's a step-by-step breakdown based on the information provided in the image:

### Districts Involved:
1. Chennai
2. Thiruvallur
3. Chengalpattu
4. Kanchipuram

### Key Information:
- The **ratio** of food packets received by Chennai and Thiruvallur is **4:3**.
- The **ratio** of food packets received by Chengalpattu and Kanchipuram is **7:10**.
- **Chennai** received **double** the number of food packets compared to Kanchipuram.
- The **percentage of food packets consumed** in:
  - Chennai = 75%
  - Thiruvallur = 80%
  - Kanchipuram = 80%
- Wastage in **Kanchipuram** and **Chengalpattu** are **equal**.

Let's assign variables for each district:

- Let the number of food packets sent to **Kanchipuram** be \( x \).
- Therefore, the number of packets sent to **Chennai** is \( 2x \), as Chennai received double the number of food packets compared to Kanchipuram.
- The number of packets sent to **Thiruvallur** is \( \frac{3}{4} \times 2x = \frac{3}{2}x \) based on the 4:3 ratio between Chennai and Thiruvallur.
- The number of packets sent to **Chengalpattu** is \( \frac{7}{10} \times x = \frac{7}{10}x \) based on the 7:10 ratio between Chengalpattu and Kanchipuram.

### Consumption & Wastage:
- Chennai consumed 75% of its food packets: \( 0.75 \times 2x \).
- Thiruvallur consumed 80% of its food packets: \( 0.80 \times \frac{3}{2}x \).
- Kanchipuram had 20% wastage, implying 80% consumption: \( 0.80 \times x \).
- Chengalpattu had the same wastage as Kanchipuram, meaning it also had 20% wastage and 80% consumption: \( 0.80 \times \frac{7}{10}x \).

Now, I'll calculate the total number of food packets.It seems that the calculation resulted in an unexpected outcome. Specifically, the number of packets sent to **Kanchipuram** turned out to be \( 0 \), which suggests there might be an inconsistency in the problem constraints, particularly the equal wastage condition.

Let's review this carefully. Since the setup is leading to an impossible value, I recommend revisiting the assumptions or double-checking the problem's details, especially the wastage relationship.

Would you like further clarification on this issue, or should I attempt another approach? Here are five questions to consider:

1. Can we revisit the ratios between the districts' packet distributions?
2. Should we adjust the percentage of consumed packets for some districts?
3. Can we explore a different relationship between Kanchipuram and Chengalpattu's wastage?
4. Should we try solving the problem without assuming equal wastage?
5. Could other pieces of information about packet distribution or wastage clarify the issue?

**Tip:** In such problems, always ensure consistency in your assumptions before proceeding to solve the equations.

This problem involves calculating the total number of food packages sent to four districts after a cyclone. Ratios between districts and percentage consumption data are used to solve the problem. Suitable for Grades 9-10.

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