John, Micheal and Christopher are running a supermarket. To deliver the products they use three 
different types of carry bags, they are polythene bags, handmade bags and newspaper envelopes. 
It is found that John, Michael, and Christopher are using 20, 30 and 40 polythene bags. 30, 40 and 
20 handmade bags, and finally 40, 20 and 30 newspaper envelopes respectively in a month. The
expenditures for procuring these bags are 250, 270 and 200. 
Use the above situation to answer 
1. Cost of each bag 
2. Which shopkeeper is best financially?
3. Which shopkeeper is best environmentally

Let's analyze the problem step by step.

### Step 1: Setting up the Equations
Let:
- $ x $ be the cost of one polythene bag.
- $ y $ be the cost of one handmade bag.
- $ z $ be the cost of one newspaper envelope.

Given data for each shopkeeper:

1. **John:**
   - Polythene bags: 20
   - Handmade bags: 30
   - Newspaper envelopes: 40
   - Total expenditure: 250

   This gives us the equation:
   \[
   20x + 30y + 40z = 250
   \]

2. **Michael:**
   - Polythene bags: 30
   - Handmade bags: 40
   - Newspaper envelopes: 20
   - Total expenditure: 270

   This gives us the equation:
   \[
   30x + 40y + 20z = 270
   \]

3. **Christopher:**
   - Polythene bags: 40
   - Handmade bags: 20
   - Newspaper envelopes: 30
   - Total expenditure: 200

   This gives us the equation:
   \[
   40x + 20y + 30z = 200
   \]

### Step 2: Solving the System of Equations
We have the following system of linear equations:

1. $ 20x + 30y + 40z = 250 $
2. $ 30x + 40y + 20z = 270 $
3. $ 40x + 20y + 30z = 200 $

Let's solve these equations to find $ x $, $ y $, and $ z $.

I'll calculate the solution next.### Step 3: Interpretation of Results
The solution to the system of equations is:
- Cost of one polythene bag $ x $ = $1
- Cost of one handmade bag $ y $ = $5
- Cost of one newspaper envelope $ z $ = $2

### Step 4: Analyzing Financial Efficiency
Let's calculate the total expenditure for each shopkeeper using these costs.

- **John's expenditure**:
  \[
  20 \times 1 + 30 \times 5 + 40 \times 2 = 20 + 150 + 80 = 250
  \]
- **Michael's expenditure**:
  \[
  30 \times 1 + 40 \times 5 + 20 \times 2 = 30 + 200 + 40 = 270
  \]
- **Christopher's expenditure**:
  \[
  40 \times 1 + 20 \times 5 + 30 \times 2 = 40 + 100 + 60 = 200
  \]

Since we have the same expenditure as initially provided, the calculated costs are verified.

### Step 5: Environmental Consideration
For environmental impact:
- **Polythene bags** are the least environmentally friendly.
- **Handmade bags** are the most environmentally friendly.
- **Newspaper envelopes** are a moderate choice in terms of environmental impact.

Thus, the shopkeeper using the fewest polythene bags and the most handmade or newspaper bags is more environmentally friendly.

### Answers:
1. **Cost of each bag**:
   - Polythene bag: $1
   - Handmade bag: $5
   - Newspaper envelope: $2

2. **Financially Best Shopkeeper**:
   - **Christopher** is the best financially as he has the lowest total expenditure of $200.

3. **Environmentally Best Shopkeeper**:
   - **John** is the best environmentally, as he uses the fewest polythene bags (20) and the most newspaper envelopes (40).

Would you like more details or have any questions? 

Here are 5 related questions for further exploration:
1. How would the results change if the costs of the bags were different?
2. What if we introduced a new type of bag? How would that impact the analysis?
3. How do different environmental impact factors (like recyclability) affect which shopkeeper is best environmentally?
4. If John decided to reduce his polythene bag usage by half, what would be the new total expenditure?
5. What if the shopkeepers could negotiate discounts for bulk purchases? How would that affect the total costs?

**Tip**: When analyzing environmental impacts, always consider both the material used and the volume of usage.

Explore the cost analysis of polythene bags, handmade bags, and newspaper envelopes used by John, Michael, and Christopher in their supermarket. Discover who is financially and environmentally best based on their bag usage and expenditures. Suitable for advanced high school students and beyond.

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