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The problem asks whether it's cheaper to buy packs of 6 bottles or packs of 9 bottles, given that:

- A pack of 6 bottles costs £4.
- A pack of 9 bottles costs £5.
- The school needs enough water for 268 pupils.

### Step-by-step analysis:
1. **Cost per bottle for each pack**:
   - Pack of 6 bottles: £4 / 6 bottles = **£0.67 per bottle**.
   - Pack of 9 bottles: £5 / 9 bottles = **£0.56 per bottle**.

2. **Which is cheaper**: Since £0.56 per bottle (9-bottle pack) is less than £0.67 per bottle (6-bottle pack), the pack of 9 bottles is cheaper.

3. **How much cheaper**: The difference between the two costs per bottle is:
   - £0.67 - £0.56 = **£0.11** cheaper per bottle with the 9-bottle pack.

### Calculating Total Packs Needed:
- The school needs water for 268 pupils, so 268 bottles are required.
   - For 6-bottle packs: \( \frac{268}{6} \approx 44.67 \) → 45 packs (rounding up).
   - For 9-bottle packs: \( \frac{268}{9} \approx 29.78 \) → 30 packs (rounding up).

### Total Cost:
- **Cost for 6-bottle packs**: 45 packs × £4 = **£180**.
- **Cost for 9-bottle packs**: 30 packs × £5 = **£150**.

Thus, the pack of 9 bottles saves **£30**.

Would you like more details on this or have any specific questions?

### 5 Relative Questions:
1. How would the calculations change if the total number of pupils was different?
2. Can you find the total cost if you bought mixed packs of 6 and 9 bottles?
3. What is the price difference per bottle if the pack sizes were larger?
4. How would the calculation be affected if the price per pack was changed?
5. Can you calculate the savings if only a portion of the students need bottles?

### Tip:
Always compare the cost per unit (in this case, per bottle) to identify the most cost-effective option.

Is it cheaper to buy only packs of 6 bottles or packs of 9 bottles for 268 pupils, given that a pack of 6 bottles costs £4 and a pack of 9 bottles costs £5?

This problem involves determining whether it's cheaper to buy packs of 6 or 9 bottles for 268 pupils. By comparing the cost per bottle and calculating the total cost for each option, we find that the 9-bottle packs are cheaper. The difference in cost per bottle is 11p, and using packs of 9 bottles saves £30 in total.

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