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Zachary wants to buy exactly 73 pencils, and the pricing options are as follows:

- **40p per pencil** when bought individually.
- **£2 for a pack of 10 pencils**, which means 20p per pencil when bought in packs.

To minimize the cost, we should try to buy as many packs of 10 pencils as possible and buy the remaining pencils individually.

### Step-by-step solution:

1. **Buy packs of 10 pencils**:  
   \( \left\lfloor \frac{73}{10} \right\rfloor = 7 \) packs of 10 pencils.  
   Cost for 7 packs:  
   \( 7 \times 2 = £14 \)  
   This gives Zachary \( 7 \times 10 = 70 \) pencils.

2. **Remaining pencils**:  
   Zachary still needs \( 73 - 70 = 3 \) pencils.  
   Buying 3 individual pencils at 40p each will cost:  
   \( 3 \times 0.40 = £1.20 \).

3. **Total cost**:  
   Total cost for 7 packs and 3 individual pencils:  
   \( 14 + 1.20 = £15.20 \).

### Final Answer:  
The lowest amount Zachary can pay is **£15.20**.

Would you like further details on any part of this process or have any questions? Here are some related questions to expand on this:

1. How would the total change if Zachary needed 50 pencils instead of 73?
2. What is the cost difference per pencil when buying individually versus in packs?
3. How many pencils can Zachary buy with £10?
4. What is the maximum number of pencils Zachary can buy with £20?
5. If the price of the individual pencil increases to 50p, what would the new total be for 73 pencils?

**Tip:** When faced with bulk pricing, always check if combining bulk and individual items gives a better deal!

Zachary wants to buy exactly 73 pencils. What is the lowest amount he can pay? Give your answer in pounds (£).

Learn how to calculate the lowest cost Zachary can pay to buy exactly 73 pencils. The solution uses both bulk and individual pricing strategies. Suitable for students in Grades 5-7.

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