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To solve this problem, we need to determine how Lewis can buy 38 cartons of juice for the least amount of money. He has two options:

1. **Buying individual cartons** at 45p each.
2. **Buying packs of 4 cartons** for £1.56.

### Step-by-Step Solution

1. **Calculate the Cost per Carton in a Pack**:
   - A pack of 4 cartons costs £1.56.
   - Cost per carton in a pack = \( \frac{1.56}{4} = 0.39 \) pounds, or 39p per carton.
   - Since 39p per carton is cheaper than 45p per individual carton, Lewis should prioritize buying packs of 4 to minimize cost.

2. **Determine the Maximum Packs of 4 Cartons for 38 Cartons**:
   - \( 38 \div 4 = 9 \) packs with a remainder of 2.
   - So, he can buy 9 packs of 4 cartons, which gives him \( 9 \times 4 = 36 \) cartons.
   - This leaves him needing \( 38 - 36 = 2 \) additional cartons.

3. **Calculate the Cost**:
   - **Cost of 9 packs**: \( 9 \times 1.56 = 14.04 \) pounds.
   - **Cost of 2 individual cartons**: \( 2 \times 0.45 = 0.90 \) pounds.
   - **Total Cost**: \( 14.04 + 0.90 = 14.94 \) pounds.

### Answer
Lewis will spend **£14.94** to buy 38 cartons of juice for the least amount of money.

Would you like more details on any step?

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Here are 5 related questions:
1. What if Lewis needed 40 cartons instead of 38?
2. How would the cost change if packs of 6 cartons were available?
3. How many individual cartons can Lewis buy with £5?
4. What if the price per individual carton was reduced to 40p?
5. How would the minimum cost change if he needed only 20 cartons?

**Tip**: Always check unit prices when deciding between bulk packs and individual items to ensure you're choosing the most economical option.

When class 11Y1 found that their favourite teacher, Mr Musson, was leaving, they decided to organise a party for him. Lewis, one of the class members, wants to buy 38 cartons of juice. He can buy a single carton of juice for 45p. He can buy a pack of 4 cartons for £1.56. Lewis buys all the cartons he needs for the least possible amount of money. How much did he spend?

Learn how to minimize the cost of buying 38 cartons of juice by comparing bulk pack prices and individual prices. Find out the most economical way to purchase the juice using division and multiplication concepts. Suitable for students in Grades 6-8.

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