Sure, let's break down the steps Liam could have taken to pay exactly £26.55 using two notes and four coins.
### 1. Identify the Notes
Liam has the option to use the following notes:
- £20
- £10
- £5
Given the total price of £26.55, the best way to get as close as possible to this amount with two notes is to use:
- One £20 note
- One £5 note
This gives us a subtotal of:
[tex]\[ £20 + £5 = £25 \][/tex]
### 2. Calculate the Remaining Amount
The remaining amount Liam needs to pay using coins is:
[tex]\[ £26.55 - £25 = £1.55 \][/tex]
### 3. Identify the Coins
Liam can use the following coins:
- £2
- £1
- 50p (0.50 pounds)
- 20p (0.20 pounds)
- 10p (0.10 pounds)
- 5p (0.05 pounds)
To pay the remaining £1.55, we aim to use the highest denomination coins first.
- £2 coin: He can't use this as it exceeds £1.55.
- £1 coin: Using one £1 coin reduces his remaining amount to:
[tex]\[ £1.55 - £1 = £0.55 \][/tex]
Next, we break down the remaining £0.55 into proper coins.
- 50p coin: Using one 50p coin reduces his remaining amount to:
[tex]\[ £0.55 - £0.50 = £0.05 \][/tex]
Finally, we use the smallest coin to cover the remaining amount.
- 5p coin: Using one 5p coin:
[tex]\[ £0.05 - £0.05 = £0 \][/tex]
### 4. List of Notes and Coins
Therefore, Liam pays a total of £26.55 using:
- Notes:
- One £20 note
- One £5 note
- Coins:
- One £1 coin
- One 50p coin
- One 5p coin
When listed from highest to lowest, Liam uses:
- Two notes: £20 and £5
- Four coins: £1, 50p, 50p, and 5p
### 5. Verification
Total amount from notes: [tex]\[ £20 + £5 = £25 \][/tex]
Total amount from coins: [tex]\[ £1 + £0.50 + £0.50 + £0.05 = £1.55 \][/tex]
Overall total:
[tex]\[ £25 + £1.55 = £26.55 \][/tex]
So the notes and coins Liam could have used to exactly pay £26.55 are:
- Notes: £20, £5
- Coins: £1, 50p, 50p, 5p
