Answer:
the two possible amounts of change are £3.01 and 39p.
Explanation:
Let's start by finding the possible prices for the pie after the 24% tip has been added. We know that the total price must be an exact number of pence, which means that the price before the tip must have been a multiple of 25 (since there are 100 pence in a pound).
The possible prices before the tip, between £1.30 and £2.99, are:
£1.30 = 130p
£1.31 = 131p
...
£2.98 = 298p
£2.99 = 299p
To find the prices after the 24% tip, we multiply each of these values by 1.24:
130p * 1.24 = 161.2p = £1.612 = £1.61 (rounded to 2 decimal places)
131p * 1.24 = 162.44p = £1.6244 = £1.62
...
298p * 1.24 = 369.52p = £3.6952 = £3.70
299p * 1.24 = 370.76p = £3.7076 = £3.71
So the possible prices for the pie after the 24% tip are between £1.61 and £3.71.
Next, we need to find the possible amounts of change that would result from paying with a £5 note and receiving the fewest possible coins. We can do this by subtracting the total cost of the pie from £5 and seeing which combinations of coins add up to that amount.
Let's start with the lowest possible price for the pie, £1.61. If we add 24% to that, the total cost is £1.99 (rounded to 2 decimal places), which means our change is £3.01. The fewest possible coins we could receive for that amount are:
£2 coin
£1 coin
1p coin
So the first possible combination of change is:
£2 + £1 + 1p = £3.01
Now let's try the highest possible price for the pie, £3.71. If we add 24% to that, the total cost is £4.61, which means our change is 39p. The fewest possible coins we could receive for that amount are:
20p coin
10p coin
5p coin
2p coin
2p coin
So the second possible combination of change is:
20p + 10p + 5p + 2p + 2p = 39p
Therefore, the two possible amounts of change are £3.01 and 39p.