1. Rowan lives in New Zealand. He is coming to Wales on holiday. The currency used in New Zealand is the New Zealand dollar ($). 1 New Zealand dollar = 100 cents. The conversion rate at the exchange shop is $1 = £0.53. The exchange shop only has £10 and £20 notes. Rowan only has $550 saved. He wants to exchange as close to $550 as possible. He asks for as few notes as possible. Calculate: how many of each British note Rowan gets, how much he pays for his currency, correct to the nearest cent. You must show all your working.
To exchange $550 into British pounds, we need to use the conversion rate of $1 = £0.53.
First, let's calculate how much money Rowan will get in British pounds.
550 dollars * £0.53/1 dollar = £291.50
Now, let's determine how many notes Rowan will receive.
The exchange shop only has £10 and £20 notes. Let's start with the £20 notes.
£291.50 / £20 = 14.575
Since we can't have a fraction of a note, Rowan will receive 14 £20 notes.
Now, let's calculate how much Rowan will pay for his currency exchange.
14 * £20 = £280
Rowan will pay £280 for his currency exchange.
However, we still have £11.50 remaining to exchange. Let's see how many £10 notes we need.
£11.50 / £10 = 1.15
Since we can't have a fraction of a note, Rowan will receive 1 £10 note.
Now, let's recalculate how much Rowan will pay for his currency exchange.
14 * £20 + 1 * £10 = £300
Rowan will pay £300 for his currency exchange to get as close to $550 as possible.
To calculate how many of each British note Rowan gets and how much he pays for his currency, we can follow these steps:
Step 1: Find the exchange rate from New Zealand dollars to British pounds.
Given that $1 = £0.53, we can calculate the exchange rate as follows:
$550 * £0.53 = £291.50
Step 2: Determine how many £20 notes Rowan can get.
Since the exchange shop only has £10 and £20 notes, we can calculate the number of £20 notes as follows:
£291.50 ÷ £20 = 14.575
Since we want to use as few notes as possible, Rowan can only get 14 £20 notes.
Step 3: Determine how many £10 notes Rowan can get.
To find out how many £10 notes Rowan can get, we need to calculate the remaining amount after getting the £20 notes.
Remaining amount = £291.50 - (14 * £20) = £291.50 - £280 = £11.50
Since the exchange shop only has £10 notes, Rowan can only get 1 £10 note.
Therefore, Rowan will get 14 £20 notes and 1 £10 note.
Step 4: Calculate the total cost of the currency.
To find the total cost of the currency, we can multiply the number of each note by its value:
(14 * £20) + (1 * £10) = £280 + £10 = £290
So, Rowan will pay £290 for his currency.
To calculate the number of each British note Rowan gets and how much he pays for the currency, we need to follow these steps:
Step 1: Calculate the exchange rate from NZD to GBP:
Since $1 = £0.53, we can express the exchange rate as NZD to GBP as 1 NZD = 0.53 GBP.
Step 2: Calculate the amount of GBP Rowan will get:
Rowan has $550 NZD saved. We can multiply this by the exchange rate to get the equivalent amount in GBP:
550 NZD * 0.53 GBP/NZD = 291.5 GBP
Step 3: Determine the number of £20 notes:
Rowan wants to get as few notes as possible, so we will start with the highest denomination note, which is £20. Divide the amount of GBP he will receive by the value of each £20 note:
291.5 GBP / 20 GBP/note = 14.575 notes
Since we can't have fractional notes, we need to round down to the nearest whole number. Rowan will receive 14 £20 notes.
Step 4: Calculate the remaining amount of GBP after using the £20 notes:
To find the remaining amount of GBP, we subtract the value of the notes Rowan received:
291.5 GBP - (14 notes * 20 GBP/note) = 291.5 GBP - 280 GBP = 11.5 GBP
Step 5: Determine the number of £10 notes:
Since we don't have any £10 notes yet, we will now calculate how many £10 notes Rowan will receive. Divide the remaining amount of GBP by the value of each £10 note:
11.5 GBP / 10 GBP/note = 1.15 notes
Again, we need to round down to the nearest whole number. Rowan will receive 1 £10 note.
Step 6: Calculate the total amount Rowan will pay for the currency:
To find the total amount Rowan will pay in GBP, we need to multiply the number of each note by its value and add them together. Let's calculate it:
(14 notes * £20/note) + (1 note * £10/note) = £280 + £10 = £290
Therefore, Rowan will pay a total of £290 for his currency.
In summary, Rowan will receive 14 £20 notes and 1 £10 note. He will pay a total of £290 for his currency.
Please note that rounding errors may occur in the calculations, so the final amounts may not be exact to the nearest cent.