Freya is going on holiday to South Africa.

She is going to exchange 300 euros
for some South African rand.

Freya compares the foreign currency exchange deals on offer at a building society and a supermarket.

The building society has an exchange rate of 1 euro = 23.3 rand
.
It charges a commission fee of %4
per transaction.

The supermarket has an exchange rate of 1 euro = 23.1 rand
.
It charges commission at a flat rate of 7 euro
per transaction.

Work out the difference in the total amount of holiday cash she can get from both deals.
Give your answer in South African rand.

To determine the difference in the total amount of holiday cash Freya can get from both the building society and the supermarket, we need to calculate how much South African rand (ZAR) she will receive from each option, taking into account the respective exchange rates and commission fees.

### 1. Building Society Calculation:
- **Exchange rate**: 1 euro = 23.3 rand
- **Commission fee**: 4% of the total transaction

First, calculate how much rand Freya would get before commission:
\[
\text{Rand before commission} = 300 \times 23.3 = 6990 \text{ rand}
\]
Now calculate the commission fee (4% of 300 euros):
\[
\text{Commission fee in euros} = 0.04 \times 300 = 12 \text{ euros}
\]
Convert the commission fee into rand:
\[
\text{Commission fee in rand} = 12 \times 23.3 = 279.6 \text{ rand}
\]
Subtract the commission fee from the total amount in rand:
\[
\text{Rand after commission} = 6990 - 279.6 = 6710.4 \text{ rand}
\]

### 2. Supermarket Calculation:
- **Exchange rate**: 1 euro = 23.1 rand
- **Flat commission**: 7 euros per transaction

First, subtract the flat commission from the 300 euros to get the amount left for the currency exchange:
\[
\text{Euros after commission} = 300 - 7 = 293 \text{ euros}
\]
Now, calculate how much rand Freya would get with the remaining 293 euros:
\[
\text{Rand after commission} = 293 \times 23.1 = 6768.3 \text{ rand}
\]

### 3. Calculate the difference:
Now that we have the total amounts of rand Freya would get from each option:
- **Building society**: 6710.4 rand
- **Supermarket**: 6768.3 rand

The difference between the two amounts is:
\[
\text{Difference} = 6768.3 - 6710.4 = 57.9 \text{ rand}
\]

### Conclusion:
Freya would receive **57.9 rand more** if she exchanged her money at the supermarket instead of the building society.

---
Would you like more details on how we worked with percentages, currency exchange, or flat fees? Here are 5 related questions to explore:

1. How does the percentage commission affect currency exchange rates in general?
2. What happens if the commission rate at the building society increases to 5%?
3. How would a higher flat fee from the supermarket impact Freya’s exchange?
4. What if Freya had 500 euros to exchange? How would this change the outcome?
5. Could Freya benefit from a different exchange service with no commission?

**Tip**: Always compare both commission fees and exchange rates when exchanging money, as either factor can significantly impact the amount you receive.

Freya is going on holiday to South Africa. She is going to exchange 300 euros for some South African rand. Freya compares the foreign currency exchange deals on offer at a building society and a supermarket. The building society has an exchange rate of 1 euro = 23.3 rand. It charges a commission fee of 4% per transaction. The supermarket has an exchange rate of 1 euro = 23.1 rand. It charges commission at a flat rate of 7 euro per transaction. Work out the difference in the total amount of holiday cash she can get from both deals. Give your answer in South African rand.

Compare foreign currency exchange rates between a building society and a supermarket for 300 euros to South African rand. Learn how commission fees and exchange rates affect the total holiday cash. Detailed step-by-step calculations provided. Suitable for students in Grades 9-12.

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