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.

We can solve this step by step for both the building society and the supermarket, then calculate the difference in South African rand (ZAR) Freya would receive.

### 1. Building Society Deal:
- Exchange rate: \( 1 \, \text{euro} = 23.3 \, \text{rand} \)
- Commission: 4% of the total amount of euros exchanged.

#### Step 1: Calculate the commission charged.
The commission is 4% of 300 euros:
\[
\text{Commission} = 300 \times \frac{4}{100} = 12 \, \text{euros}.
\]

#### Step 2: Calculate the net euros available after commission.
The amount left after subtracting the commission:
\[
\text{Net euros} = 300 - 12 = 288 \, \text{euros}.
\]

#### Step 3: Calculate the amount of rand received.
At the exchange rate of 1 euro = 23.3 rand, the total amount of rand Freya would receive is:
\[
\text{Rand from building society} = 288 \times 23.3 = 6710.4 \, \text{rand}.
\]

---

### 2. Supermarket Deal:
- Exchange rate: \( 1 \, \text{euro} = 23.1 \, \text{rand} \)
- Flat commission: 7 euros.

#### Step 1: Calculate the net euros available after commission.
The amount left after subtracting the flat commission:
\[
\text{Net euros} = 300 - 7 = 293 \, \text{euros}.
\]

#### Step 2: Calculate the amount of rand received.
At the exchange rate of 1 euro = 23.1 rand, the total amount of rand Freya would receive is:
\[
\text{Rand from supermarket} = 293 \times 23.1 = 6778.3 \, \text{rand}.
\]

---

### 3. Calculate the difference:
Now, we calculate the difference between the two amounts:
\[
\text{Difference} = 6778.3 - 6710.4 = 67.9 \, \text{rand}.
\]

### Final Answer:
Freya will get **67.9 rand** more from the supermarket deal.

---

Would you like further details or have any questions? Here are some related questions you might consider:
1. How much would Freya receive if she exchanged 500 euros?
2. What would the commission be if the building society reduced the rate to 2%?
3. If the supermarket had a commission rate of 5 euros instead, what would be the difference?
4. How would the difference change if the building society increased its exchange rate to 23.5 rand per euro?
5. What would the total cost be if Freya used both the building society and the supermarket for equal amounts?

**Tip:** Always compare not just the exchange rate but also commissions when dealing with currency exchanges!

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 euros 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.

Find out how to calculate the best currency exchange deal for Freya who is exchanging 300 euros to South African rand. This problem explores exchange rates, commission fees, and provides a step-by-step solution to determine the difference in cash she receives between a supermarket and a building society. Suitable for students in Grades 6-8.

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