(Marks $$ =3 $$ ) Question 3 On a holiday touring Australia, New Zealand and Fiji, a family of five decided to take an oquivalent of PGK2, 000 abroad. The travel agent charges a commission on each currency exchange at a rate of K3 or $$ 2 \% $$ (whichever is larger) for cash and K3 or $$ 1 \% $$ (whichever is larger) for travelers Cheque. (i) They changed K200 in Australian dollar, K300 into New Zealand dollar and K150 into Fijian dollar. How much of each currency did they receive after the commission was deducted? (ii) After buying foreign currencies they changed as much as possible of the remaining money into travelers' Cheque. The smallest value of travelers' Cheque which can be paid is K10. a. How much did they exchange for travelers Cheque? b. How much commission did they pay for the Cheque? (iii) What was the total cost per person of foreign currencies and travelers Cheque? Use the following exchange rates: K1 = 2.798 Australian dollar K1 $$ =\quad $$ 2.458 New Zealand dollar Asolgomenent 1_2uantitatlive Mhethods. docx Page 1 of 2

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Alright, I need to solve this multi-part problem involving currency exchange and commissions for a family traveling in Australia, New Zealand, and Fiji. Let's break it down step by step to ensure I cover all aspects thoroughly.

**Given:**
- Total amount abroad: PGK2,000
- Travel agent's commission:
  - For cash: K3 or 2% (whichever is larger)
  - For travelers' Cheque: K3 or 1% (whichever is larger)
- Exchange rates:
  - K1 = 2.798 Australian dollars
  - K1 = 2.458 New Zealand dollars
- Smallest value of travelers' Cheque: K10

**Part (i): Calculating the amount received after commission deduction**

The family exchanged:
- K200 into Australian dollars
- K300 into New Zealand dollars
- K150 into Fijian dollars

First, I need to determine the commission for each currency exchange.

1. **Australian Dollars:**
   - Amount exchanged: K200
   - Commission: K3 or 2% of K200
   - 2% of K200 = 0.02 * 200 = K4
   - Since K3 is larger than K4, the commission is K3
   - Amount received = K200 - K3 = K197

2. **New Zealand Dollars:**
   - Amount exchanged: K300
   - Commission: K3 or 2% of K300
   - 2% of K300 = 0.02 * 300 = K6
   - Since K3 is larger than K6, the commission is K3
   - Amount received = K300 - K3 = K297

3. **Fijian Dollars:**
   - Amount exchanged: K150
   - Commission: K3 or 2% of K150
   - 2% of K150 = 0.02 * 150 = K3
   - Since K3 is equal to K3, the commission is K3
   - Amount received = K150 - K3 = K147

**Summary for Part (i):**
- Australian Dollars: K197
- New Zealand Dollars: K297
- Fijian Dollars: K147

**Part (ii): Exchanging remaining money into travelers' Cheque**

After the initial exchanges, the family has:
- K197 (Australian)
- K297 (New Zealand)
- K147 (Fijian)
- Total remaining: K197 + K297 + K147 = K641

They decide to change as much as possible into travelers' Cheque, with the smallest value being K10.

1. **Determining the amount to exchange into Cheque:**
   - Since the smallest Cheque value is K10, they can exchange up to K641 into Cheque.
   - However, the commission for Cheque is K3 or 1% of the amount exchanged.
   - To maximize the amount exchanged, they should choose the higher commission rate, which is 1%.
   - Commission = 1% of K641 = 0.01 * 641 = K6.41
   - Amount received = K641 - K6.41 = K634.59

2. **Calculating the commission paid for Cheque:**
   - Commission = K6.41

**Summary for Part (ii):**
- Amount exchanged for Cheque: K634.59
- Commission paid for Cheque: K6.41

**Part (iii): Calculating the total cost per person**

First, let's find the total amount spent on foreign currencies and travelers' Cheque.

1. **Total foreign currency exchanged:**
   - Australian: K200
   - New Zealand: K300
   - Fijian: K150
   - Total = K200 + K300 + K150 = K650

2. **Total commission paid:**
   - Cash commission: K3 (Australian) + K3 (New Zealand) + K3 (Fijian) = K9
   - Cheque commission: K6.41
   - Total commission = K9 + K6.41 = K15.41

3. **Total cost:**
   - Total foreign currency + Total commission = K650 + K15.41 = K665.41

4. **Cost per person:**
   - Total cost divided by number of people = K665.41 / 5 = K133.082

**Rounding to two decimal places:**
- Cost per person ≈ K133.08

**Summary for Part (iii):**
- Total cost per person: K133.08

**Double-Checking Calculations:**
- Ensuring that commissions are correctly applied based on the higher rate.
- Verifying the total amount exchanged and the final amount after commissions.
- Confirming the division by the number of people to find the per-person cost.

Everything seems to add up correctly, and the calculations are consistent with the given exchange rates and commission rules.

**Part (i): Amount Received After Commission Deduction** - **Australian Dollars:** K197 - **New Zealand Dollars:** K297 - **Fijian Dollars:** K147 **Part (ii): Exchanging Remaining Money into Travelers' Cheque** - **Amount Exchanged for Cheque:** K634.59 - **Commission Paid for Cheque:** K6.41 **Part (iii): Total Cost per Person** - **Total Cost per Person:** K133.08

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