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Keitumetse is a South African student who is on holiday in Australia - NSC Mathematical Literacy - Question 4 - 2020 - Paper 2
Question 4
Keitumetse is a South African student who is on holiday in Australia. He went to the Lawrence Theatre to attend a musical concert. ANNEXURE D shows the seating arra... show full transcript
Worked Solution & Example Answer:Keitumetse is a South African student who is on holiday in Australia - NSC Mathematical Literacy - Question 4 - 2020 - Paper 2
Step 1
4.1.1 Determine, as a percentage, the probability of randomly selecting an odd numbered seat for a disabled person from all the seats in the theatre.
Answer
To determine the probability of randomly selecting an odd numbered seat for a disabled person, we first need the total number of seats available in the theatre. If we assume the seating arrangement allows for a total of 100 seats, and half of them are odd numbered, then:
Total odd numbered seats = 100 / 2 = 50.
If there are 10 seats allocated for disabled persons, considering a uniform distribution:
Probability = (Number of odd numbered seats allocated to disabled) / (Total odd numbered seats)
Assuming 5 odd numbered seats are for disabled persons, the probability would be:
Probability = 5 / 50 = 0.1
To express this as a percentage: 0.1 x 100 = 10%.
Step 2
4.1.2 Identify the row and seat number for a person who is seated as follows: • In Section B • Fourth row from the stage • In the middle seat
Answer
In Section B, the fourth row from the stage typically corresponds to a row number of 4. The middle seat in any row can be calculated based on the total number of seats in that row. Assuming there are 10 seats in Section B, the middle seat would be seat number 5. Therefore, the answer is Row 4, Seat 5.
Step 3
4.1.3 Describe the shortest possible path Keitumetse would follow to reach A11.
Answer
To reach A11 from D7, Keitumetse would first move from row D to row A. This can be achieved by moving towards the left to the nearest aisle, then proceeding to the front row A. Once at row A, Keitumetse should walk down to seat A11. The steps are therefore:
- Move left to the aisle from D7.
- Proceed to the front row A.
- Walk to seat A11.
Step 4
4.1.4 Verify, with calculations, whether the claim that an amount of exactly $5 796, excluding Australian VAT, was collected on that day is CORRECT.
Answer
To verify the claim, we will first calculate the expected total collections from Sections A, B, and C:
Calculating total attendance:
- Adults = 53 + 57 + 40 = 150
- Students = 15 + 32 + 10 = 57
- Children = 9 + 15 + 5 = 29
Calculating ticket sales:
- Adult tickets = 150 x 34.70 = $5,205
- Student tickets = 57 x 30.50 = $1,734.50
- Children tickets = 29 x 17.60 = $510.40
Total collections before VAT = 1,734.50 + 7,449.90
Including VAT at 10% should be: Total including VAT = 8,194.89
Since the claim suggested $5,796 without VAT is based on faulty calculations, the claim is incorrect.
Step 5
4.1.5 Calculate how much the ticket costs in South African rand.
Answer
Keitumetse bought a ticket for a Friday show, and according to Table 5, the ticket price for a student is $30.50 AUD.
Using the exchange rate provided: 1 AUD = 14.43 ZAR
Calculating the conversion: Cost in ZAR = 30.50 AUD x 14.43 ZAR/AUD = 440.315 ZAR
Therefore, the ticket costs approximately 440.32 ZAR.