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The South African taxi association, Transaction Capital, published its results for the current state of the South African minibus taxi industry for the year ended September 2019 - NSC Mathematical Literacy - Question 4 - 2021 - Paper 2
Question 4
The South African taxi association, Transaction Capital, published its results for the current state of the South African minibus taxi industry for the year ended Se... show full transcript
Worked Solution & Example Answer:The South African taxi association, Transaction Capital, published its results for the current state of the South African minibus taxi industry for the year ended September 2019 - NSC Mathematical Literacy - Question 4 - 2021 - Paper 2
Step 1
4.1.1 Determine, to the nearest thousand, the number of buses needed to replace the minibus taxis.
Answer
To find the number of buses needed, we divide the total number of minibus taxis by the number of minibus taxis per bus:
Number of buses = ( \frac{250,000}{13.2} \approx 18,939.39 )
Rounding to the nearest thousand gives:
Number of buses needed = 19,000.
Step 2
4.1.2 (a) Calculate (in euros) the difference in net worth of the minibus taxi industry using exchange rates A and B.
Answer
Using Exchange Rate A:
Net worth in euros = ( \frac{50,000,000,000}{15.97} \approx 3,129,847,033.88 \ euros )
Using Exchange Rate B:
Net worth in euros = ( \frac{50,000,000,000}{15.966728} \approx 3,129,451,682.53 \ euros )
Difference = ( 3,129,847,033.88 - 3,129,451,682.53 \approx 395,351.35 \ euros )
Step 3
4.1.2 (b) Justify which exchange rate (A or B) they should use when doing the presentation to their European clients.
Answer
Transaction Capital should use Exchange Rate B because it is more favorable for converting ZAR to euros, providing a higher euro amount for their net worth when discussing with European businessmen.
Step 4
4.1.3 Calculate the number of commuters who do NOT use a minibus taxi.
Answer
The total number of commuter trips is 15,000,000 daily. The ratio of trips is train : bus : minibus taxi = 4 : 5 : 7. Total parts = 4 + 5 + 7 = 16.
Commuter trips using minibus taxis = ( \frac{7}{16} \times 15,000,000 = 6,562,500 )
Commuters not using minibus taxis = 15,000,000 - 6,562,500 = 8,437,500.
Step 5
4.1.4 Verify, showing ALL calculations, whether the statement is valid.
Answer
Total distance travelled by minibus taxis in a year:
Distance per trip = 19,000,000,000 km/year
Trips to the moon and back = 384,402 km (one way) * 2 = 768,804 km.
Number of trips to the moon and back = ( \frac{19,000,000,000}{768,804} \approx 24,705 )
The statement is valid as it confirms that minibus taxis travel more than 24,000 trips to the moon and back.