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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 first calculate the total number of minibus taxis: 250,000 taxis. Given that there is one bus for every 13.2 minibus taxis, we can calculate the number of buses as follows:
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Calculate the number of buses:
Number of buses = Total minibus taxis / Ratio of taxis to buses
Number of buses = 250,000 / 13.2
Number of buses ≈ 18,939.39
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Round to the nearest thousand:
Therefore, the number of buses needed is approximately 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
To calculate the difference in the net worth of the minibus taxi industry between exchange rates A and B:
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Convert the net worth using both exchange rates:
Net worth in euros (A) = R50 billion / 15.937
Net worth in euros (A) ≈ 3,134,146,069.78 euros
Net worth in euros (B) = R50 billion / 15.966728
Net worth in euros (B) ≈ 3,127,649,321.78 euros
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Find the difference:
Difference = Net worth (A) - Net worth (B)
Difference ≈ 3,134,146,069.78 - 3,127,649,321.78 ≈ 6,496,748 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
When deciding which exchange rate to use, Transaction Capital should consider that using a higher exchange rate (like A) will show a higher valuation of their net worth in euros, which could be advantageous in a presentation. Thus, using Exchange Rate A (1 euro = 15.937 ZAR) is preferable for presenting their business model.
Step 4
4.1.3 Calculate the number of commuters who do NOT use a minibus taxi.
Answer
To find the number of commuters who do not use a minibus taxi:
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Find the total number of commuter trips using the ratios given:
Total trips = Minibus taxi trips + Train trips + Bus trips Ratio = 4 : 5 : 7 Total parts = 4 + 5 + 7 = 16 Let x be the common factor:
Train trips = 4x, Bus trips = 5x, Minibus taxi trips = 7x
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Given minibus taxis are responsible for 15 million commuter trips:
7x = 15,000,000
x = 15,000,000 / 7 ≈ 2,142,857.14.
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Calculate other trips:
Train trips = 4x = 4 * 2,142,857.14 ≈ 8,571,428.57
Bus trips = 5x = 5 * 2,142,857.14 ≈ 10,714,285.71
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Total commuters: Total commuters ≈ 15,000,000 + 8,571,428.57 + 10,714,285.71 = 34,285,714.28
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Commuters who do NOT use a minibus taxi:
Total commuters - Minibus taxi trips ≈ 34,285,714.28 - 15,000,000 ≈ 19,285,714.28.
Therefore, approximately 19,285,714 commuters do not use a minibus taxi.
Step 5
4.1.4 Verify, showing ALL calculations, whether the statement is valid.
Answer
To verify the statement:
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Calculate the distance travelled by a minibus taxi in one year:
Minibus taxis travel 19 billion kilometres a year.
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Calculate the total distance to moon and back: Distance to the moon ≈ 384,402 km, thus round trip = 384,402 km * 2 = 768,804 km.
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Calculate the number of trips:
Total trips in one year = Total distance travelled / Distance round trip
Total trips = 19,000,000,000 / 768,804 ≈ 24,693.78 trips.
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Since 24,693.78 trips > 24,000 trips, the statement is valid.