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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

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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 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

Determine, to the nearest thousand, the number of buses needed to replace the minibus taxis.

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Answer

To find the number of buses needed, divide the total number of minibus taxis by the number of taxis per bus:

Number of buses=25000013.218939.39\text{Number of buses} = \frac{250000}{13.2} \approx 18939.39

Rounding to the nearest thousand gives us:

Number of buses19000\text{Number of buses} \approx 19000

Step 2

Calculate (in euros) the difference in net worth of the minibus taxi industry using exchange rates A and B.

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Answer

Using exchange rate A:

Net Worth in Euros (A)=5000000000015.9873127524840.66\text{Net Worth in Euros (A)} = \frac{50000000000}{15.987} \approx 3127524840.66

Using exchange rate B:

Net Worth in Euros (B)=5000000000015.9667283128312422.06\text{Net Worth in Euros (B)} = \frac{50000000000}{15.966728} \approx 3128312422.06

Difference:

Difference=3128312422.063127524840.667875881.40 euros\text{Difference} = 3128312422.06 - 3127524840.66 \approx 7875881.40 \text{ euros}

Step 3

Justify which exchange rate (A or B) they should use when doing the presentation to their European clients.

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Answer

It is advisable to use exchange rate B for the presentation because it reflects a more favorable conversion rate, thus showcasing a higher net worth in euros, which can positively influence the perception of potential clients.

Step 4

Calculate the number of commuters who do NOT use a minibus taxi.

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Answer

The total number of trips made by all minibus taxis daily is 15 million. The ratio of daily commuter trips for train, bus, and minibus taxi is given:

Total ratio=4+5+7=16\text{Total ratio} = 4 + 5 + 7 = 16

To find the number of trips for each mode of transport:

Minibus taxi trips=716×15000000=6562500\text{Minibus taxi trips} = \frac{7}{16} \times 15000000 = 6562500

Thus, the number of commuters who do NOT use a minibus taxi is:

Commuters NOT using minibus taxis=150000006562500=8437500\text{Commuters NOT using minibus taxis} = 15000000 - 6562500 = 8437500

Step 5

Verify, showing ALL calculations, whether the statement is valid.

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Answer

Minibus taxis travel approximately 19 billion kilometers a year.

To find the average distance covered in one trip:

Distance per trip=1900000000024000791666.67 km/trip\text{Distance per trip} = \frac{19000000000}{24000} \approx 791666.67 \text{ km/trip}

The distance to the moon and back is: 2 x 384,402 km = 768,804 km.

Now, comparing:

Number of return trips to the moon=1900000000076880424769.56\text{Number of return trips to the moon} = \frac{19000000000}{768804} \approx 24769.56

Since 24769.56 is greater than 24000, the owner's statement is valid.

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