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The cost of fuel in South Africa is made up of the basic fuel price and other costs, as shown in the infographics below - NSC Mathematical Literacy - Question 2 - 2017 - Paper 2
Question 2
The cost of fuel in South Africa is made up of the basic fuel price and other costs, as shown in the infographics below. **COASTAL FUEL PRICE** Cost per litre fuel,... show full transcript
Worked Solution & Example Answer:The cost of fuel in South Africa is made up of the basic fuel price and other costs, as shown in the infographics below - NSC Mathematical Literacy - Question 2 - 2017 - Paper 2
Step 1
Explain why the inland and coastal fuel prices are not the same.
Answer
The inland fuel prices are typically higher due to increased transportation and storage costs, as well as the remoteness of certain areas from refineries. Additionally, fuel levies may also reflect the accompanying infrastructure costs required for distribution.
Step 2
Step 3
Verify, showing ALL calculations, whether Jabu's statement is valid.
Answer
To calculate Jabu's fuel consumption:
-
Find total litres consumed for inland travel:
Total distance = 1250 km Fuel consumption = 3.7 L/100 km
Total litres for inland = (\frac{1250}{100} \times 3.7 = 46.25 \text{ litres})
-
Cost of fuel for inland:
Cost per litre inland = R11.54
Total cost for inland = 46.25 L (\times R11.54 = R534.94)
-
Similarly, find total litres for coastal travel:
Cost per litre coastal = R11.26
Total cost for coastal = 46.25 L (\times R11.26 = R520.91)
-
Difference = R534.94 - R520.91 = R14.03
Since the difference is not R50, Jabu's statement is NOT valid.
Step 4
Determine the percentage increase in the income received from the fuel levies for 2017/2018.
Answer
The percentage increase is calculated by:
[\text{Percentage Increase} = \frac{(R70.9 \text{ billion} - R54 \text{ billion})}{R54 \text{ billion}} \times 100] [= \frac{16.9}{54} \times 100 = 31.296% \approx 31.3%]
Step 5
Calculate (to the nearest billion rand) the total national budgeted income for 2017/2018.
Answer
Using the given ratio:
Let Total Budgeted Income = x.
Using the formula: [x = R70.9 \text{ billion} \times \frac{118}{7}]
After calculations: [x = R195.17 \text{ billion} + R70.9 \text{ billion} = R266.07\text{ billion}] Thus, rounding to the nearest billion gives us R266 billion.
Step 6
Identify the country that is the median of the percentage mean income spent on fuel.
Answer
To identify the median, you must list the countries in the order of their percentage mean income spent on fuel and find the middle value. Assuming the values have been calculated previously, the country at the median position (6th in a list of 11) is India.
Step 7
Determine the interquartile range of the mean income spent on fuel.
Answer
The interquartile range (IQR) is calculated as: [\text{IQR} = Q3 - Q1] Where Q3 is the third quartile and Q1 is the first quartile of the income percentages. Assuming the percentiles are already calculated, you will subtract the values of Q1 from Q3.
Step 8
Give ONE valid reason why the sample is considered unbiased with respect to the percentage mean income spent on fuel.
Answer
The sample is considered unbiased because it includes countries from various continents and economic backgrounds, ensuring a diverse representation of the global fuel pricing context.
Step 9
Determine the difference (in Russian rouble) between the mean daily wage in India and South Africa.
Answer
Calculating the difference involves the mean daily wages:
- South Africa: R237.35 (about R905.92 Rouble)
- India: R236.51 (about R905.52 Rouble)
- Difference = R905.92 - R905.52 = R0.4 Russian Rouble.
Step 10
Verify, showing ALL calculations, whether the learner's solution is correct.
Answer
To verify the learner's calculation, check each step: 425.52 - 21.44 = 404.08 Russian Rouble should yield the correct value, which must then be converted back to Rand correctly using the conversion factors indicated. Each step needs to corroborate the final result they provided.