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ANNEXURE D shows a strip chart from Pretoria to Windhoek - NSC Mathematical Literacy - Question 3 - 2017 - Paper 2
Question 3
ANNEXURE D shows a strip chart from Pretoria to Windhoek. A couple with two adult children (both females), from Johannesburg, plan a holiday and decide to go to Win... show full transcript
Worked Solution & Example Answer:ANNEXURE D shows a strip chart from Pretoria to Windhoek - NSC Mathematical Literacy - Question 3 - 2017 - Paper 2
Step 1
3.1.1 How many kilometres do they travel to Windhoek?
Answer
To find the total distance traveled from Pretoria to Windhoek using the strip chart, we add up the indicated distances:
- From Pretoria to Lobatse: 58 km
- From Lobatse to Maun: 279 km
- From Maun to Ghanzi: 455 km
- From Ghanzi to Windhoek: 455 km
- Additional distance: 280 km
- From Windhoek to the destination: 498 km
Total distance = 58 + 279 + 455 + 455 + 280 + 498 = 199 km.
Step 2
3.1.2 Apart from route A1, which other routes do they travel on from Johannesburg? Also, give the names of the countries where these routes are found.
Answer
Apart from route A1, the couple travels on the following routes:
- Route N1 in South Africa
- Route N4 in South Africa
- Route A2 in Botswana
- Route B6 in Namibia.
Step 3
3.1.3 At Moremi Wildlife Reserve there are two accommodation options: Option 1: Self-catering chalets for 4 people at R 550 per chalet per night Option 2: A bed and breakfast at R550 per person per night. The couple stated that if they choose Option 1 and do not take breakfast at R95 per person, they will be able to save R270. Show, with the necessary calculations, whether their statement is true, or not.
Answer
Let's evaluate both options:
Option 1 (Self-catering):
- Cost for accommodation = R550
- Total cost including breakfast (4 people * R95) = R380
- Total amount = R550 + R380 = R930
Option 2 (Bed and breakfast):
- Accommodation cost for 4 people = R550 * 4 = R2200
Difference: R2200 - R930 = R1270. The couple will save R270, confirming that their statement is inaccurate.
Step 4
3.1.4 At Moremi Wildlife Reserve there are 5 self-catering units accommodating 4 people and 3 self-catering units accommodating 6 people at extra cost if there are only 4 people. If all self-catering units are still available when they are making their booking, determine the probability of getting a self-catering unit at no extra cost. Give your answer to the nearest percentage.
Answer
To determine the probability of getting a self-catering unit at no extra cost:
- Total self-catering units = 5 (4-person units) + 3 (6-person units) = 8 units
- Probability of choosing any of the 5 available units = ( \frac{5}{8} ) = 62.5%.
To the nearest percentage, the probability is 63%.
Step 5
3.1.5 Mr and Mrs Smith, who are friends to the couple, are also on their way from Johannesburg to Windhoek. They take a different route and spend a night at Sun City. From Sun City they proceed to Tshane to visit some friends. After their visit, they travelled on the A2 route to Windhoek. The two families are claiming that the difference between the distance travelled by the couple with the two children and the distance travelled by Mr and Mrs Smith, is 463 km. Verify, with the necessary calculations, whether the statement is valid.
Answer
Calculating the total distances:
For the couple:
- Total distance = 58 + 279 + 455 + 455 + 280 + 498 = 199 km.
For Mr and Mrs Smith:
- Distance traveled (given): 58 + 948 + 4 + 550 + 105 + 105 + 738 = 736 km.
Finding the difference: 736 km - 199 km = 463 km.
The families' claim that their difference is 463 km is valid.