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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
How many kilometres do they travel to Windhoek?
Answer
To determine the total distance travelled to Windhoek, we will sum the distances from the strip chart:
- Pretoria to Johannesburg: 58 km
- Johannesburg to Lobatse via A1: 279 km
- Lobatse to Maun: 455 km
- Maun to Moremi Wildlife Reserve: 232 km
- Moremi Wildlife Reserve to Ghanzi: 280 km
- Ghanzi to Windhoek: 498 km
Adding these distances together:
km
Thus, the couple travels a total distance of 1998 km.
Step 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
The routes taken apart from A1 are:
- Route N1: This route is in South Africa.
- Route N4: Also located in South Africa.
- Route A2: This route is in Botswana.
- Route B6: This route is in Namibia.
Step 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 have breakfast for R95 per person, they will be able to save R270. Show, with the necessary calculations, whether their statement is true, or not.
Answer
Calculating both accommodation costs:
Option 1: Self-catering
- Cost: R 550 (for 4 people)
- Breakfast cost: R 95 * 4 = R 380
- Total cost = R 550 + R 380 = R 930
Option 2: Bed and Breakfast
- Cost: R 550 * 4 = R 2200
Difference:
They stated they would save R 270, which is incorrect. Instead, they would save R 1270.
Step 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
Probability of getting a self-catering unit not incurring extra cost:
- Total self-catering units = 5 (accommodating 4 people) + 3 (accommodating 6 people) = 8
- Successful outcomes (units accommodating 4 only) = 5
Thus, the probability is: or 63%, when rounded to the nearest percentage.
Step 5
The two families are claiming that the difference between the distance travelled by the couple with the two adults 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 distance travelled by Mr and Mrs Smith:
- Route travelled includes: 58 + 494 + 105 + 105 + 738 = 736
- Total distance = 736 km
Now, calculating the difference:
- Distance travelled by the couple is 1998 km, thus:
- Difference = 1998 km - 736 km = 1262 km.
The statement claiming a difference of 463 km is not valid.