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Pablo, a Mexican student, is studying in the United Kingdom (UK) - NSC Mathematical Literacy - Question 3 - 2016 - Paper 2

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Pablo, a Mexican student, is studying in the United Kingdom (UK). He plans to meet his family in Las Vegas, USA, to attend a boxing match. He will travel by air from... show full transcript

Worked Solution & Example Answer:Pablo, a Mexican student, is studying in the United Kingdom (UK) - NSC Mathematical Literacy - Question 3 - 2016 - Paper 2

Step 1

3.1.1 Determine the total number of Economy Plus seats.

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Answer

The total number of Economy Plus seats can be determined by inspecting the seating chart provided in ANNEXURE C. The number of seats allocated to this category should be counted directly from the diagram.

Step 2

3.1.2 Determine the simplified ratio of the number of Business Class seats to Economy Class seats.

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Answer

From the seating chart, we find the number of Business Class seats is 26 and Economy Class seats is 80. The simplified ratio can be calculated as follows:

Ratio=2680=1340\text{Ratio} = \frac{26}{80} = \frac{13}{40}.

Step 3

3.1.3 Give a detailed description of the route a passenger in seat 2K will take.

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The passenger should first get up and turn left, walking down the aisle towards the galley/kitchen. Upon reaching the first galley area, they should then turn right to proceed down the next aisle. Continuing forward, they will walk straight until they reach row 38. At row 38, the passenger's friend is seated on the right-hand side.

Step 4

3.1.4 Determine the number of Business Class passengers.

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Answer

Based on the seating chart from ANNEXURE C, there are 26 Business Class seats. Assuming all seats are filled, there will be 26 Business Class passengers.

Step 5

3.1.5 Determine the probability (as a percentage) that this passenger did not have an aisle seat.

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Answer

The number of aisle seats should be considered first. If we count the seats in Business Class and assume 2 of the 26 seats are aisle seats, the probability that a passenger in seat 2K does not have an aisle seat is:

Probability=26226×100=34.62%\text{Probability} = \frac{26 - 2}{26} \times 100 = 34.62\%.

Step 6

3.2 Calculate the average speed, in knots.

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Answer

First, calculate the distance travelled in kilometers: 522,086 km. The flight time was from 17:14 to 04:11, which is 10.95 hours. The average speed in km/h can be calculated using:

Average Speed=DistanceTime=522,086 km10.95 h=47,728.96 km/h\text{Average Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{522,086 \text{ km}}{10.95 \text{ h}} = 47,728.96 \text{ km/h}.

To convert km/h to knots, use the conversion factor (1 knot = 1.852 km/h):

Average Speed in knots=47,728.961.85225,755.23extknots\text{Average Speed in knots} = \frac{47,728.96}{1.852} \approx 25,755.23 ext{ knots}.

Step 7

3.3.1 Calculate the missing values A, B and C.

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Answer

From Table 3, use the production cost formula:

  • For A (800 belts):

Total cost=27,000+75×800=87,000\text{Total cost} = 27,000 + 75 \times 800 = 87,000

  • For B (400 belts):

Total cost=27,000+75×400=57,000\text{Total cost} = 27,000 + 75 \times 400 = 57,000

  • For C (total income from belts):

Total income=250×400=100,000\text{Total income} = 250 \times 400 = 100,000.

Step 8

3.3.2 Determine the total income if the WBC sells 800 belts and 1,000 T-shirts.

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Answer

The total income from the belts is:

Income from belts=250×800=200,000\text{Income from belts} = 250 \times 800 = 200,000

And from T-shirts:

Income from T-shirts=175×1,000=175,000\text{Income from T-shirts} = 175 \times 1,000 = 175,000

Total Income = 200,000 + 175,000 = 375,000.

Step 9

3.3.3 The straight-line graphs.

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Answer

Graph points for selling belts will be created for the axes provided. For T-shirts, the income and production cost must be plotted accordingly to form the required graph.

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