NCV 2 Mathematical Literacy Hands-On Training Case Studies Module 1

Mathematical Literacy 2Module 1

Answers to Case Studies

Case studies module 1 1Future Managers

Case Study 11. Why do you think the guest house is called

“Cloud Nine”

2. Locate both businesses on the map provided. How far away from each other are they? Why do you think that is?

Cloud nine means a state of perfect happiness

Case studies module 1 2Future Managers

Cloud nine

Squeaky

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3. Why are the rates at Cloud 9 cheaper on the weekend than during the week?

4. The rate for a double room is also less per person than for a single room. Why is that?

More people are likely to stay there during the week than the weekend

Two people staying in a double room, use up less space, and will require less cleaning and laundry

Case studies module 1 4Future Managers

5. If Cloud 9 is 80% full during the week (Mon – Thurs), how many guests in total would have stayed there during the week if you assume that each double room was occupied by two people?

=30 Double rooms x 2 people x 80%

=48 people per day

4 x 48 = 192 people per week

Case studies module 1 5Future Managers

6. How much cheaper is it to stay over weekends, Rand and percentage?

Single room:

R400-R360 = R40

R40 / R400 x 100 = 10%

Double Room:

R560 – R500 = R60

R60 / R560 x 100 = 10.71%Case studies module 1 6Future Managers

7. On average Cloud 9 has 35 guests per night over the weekend. What is the minimum number of rooms that will remain unoccupied over the weekend? Express your answer as a common fraction. What percentage is this?

Number of rooms = 35 / 2 = 17.5

Therefore 18 rooms are occupied

Expressed as a percentage:

18 / 30 x 100 = 60%

Case studies module 1 7Future Managers

8. Estimate the total number of guests staying at Cloud 9 during any particular month

Assuming different guests every night

Total guests = 4 x (4 days x guests per week day + 3 x guests per weekend day)

= 4 x (192 + 3 x 35)

= 1188 people

Therefore approximately 1200 people

Case studies module 1 8Future Managers

9. Cloud 9 is over the moon about the Soccer World Cup in 2010. The construction of the Peter Mokoba stadium is progressing well and the owners are smiling. In your opinion (estimate) how many guests should they expect during the month of September 2010?

Assuming 100% occupancy

Total guests = 4 x (4 days x 60 guests per week day + 3 x 60 guests per weekend day)

= 4 x (420)

= 1680 people

Case studies module 1 9Future Managers

10. The owners are already starting to get bookings for the world cup month, but they are unsure how much they should charge per night. One factor that they do know is that our inflation rate is about 6% per year. This is the minimum % by which rates should increase every year to maintain the same amount of profit. Advise the owners how much you think they should charge during this period. If you made certain assumptions or estimations write them down and explain them.

Case studies module 1 10Future Managers

11. What unit of measurement will you use to calculate the weight of a set of double bed linen?

12. How much do you think a set of double bed linen weighs?

grams

500 grams

Case studies module 1 11Future Managers

13. Calculate the total weight of the linen that Cloud 9 is sending to Squeaky every week and how much it will cost.

14. Following the instructions on your own box of washing powder, how many boxes of powder will they use each weekend?

Total weight = grams per bed linen x 30 rooms

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15. Calculate the total surface area of the washing powder box

Surface area of box = 2 x Area side 1 + 2 x area side 2 + 2 x area side 3

Area = length x breadth

1

2

3

Case studies module 1 13Future Managers

Case Study: Driving1. List the number of different measurement tools

that are used on this car console

•Speedometer

•Rev counter

•Economy gauge

•Clock

•Thermometer

•Odometer

•Fuel consumption meter

Case studies module 1 14Future Managers

Case Study: Driving

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Case Study: Driving2. How fast was this car driving?

3. What rate is used to measure how fast the car is driving?

55 km / h

kilometres per hour

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Case Study: Driving4. Is this a direct ratio or indirect ratio

5. Was this car driven in the morning or in the evening?

Direct. The greater the number of kilometres travelled per hour, the greater your speed

Evening (the clock says PM)

Case studies module 1 17Future Managers

Case Study: Driving4. What is the “044607” and the “735.8”

measurement on the screen?

“044607” represents the total distance travelled by the car

735.8 is a settable distance measurement, usually reset when refuelling

Case studies module 1 18Future Managers

Case Study: Driving7. Estimate how far this car can still drive before

it must fill up again.

??????

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8. What type of fraction is used to determine how much petrol is in the car’s tank?

9. What is the “outside” temperature and what does it mean?

Common fraction

18.0°C. It means the air temperature outside of the car

Case studies module 1 20Future Managers

10. What answer do you think the owner will give if a friend asks him while having a cup of coffee somewhere, “what is the mileage of your car?”

11. What is the actual RPM reading of this vehicle and what does it mean?

The answer will probably be: “44 thousand kilometres”

1800 revolutions per minute. It means that the engine turns 1800 times per minute.

Case studies module 1 21Future Managers

12. How many litres of petrol will this car need to drive 150km?

Litres of petrol = 9.6 litres / 100 km 100 x 150 km = 14.4 litres

Case studies module 1 22Future Managers