This document contains a case study about a guest house called Cloud Nine and examples and questions related to mathematical literacy concepts like rates, percentages, ratios, fractions, measurement, and data interpretation. Some key details include that Cloud Nine charges lower rates on weekends to attract more guests, a double room can accommodate two people more economically than a single room, and the owners are making plans and calculations for an expected busy period during the 2010 Soccer World Cup when occupancy could reach 100%.

1. Mathematical Literacy 2
Module 1
Answers to Case Studies
Case studies module 1 Future Managers 1

2. Case Study 1
1. Why do you think the guest house is called
“Cloud Nine”
Cloud nine means a state of perfect happiness
4. Locate both businesses on the map provided.
How far away from each other are they? Why
do you think that is?
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3. Cloud nine
Squeaky
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4. 1. Why are the rates at Cloud 9 cheaper on the
weekend than during the week?
More people are likely to stay there during the
week than the weekend
5. The rate for a double room is also less per
person than for a single room. Why is that?
Two people staying in a double room, use up
less space, and will require less cleaning and
laundry
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5. 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
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6. 1. 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%
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7. 1. 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%
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8. 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
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9. 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
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10. 1. 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.
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11. 1. What unit of measurement will you use to
calculate the weight of a set of double bed
linen?
grams
3. How much do you think a set of double bed
linen weighs?
500 grams
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12. 1. Calculate the total weight of the linen that
Cloud 9 is sending to Squeaky every week and
how much it will cost.
Total weight = grams per bed linen x 30 rooms
4. Following the instructions on your own box of
washing powder, how many boxes of powder
will they use each weekend?
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13. 1. 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
2
3
1
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14. Case Study: Driving
1. 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
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15. Case Study: Driving
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16. Case Study: Driving
1. How fast was this car driving?
55 km / h
4. What rate is used to measure how fast the car is
driving?
kilometres per hour
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17. Case Study: Driving
4. Is this a direct ratio or indirect ratio
Direct. The greater the number of kilometres
travelled per hour, the greater your speed
5. Was this car driven in the morning or in the
evening?
Evening (the clock says PM)
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18. Case Study: Driving
4. 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
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19. Case Study: Driving
7. Estimate how far this car can still drive before
it must fill up again.
??????
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20. 1. What type of fraction is used to determine how
much petrol is in the car’s tank?
Common fraction
4. What is the “outside” temperature and what
does it mean?
18.0°C. It means the air temperature outside
of the car
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21. 1. 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?”
The answer will probably be: “44 thousand
kilometres”
11. What is the actual RPM reading of this vehicle
and what does it mean?
1800 revolutions per minute. It means that
the engine turns 1800 times per minute.
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22. 1. 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
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