3.2 How do we solve problems? 85
continues until a winner is established.
The results of the first count are shown
below. How many candidates still have a
chance of winning?Patel 323
Brown 211
Walsh 157
Ndelo 83
Macpherson 54
Gonzalez 21
3 Rajesh is cooking a meal for some friends.
This will involve roasting a chicken,
which takes 2 hours’ cooking time plus
15 minutes resting on removal from the
oven. The oven takes 15 minutes to
warm up. He will also cook some rice
(30 minutes’ soaking plus 15 minutes’
cooking), broccoli (5 minutes to prepare
and 5 minutes to cook) and a sauce
(10 minutes to prepare and 15 minutes
to cook).
What should be the timing of events if the
friends are to eat at 7 p.m.?
4 Joseph is making a bookcase. This
requires two vertical side-pieces of wood
1.2 m high and three shelves 1.6 m long.
All are 20 cm wide. He will cut these from
a sheet of wood 2.4 m × 1.2 m.
Draw a diagram showing how the pieces may
be cut to leave the largest possible uncut
rectangle. Are there other ways to cut it?Answers and comments are on pages 316–17.1 The petrol usage of a number of cars has
been measured. Each car started with a
full tank, then made a journey (all journeys
were over similar roads). After the journey
the tank was filled to the top, the amount
of petrol needed to fill it being recorded.
The results are shown below. Put the cars
in order of their petrol efficiency (km/litre),
from lowest to highest.Car Length of
journey
(km)Petrol
used
(litres)Montevideo 120 10Stella 150 16Riviera 200 25Roamer 185 21Carousel 230 162 The votes have recently been cast at the
local elections. Voting is carried out using
the alternative vote system. This means that
each voter ranks the candidates in order of
preference. Votes are counted initially on the
basis of all voters’ number one ranking. The
candidate with the least votes is excluded
and the votes of those people who placed
him or her number one are reallocated using
their second preferences. The process thenEnd-of-chapter assignments