Thinking Skills: Critical Thinking and Problem Solving

Answers to assignments 317

expect to get the least expensive item

free. After discount this will have cost $21

(70% of $30), so my bill will be reduced

to $56. Did you remember to reduce the

price of the least expensive item rather

than subtracting a further $30?

2    Sylvia’s total time for the first 5 laps is 5 ×

73 = 365 seconds. The time she is trying

to beat is 14 minutes 35 seconds or 875

seconds, so she must run within 875 −

365 = 510 seconds for the last 7.5 laps, or

68 seconds (1 minute 8 seconds) per lap.

3    The savoury pancakes come in these

types: egg; ham; tomato; egg and ham;

egg and tomato; ham and tomato; and

egg, ham and tomato – seven in total.

The sweet pancakes come in three types

(orange, lemon or strawberry) times two

toppings (cream or ice cream), making

six in total.

The number of combinations sold by

the stall is 13.

4    The monthly contract will cost me $30.

Texts are free but I will have to pay for

25 minutes of calls at 10¢ per minute, an

additional $2.50. The total is $32.50.

‘Pay as you go’ costs me 30¢ per minute

for 100 minutes of calls ($30) plus 60 text

messages at 10¢ each ($6), a total of $36

per month.

The monthly contract is better by $3.50.

3.5 Finding methods of solution

1    The difference in length between the

two pieces of chain is 8 cm and this

corresponds to the effective length of 10

links. The effective length of each link

is 0.8 cm but, because they overlap, the

actual length of each link is 1.2 cm (we

need to add twice the metal thickness as

can be seen in the diagram). The 34.2 cm

length has a 1 cm fitting at the end, so

without this it would be 33.2 cm long. This

length is made up of one full link length

(1.2 cm) plus a number of effective link

lengths (0.8 cm); you can also see this from

Uncut rectangle

2.0 m × 0.6 m

Uncut

rectangle

1.2 m × 0.8 m

3.3 Selecting and using information
1 This graph can be drawn as either a bar
chart or a pie chart.
2 In 1984, vinyl single sales were 44% of
170 million, or 74.8 million; in 1994, they
were 26% of 234 million, or 60.8 million.
So A is correct – they fell by 14 million.
3 The five teams played each other once,
so there were ten games. The maximum
total number of points scored if each
resulted in a win for one of the teams
would have been 30. The actual total
number of points scored was 26. In
each drawn game a total of two points is
scored (i.e. one less than in a game with
a winner), so there must have been four
drawn games.
4 Each shelf requires 30 mm gap, 210 mm
for books and 20 mm for the shelf
thickness, or 260 mm in total. The
available gap is 2.5 m less 300 mm (as the
bottom shelf must not be too close to the
ground), or 2200 mm.
A maximum of 8 shelves at 260 mm total
can be fitted into 2200 mm.

3.4 Processing data
1 I buy three items at a total of $110. If I
deduct the least expensive ($30) before
the discount, I pay $80, with no discount.
If I get the discount first, the reduction is
$33, making the bill $77. However, I then