Maths quest general mathematicspreliminary course

MATHS
QuestGeneral Mathematics
PRELIMINARY COURSE
Robert Rowland

Second edition published 2008 by
John Wiley & Sons Australia, Ltd
42 McDougall Street, Milton, Qld 4064
First edition published 2000
Typeset in 10.5/12.5 pt Times
© John Wiley & Sons Australia, Ltd 2000, 2008
The moral rights of the author have been asserted.
National Library of Australia
Cataloguing-in-Publication data
Rowland, Robert, 1963–.
Maths quest general mathematics: preliminary course.
2nd ed.
For secondary school students.
ISBN 978 0 7314 0570 1 (student edition)
ISBN 978 0 7314 0571 8 (teacher edition)
1. Mathematics — Textbooks. I. Title.
510
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Contents
Introduction viii
About eBookPLUS x
Acknowledgements xi
CHAPTER 1
Earning money 1
Are you ready? 2
Calculating salary payments 3
Exercise 1A 4
Calculating wages 6
Exercise 1B 8
10 Quick Questions 1 11
Commission and royalties 11
Exercise 1C 14
Payment by piece 16
Exercise 1D 17
Working overtime 19
Exercise 1E 21
Investigation — Investigating government
payments 24
Additions to and deductions from gross
pay 25
Exercise 1F 27
Investigation — Examining bank fees and
taxes 30
Budgeting 31
Exercise 1G 35
Summary 40
Chapter review 41
Practice examination questions 43
CHAPTER 2
Units of measurement 45
Are you ready? 46
Units of measurement 47
Exercise 2A 50
Relative error 52
Exercise 2B 54
Investigation — Measuring heights 56
Significant figures 57
Exercise 2C 60
Rates 61
Exercise 2D 65
Percentage change 67
Exercise 2E 68
Using ratios 69
Exercise 2F 72
Summary 74
Chapter review 75
CHAPTER 3
Applications of area and
volume 77
Are you ready? 78
Review of area 79
Exercise 3A 81
Investigation — Maximising an area of
land 84
Calculating irregular areas from a field
diagram 85
Investigation — Land survey 86
Exercise 3B 87
Solid shapes 89
Exercise 3C 91
Surface area 92
Exercise 3D 94
Volume of a prism 97
Investigation — Exploring the volume of a
prism 97
Exercise 3E 99
Volume of other solids 103
Exercise 3F 105
Summary 108
Chapter review 109
CHAPTER 4
Basic algebraic skills 113
Are you ready? 114
General number patterns 115
Exercise 4A 117
Number pattern notation 119
Exercise 4B 122
Adding and subtracting like terms 125
Exercise 4C 126
Substitution 127
Exercise 4D 128

iv
Multiplication and division of algebraic
expressions 131
Exercise 4E 133
Solving linear equations 134
Exercise 4F 137
Equations arising from substitution 139
Exercise 4G 141
Summary 143
Chapter review 144
CHAPTER 5
Statistics and society 147
Are you ready? 148
Analysing data 149
Investigation — Why statistical
investigation? 149
Investigation — A statistical investigation – 1
149
Statistical processes 150
Investigation — Posing questions 150
150
Exercise 5A 152
153
Exercise 5B 155
155
Exercise 5C 159
159
159
159
Quality control 160
Exercise 5D 162
Privacy and ethical issues 163
Investigation — Privacy issues 163
Investigation — Organisations that use
statistics 164
Summary 165
Chapter review 166
CHAPTER 6
Data collection and
sampling 167
Are you ready? 168
Target populations and sampling 169
Investigation — Gallup poll 169
Investigation — Identifying the target
population 169
Exercise 6A 172
Investigation — Census or sample 174
Population characteristics 174
Investigation — Population
characteristics 175
Exercise 6B 177
Investigation — Choosing a sample 179
Bias 180
Investigation — Bias in statistics 181
Investigation — Biased sampling 182
Investigation — Spreadsheets creating
misleading graphs 182
Exercise 6C 184
Investigation — Bias 185
Types of data 186
Exercise 6D 188
Estimating populations 191
Investigation — Estimating a population 192
Exercise 6E 193
Summary 194
Chapter review 195
CHAPTER 7
Modelling linear
relationships 199
Are you ready? 200
Graphing linear functions 201
Exercise 7A 204
Investigation — Graph of height versus
age 205
Gradient and intercept 205
Exercise 7B 209
Drawing graphs using gradient and
intercept 211
Exercise 7C 214
Graphing variations 216
Exercise 7D 217
Investigation — Currency conversions 218
Step and piecewise functions 218
Exercise 7E 220
Simultaneous equations 221
Exercise 7F 222

v
Summary 224
Chapter review 225
CHAPTER 8
Investing money 229
Are you ready? 230
Calculation of simple interest 231
Exercise 8A 234
Graphing simple interest functions 236
Exercise 8B 239
Calculation of compound interest 241
Exercise 8C 244
Calculating compound interest from a table of
compounded values 248
Exercise 8D 251
Graphing compound interest functions 253
Exercise 8E 255
Share dividends 257
Exercise 8F 258
Graphing share performance 260
Exercise 8G 262
Investigation — Researching share prices 263
Inflation and appreciation 264
Exercise 8H 265
Summary 267
Chapter review 268
CHAPTER 9
Displaying single data
sets 271
Are you ready? 272
Frequency tables 273
Exercise 9A 276
Types of graphs 277
Exercise 9B 280
Investigation — Choice of graph 283
Investigation — Producing graphs using
technology 283
Statistical graphs 283
Exercise 9C 287
Range and interquartile range 292
Exercise 9D 297
Stem-and-leaf plots 302
Exercise 9E 306
Five-number summaries 308
Exercise 9F 312
Summary 315
Chapter review 316
CHAPTER 10
Summary statistics 321
Are you ready? 322
Calculating the mean 323
Investigation — Average — what does it
mean? 323
Exercise 10A 328
Standard deviation 333
Exercise 10B 337
Median and mode 341
Exercise 10C 345
Best summary statistics 350
Exercise 10D 351
Investigation — Wage rise 354
Investigation — Best summary statistics and
comparison of samples 354
Summary 355
Chapter review 356
CHAPTER 11
Similarity of two-dimensional
figures 363
Are you ready? 364
Similar figures and scale factors 365
Exercise 11A 367
Investigation — Enlarging a figure 369
Investigation — Investigating scale
factors 369
Investigation — Similar triangles 370
Solving problems using similar figures 371
Exercise 11B 372
Investigation — Scale drawing of the
classroom 373
House plans 374
Exercise 11C 376
Investigation — House plans 378

vi
Summary 379
Chapter review 380
CHAPTER 12
Taxation 383
Are you ready? 384
Calculating allowable deductions 385
Exercise 12A 388
Taxable income 390
Exercise 12B 392
Medicare levy 395
Exercise 12C 397
Investigation — Medicare levy 397
Calculating tax 398
Exercise 12D 402
Calculating GST and VAT 405
Exercise 12E 407
Graphing tax functions 409
Exercise 12F 409
Summary 411
Chapter review 412
CHAPTER 13
Right-angled triangles 415
Are you ready? 416
History of mathematics — Pythagoras of
Samos (circa 580 BC–500 BC) 417
Pythagoras’ theorem 418
Exercise 13A 421
Calculating trigonometric ratios 423
Investigation — Looking at the tangent
ratio 423
Investigation — Looking at the sine ratio 425
Investigation — Looking at the cosine
ratio 426
Exercise 13B 429
Finding an unknown side 431
Exercise 13C 435
Finding angles 438
Exercise 13D 442
Angles of elevation and depression 445
Exercise 13E 448
Investigation — Calculation of heights 449
Proportional diagrams 450
Investigation — Checking with a proportional
diagram 450
Investigation — Using proportional
diagrams 450
Summary 451
Chapter review 452
CHAPTER 14
The language of chance 455
Are you ready? 456
Informal description of chance 457
Exercise 14A 460
Investigation — Common descriptions of
chance 462
Sample space 462
Exercise 14B 464
Investigation — Matching actual and expected
results 465
Tree diagrams 467
Exercise 14C 470
Investigation — Two-stage experiments 471
Equally likely outcomes 472
Exercise 14D 474
Using the fundamental counting
principle 476
Exercise 14E 479
Summary 481
Chapter review 482
CHAPTER 15
Relative frequency and
probability 485
Are you ready? 486
Relative frequency 487
Exercise 15A 489
Investigation — Researching relative
frequencies 491
Single event probability 492
Exercise 15B 494
Investigation — Comparing probabilities with
actual results 497

vii
Writing probabilities as decimals and
percentages 499
Exercise 15C 500
Range of probabilities 502
Exercise 15D 504
Investigation — Graphing results 506
Complementary events 507
Exercise 15E 509
Summary 512
Chapter review 513
Glossary 515
Answers 521
Index 559

Introduction
Maths Quest General Mathematics — Preliminary course is the first book
in a series specifically designed for the General Mathematics Stage 6
Syllabus starting in 2000. This course replaces the current syllabuses for
Mathematics in Society (1981) and Mathematics in Practice (1989).
There are five new areas of study:
• Financial mathematics
• Data analysis
• Measurement
• Probability
• Algebraic modelling.
This resource contains:
• a student textbook with accompanying eBookPLUS and
• a teacher edition with accompanying eGuidePLUS.
Student textbook
Full colour is used throughout to produce clearer graphs and diagrams, to pro-
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Clear, concise theory sections contain worked examples, highlighted impor-
tant text and remember boxes.
Worked examples in a Think/Write format provide a clear explanation of key
steps and suggest a presentation for solutions.
Exercises contain many carefully graded skills and application problems,
including multiple-choice questions. Cross-references to relevant worked
examples appear beside the first ‘matching’question throughout the exercises.
Investigations, including spreadsheet investigations, provide further learning
opportunities through discovery.
Sets of 10 Quick Questions allow students to quickly review the concepts
just learnt before proceeding further in the chapter.
A glossary of mathematical terms is provided to assist students’ under-
standing of the terminology introduced in each unit of the course. Words in
bold type in the theory sections of each chapter are defined in the glossary at
the back of the book.
Each chapter concludes with a summary and chapter review exercise, con-
taining questions in a variety of forms (multiple-choice, short-answer and
analysis) that help consolidate students’ learning of new concepts.
Practice examination questions provide a ready source of problems for stu-
dents to use to gain further confidence in each topic.

ix
Technology is fully integrated, in line with Board of Studies recommen-
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dynamic geometry software and several graphing packages. Not only does
the text promote these technologies as learning tools, but demonstration
versions of the programs (with the exception of Microsoft Excel) are also
included, as well as hundreds of supporting ﬁles on the bonus accompanying
online resources.
Graphics calculator tips are incorporated throughout the text.
All formulae, which are given on the HSC examination formula sheet, are
marked with the symbol .
Programs included
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Equation grapher and regression analyser: like a graphics calculator for
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GrafEq: graphs any relation, including complicated inequalities
Poly: for visualising 3D polyhedra and their nets
Tess: for producing tessellations and other symmetric planar illustrations
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Adobe® Acrobat® Reader 4.0
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eGuidePLUS
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next to most questions in the exercises. Each exercise is annotated with rel-
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available resources and provides curriculum coverage information.
The accompanying teacher eGuidePLUS contains everything in the student
eBookPLUS and more. Two tests per chapter, fully worked solutions to
WorkSHEETs, the work program and other curriculum advice in editable
Word 2000 format are provided.
Maths Quest is a rich collection of teaching and learning resources within
one package.
Maths Quest General Mathematics Preliminary course, Second edition,
provides ample material, such as exercises, analysis questions, investi-
gations, worksheets and technology ﬁles, from which teachers may set
assessment tasks.

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Acknowledgements
The Maths Quest project began in 1997, and the first edition of this book
was printed in 2000. In that time we believe that Maths Quest has become
the best-resourced mathematical database in Australian education. I would
like to thank all of those people who have supported us with our first edition.
I hope that we have been able to help you in achieving your goals and have
also played a part in your successes.
Technology has evolved greatly since our first edition was published.
The second edition has evolved from the first textbook into an interactive
resource for both students and teachers. I would like to thank everyone at
John Wiley & Sons Australia, Ltd for giving me the opportunity to do
this.
There are three people in particular whom I would like to single out for
special mention: Jennifer Nolan, whose support for the Maths Quest
project and for me personally has made everything possible; Ingrid Kemp,
the newest addition to our team, who has brought a new set of eyes to our
project and kept the ball rolling — thanks Ingrid; and finally Keith
Hartmann, who has tirelessly reviewed all of the new material and has
completed all of the answer checking — thanks Keith — I hope you’re
enjoying retirement!
Finally, and most importantly, to my family — thank you. Without your
support this book and online resources would never have been completed.
The author and publisher would like to thank the following copyright
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About the author
Robert Rowland has been teaching Mathematics for over 20 years and cur-
rently holds the position of Head teacher, Teaching and learning at Ulladulla
High School. He taught at Cabramatta High School from 1985 to 1988 before
taking up his appointment at Ulladulla High School in 1989. Robert has suc-
cessfully taught all levels of Mathematics to Year 12 as well as Computing
Studies 7–12 and Information Processes and Technology. Robert is the co-
author of New South Wales Maths Year 9 Standard and New South Wales
Maths Year 10 Standard as well as being the author of Maths Quest General
Mathematics — Preliminary Course and Maths Quest General Mathematics
— HSC Course.

In this chapter
1A Calculating salary
payments
1B Calculating wages
1C Commission and royalties
1D Payment by piece
1E Working overtime
1F Additions to and
deductions from gross pay
1G Budgeting
syllabusreference
Financial Mathematics 1
• Earning money
1
Earning money

READY?
areyou
Are you ready?
Try the questions below. If you have difﬁculty with any of them, extra help can be
obtained by completing the matching SkillSHEET. Either click on the SkillSHEET icon
next to the question on the Maths Quest Preliminary Course CD-ROM or ask your
teacher for a copy.
Converting units of time
1 Convert each of the following to the units shown in brackets.
a 2 years (months) b 3 years (weeks)
c 42 weeks (fortnights) d 60 months (years)
Multiplying and dividing a quantity (money) by a whole number
2 Calculate each of the following.
a $23.50 × 26 b $31 432.70 ÷ 12
c $528.72 × 52 d $45 600 ÷ 52
Converting a percentage into a decimal
3 Convert each of the following percentages to a decimal.
a 34% b 79% c 4%
d 67.2% e 8.25% f 17.5%
Finding a percentage of a quantity (money)
4 Find each of the following.
a 10% of $350 b 25% of $1424
c 18% of $9000 d 12.5% of $4570
Multiplying a quantity (money) by a decimal
5 Calculate each of the following.
a $8.56 × 1.5 b $12.90 × 2.5
Adding periods of time
6 Jessica has worked the following hours in one week.
Thursday 6.30 pm to 9.00 pm
Friday 5.45 pm to 9.00 pm
Saturday 8.00 am to 2.30 pm
How many hours has she worked?
Expressing one quantity as a percentage of another
7 For each of the following pairs, express the ﬁrst quantity as a percentage of the second quantity.
a $56, $400 b $13, $20 c $125, $625
Increasing a quantity by a percentage
8 Increase each of the following by the percentage indicated.
a $560 by 10% b $1120 by 5% c $2560 by 15%
1.1
1.2
1.3
1.4
1.5
1.6
1.8
1.9

C h a p t e r 1 E a r n i n g m o n e y 3
Calculating salary payments
Methods of payment
A payment received by an employee for doing a job is called
income. There are many different ways people are paid for
performing a job. In this section we are going to look at
some of these methods of payment: salaries, wages,
commission, royalties, piecework and overtime.
Salaries
Many people employed in professional occupations
are paid a salary. Such employees include teachers,
lawyers, accountants and some doctors.
A salary is a ﬁxed amount of money that is paid to
employees to do their jobs. The amount paid does not
change, regardless of the number of hours worked.
Salaries are usually calculated on an annual basis.
A salary is therefore usually stated as an amount per
annum, which means per year. Salaries are paid in
weekly, fortnightly or monthly amounts. To make calcu-
lations about salaries, you will need to remember the
following information.
1 year = 52 weeks
= 26 fortnights
= 12 months
We reverse this calculation when we are given the weekly, fortnightly or monthly pay
of a person and are then asked to calculate the annual salary.
Dimitri works as an accountant and receives an annual salary of $46 800. Calculate the
amount that Dimitri is paid each fortnight.
THINK WRITE
There are 26 fortnights in a year, so we
divide $46 800 by 26.
Fortnightly pay = $46 800 ÷ 26
Evaluate. Fortnightly Pay = $1800
1
2
1WORKEDExample
Grace is a solicitor who is paid $3500 per month. Calculate Grace’s annual salary.
THINK WRITE
There are 12 months in a year, so
multiply $3500 (monthly pay) by 12.
Annual salary = $3500 × 12
Evaluate. Annual salary = $42 000
1
2
2WORKEDExample
A lecturer is paid a salary.

4 M a t h s Q u e s t G e n e r a l M a t h e m a t i c s P r e l i m i n a r y C o u r s e
To compare a salary payment with other forms of income it may be necessary to calcu-
late the equivalent daily or hourly payment. To do this, we need to know the number of
days or hours worked per week.
Calculating salary payments
1 Toni is paid a salary of $44 200 per annum. Calculate Toni’s fortnightly pay.
2 Roger is paid a salary of $49 920 per annum. Calculate Roger’s weekly pay.
3 Frieda is paid a salary of $54 000 per annum. Calculate Frieda’s monthly pay.
4 Wendy works as an ofﬁce secretary and is paid a salary of $38 740 per annum.
Calculate Wendy’s pay if she is paid:
a weekly b fortnightly c monthly.
5 Darren earns a salary of $43 000 per annum. Calculate Darren’s fortnightly pay,
correct to the nearest cent.
Charlotte works as a laboratory technician and is
paid an annual salary of $41 560. If Charlotte works
an average of 42 hours per week, calculate her
equivalent hourly rate of pay.
THINK WRITE
Calculate the weekly
pay by dividing the
salary by 52.
Weekly pay = $41 560 ÷ 52
= $799.23
Calculate the hourly
rate by dividing the
weekly pay by 42.
Hourly rate = $799.23 ÷ 42
= $19.03
1
2
3WORKEDExample
1. A salary is a ﬁxed payment made for doing a job.
2. A salary is usually calculated on an annual basis and can be paid in weekly,
fortnightly or monthly instalments.
3. To calculate information about equivalent daily or hourly rates of pay, we need
information about the number of days and hours worked by the employee.
remember
1A
SkillS
HEET 1.1
Converting
units of
time
SkillS
HEET 1.2
Multiplying
and dividing a
quantity (money)
by a whole number
WORKED
Example
1
EXCE
LSpreadshe
et
Payroll
calculations

6 Copy and complete the table below for food production employees.
7 Maxine is paid a salary. She receives $460 per week. Calculate Maxine’s annual
salary.
8 Thao receives $1250 per fortnight. Calculate Thao’s annual salary.
9 Deidre is paid monthly and receives $5800. Calculate Deidre’s annual salary.
10
Which of the following people receives the greatest salary?
A Goran, who receives $530 per week.
B Bryan, who receives $1075 per fortnight.
C Wayne, who receives $2330 per month.
D Ron, who receives $27 900 per annum.
11 Fiona receives a salary of $29 700 per annum. If Fiona works an average of 40 hours
per week, calculate the equivalent hourly rate of pay.
12 Jade receives a salary of $33 000 per annum.
a Calculate Jade’s weekly pay, correct to the nearest cent.
b Jade works an average of 36 hours each week. Calculate the hourly rate to which
Jade’s salary is equivalent. Give your answer correct to the nearest cent.
13 Karina is on an annual salary of $35 776. Letitia is on a wage and is paid $16.00 per
hour.
a Calculate Karina’s weekly pay.
b If Karina works an average of 42 hours per week, calculate whether Karina or
Letitia receive the better rate of pay.
14 Garry earns $42 500 per year while his friend Henry earns $18.50 per hour. Calculate
the number of hours that Henry will need to work each week to earn more money than
Garry does.
Annual salary Weekly pay Fortnightly pay Monthly pay
$30 000
$39 500
$42 250
$54 350
$86 475
WORKED
Example
2
multiple choice
WORKED
Example
3

Calculating wages
Most people in the workforce
earn a wage. A wage is paid at an
hourly rate.
The hourly rate at which a
person is usually paid is called
an ordinary rate. The wage for
each week is calculated by multi-
plying the ordinary rate by the
number of hours worked during
that week.
To compare two people’s wages, we can’t just look at the amount of money each
receives in a pay packet. We must also consider the number of hours each has worked.
Wages are compared by looking at the hourly rate. To calculate the hourly rate of an
employee we need to divide the wage by the number of hours worked.
Using a similar method we are able to calculate the number of hours worked by an
employee, given their wage and hourly rate of pay. The number of hours worked is
found by dividing the wage by the hourly rate.
In some cases, wages are increased because an allowance is paid for working in
unfavourable conditions. An allowance is an additional payment made when the
working conditions are difﬁcult or unpleasant.
Sadiq works as a mechanic and is paid $13.65 per hour. Calculate Sadiq’s wage in a week
where he works 38 hours.
THINK WRITE
Multiply $13.65 (the hourly rate) by 38
(the number of hours worked).
Wage = $13.65 × 38
Wage = $518.70
4WORKEDExample
Georgina works 42 hours as a data entry operator for a computer company. Her wage for
the week totalled $483.84. Calculate Georgina’s hourly rate of pay.
THINK WRITE
Divide $483.84 (the wage) by 42
(number of hours worked).
Hourly rate = $483.84 ÷ 42
Hourly rate = $11.52
5WORKEDExample

For example, a road worker may be paid an allowance for working in the rain. In
these cases, the allowance must be multiplied by the number of hours worked in the
unfavourable conditions and this amount added to the normal pay.
This type of allowance is also paid to casual workers. When you are employed on a
casual basis you do not receive any holiday pay and you do not get paid for days you
have off because you are sick. The casual rate is a higher rate of pay to compensate for
this.
Ryan is a road worker and is paid
$9.45 per hour for a 35-hour week.
For working on wet days he is paid a
wet weather allowance of 86c per
hour. Calculate Ryan’s pay if for 12
hours of the week he works in the
rain.
THINK WRITE
Calculate Ryan’s normal pay by
multiplying $9.45 (hourly rate) by 35
(number of hours worked).
Normal pay = $9.45 × 35
= $330.75
Calculate the wet weather allowance by
multiplying 0.86 (the wet weather
allowance) by 12 (number of hours
worked in the wet).
Allowance = $0.86 × 12
= $10.32
Add the normal pay to the wet weather
allowance to calculate the total pay.
Total pay = $330.75 + $10.32
= $341.07
1
2
3
6WORKEDExample
1. A wage is money earned at an hourly rate.
2. To calculate a wage we multiply the hourly rate by the number of hours worked
during the week.
3. To calculate an hourly rate we divide the wage by the number of hours worked.
4. To calculate the number of hours worked we divide the wage by the hourly
rate.
5. Allowances are paid for working under unfavourable conditions. The total
allowance should be calculated and then added to the normal pay.
6. A casual rate is a higher rate of pay for casual workers to compensate them for
having no holidays and receiving no sick leave.
remember

Calculating wages
1 Allan works in a newspaper printing mill and is paid $12.95 per hour. Calculate
Allan’s wage in a week where he works 40 hours.
2 Copy and complete the table below by calculating the wage of each of the workers.
3 Alicia is an apprentice chef. In the ﬁrst
year of her apprenticeship she earns $11.80
per hour. Calculate Alicia’s wage in a week
where she works:
a 36 hours
b 48 hours
c 42.5 hours.
4 Domonic is a fully qualiﬁed chef. He earns
$13.50 per hour. Calculate Domonic’s
wage in a week where he works:
a 32 hours
b 37 hours
c 44.5 hours.
5 Katherine works as a casual waitress.
Casual workers earn 20% more per hour
than full-time workers to compensate for
their lack of holidays and sick leave.
a A full-time waitress earns $14.45 per
hour. Calculate the casual rate earned by
casual waitresses.
b Calculate Katherine’s wage in a week
where she works 6 hours on Saturday
and 7 hours on Sunday.
6
Which of the following workers earns the highest wage for the week?
A Dylan, who works 35 hours at $13.50 per hour
B Lachlan, who works 37 hours $12.93 per hour
C Connor, who works 38 hours at $12.67 per hour
D Cameron, who works 40 hours at $12.19 per hour
Name Hourly rate Hours worked Wage
A. Smith $14.52 40
B. Brown $16.45 38
N. Tran $15.95 37.5
A. Milosevic $20.10 41
L. McTavish $18.04 36
1B
WORKED
Example
4
EXCE
LSpreadshe
et
Payroll
calculations
multiple choice

7 Calculate the hourly rate of a person who works 40 hours for a wage of $387.20.
8 Julie earns $11.42 per hour. Calculate the number of hours worked by Julie in a week
where she is paid $445.38.
9 Copy and complete the table below.
10 Calculate the hourly rate of a casual worker who earns $250.80 for 20 hours work.
11
Which of the following workers is paid at the highest hourly rate?
A Melissa, who works 35 hours for $366.45
B Belinda, who works 36 hours for $376.20
C April, who works 38 hours for $399.76
D Nicole, who works 40 hours for $419.60
12
Which of the following people worked the greatest number of hours?
A Su-Li, who earned $439.66 at $11.57 per hour
B Denise, who earned $576.00 at $14.40 per hour
C Vera, who earned $333.20 at $9.52 per hour
D Camille, who earned $707.25 at $17.25 per hour
13 Richard works as an electrical linesman and is paid $10.94 per hour for a 38-hour week.
When he has to work at heights he is paid a 46c per hour ‘height allowance’. Calculate
Richard’s pay in a week where 15 hours are spent working at heights.
14 Ingrid works as an industrial cleaner and is paid $14.60 per hour for a 35-hour working
week. When Ingrid is working with toxic substances she is paid an allowance of $1.08
per hour. Calculate Ingrid’s pay if she works with toxic substances all week.
15 Rema works as a tailor and earns $9.45 per hour.
a Calculate Rema’s wage in a week where she works 37 hours.
b Zhong is Rema’s assistant and earns $8.20 per hour. Find the least time Zhong
must work if he is to earn more money than Rema does.
16 Tamarin works 38 hours per week at $12.40 per hour.
a Calculate Tamarin’s weekly wage.
b Zoe earns the same amount each week as Tamarin does, but Zoe works a 40-hour
week. Calculate Zoe’s hourly rate of pay.
Name Wage Hours worked Hourly rate
A. White $416.16 36
B. Black $538.80 40
C. Green $369.63 37
D. Brown $813.96 $19.38
E. Scarlet $231.30 $15.42
F. Grey $776.72 $20.44
WORKED
Example
5
multiple choice
multiple choice
WORKED
Example
6

Throughout this chapter we are going to develop a number of spreadsheets that will
calculate wages. Work through the following steps.
1. Open a spreadsheet and enter the following information. Alternatively, access the
spreadsheet (Wages_1) from the Maths Quest General Mathematics Preliminary
Course CD-ROM.
2. Enter a pay rate of $11.20 per hour for each employee.
3. Enter the hours worked as follows: Frederick Astini, 40; James Carter, 38; Kelly
George, 36; Dean Jones, 15; Paul Limbrick, 45.
4. In cell E7 (in the column headed Gross Pay) enter the formula =C7*D7. This will
calculate the wage for Frederick Astini (the ﬁgure 448 should appear in the cell).
5. Format cell E7 as currency (cell E7 should now show $448.00).
6. Highlight cells E7 to E11 and select the Fill Down option. The wages for each
employee should now be calculated and be formatted as currency. (The entries in
this column should read $448.00, $425.60, $403.20, $168.00 and $504.00.)
7. If you now change the hours worked by each employee, his or her gross pay should
update automatically.
8. Choose the Save As function to save the spreadsheet as Wages_1.
Computer ApplicationComputer Application Spreadsheets1
EXCE
LSpreadshe
et
Wages_1

1 Calculate the wage of a person who works 36 hours at a pay rate of $9.56 per hour.
2 Calculate the wage of a person who works 38 hours at $13.65 per hour.
3 Donna works 15 hours on weekends at $14.56 per hour. Calculate Donna’s wage.
4 Calculate what Stephen will earn for working 8 hours at $11.88 per hour.
5 Debbie earns $489.06 for a 38-hour working week. Calculate Debbie’s hourly rate of
pay.
6 Damien earns an annual salary of $47 000 and is paid weekly. Calculate Damien’s
weekly pay.
7 Simone earns an annual salary of $70 000 and is paid fortnightly. Calculate Simone’s
fortnightly pay.
8 Ivan earns an annual salary of $56 480 and is paid monthly. Calculate Ivan’s monthly
pay.
9 Penny earns an annual salary of $44 000 and is paid weekly. Calculate Penny’s
weekly pay.
10 Penny works an average of 35 hours each week. Calculate the hourly rate to which her
salary is equivalent. (Answer to the nearest cent.)
Commission and royalties
Commission is a method of payment used mainly for salespeople. When paid com-
mission, a person receives a percentage of the value of goods sold.
A royalty is a payment made to a person who owns a copyright. For example, a
musician who writes a piece of music is paid royalties on sales of CDs; an author who
writes a book is paid according to the number of books sold. Royalties are calculated in
the same way as commission, being paid as a percentage of sales.
1

In some cases, commission may operate on a sliding scale. This means that the com-
mission rate changes with the value of sales. This type of commission is commonly
used in real estate sales. In these examples, each portion of the commission is calcu-
lated separately. The ﬁnal commission is the sum of each portion.
Jack is a computer salesman who is paid a commission of 12% of all sales. Calculate the
commission that Jack earns in a week if he makes sales to the value of $15 000.
THINK WRITE
Calculate 12% of $15 000. Commission = 12% of $15 000
Commission = 12 ÷100 × $15 000
Commission = $1800
7WORKEDExample
A real estate agent is paid com-
mission on his sales at the following
rate:
• 5% on the ﬁrst $75 000
• 2.5% on the balance of the sale
• price.
Calculate the commission earned on
the sale of a property for $235 000.
THINK WRITE
Calculate 5% of $75 000. 5% of $75 000 = $3750
Calculate the balance of the sale. Balance = $235 000 − $75 000
Balance = $160 000
Calculate 2.5% of $160 000. 2.5% of $160 000 = $4000
Add up each portion to calculate the
commission.
Commission = $3750 + $4000
Commission = $7750
1
2
3
4
8WORKEDExample

In some cases, people receive a fixed amount (called a retainer) as well as a com-
mission. This is to ensure that the person earns some money even if no sales are made.
To calculate this type of pay, you will need to add the retainer to the commission.
In some cases, the commission does not begin to be paid until sales have reached a
certain point. Here the commission is calculated only on sales above this fixed amount.
Shelley is a furniture salesperson and is paid $250 per week plus a commission of 2% of
all sales. Calculate Shelley’s pay in a week where her sales total $12 250.
THINK WRITE
Calculate the commission of 2% of
$12 250.
Commission = 2% of $12 250
Commission = 2 ÷ 100 × 12 250
Commission = $245
Add the $250 to the commission to
calculate her pay.
Pay = $250 + $245
Pay = $495
1
2
9WORKEDExample
Tony is a car salesman. Tony is paid $300 per week and 2% of all sales over $50 000.
Calculate Tony’s pay in a week where his sales total $84 000.
THINK WRITE
Calculate the amount on which
commission is to be paid.
$84 000 − $50 000 = $34 000
Find 2% of this amount. Commission = 2% of $34 000
Commission = 2 ÷ 100 × $34 000
Commission = $680
Add the $300 to the commission to
calculate Tony’s pay.
Pay = $300 + $680
Pay = $980
1
2
3
10WORKEDExample
1. A commission is earned when a person is paid a percentage of the value of
sales made.
2. Some commissions are paid on a sliding scale. In these cases, each portion of
the commission is calculated separately and then totalled at the end.
3. Some commissions are paid together with a fixed payment called a retainer. To
calculate an employee’s pay, the fixed payment needs to be added to the
commission.
4. In some cases where a fixed payment is made, commission may not be paid on
all sales, but rather on a section of sales above a certain point.
remember

Commission and royalties
1 Kylie is an insurance salesperson and she is paid 8% of the value of any insurance that
she sells. Calculate the amount that Kylie is paid for selling insurance to the value of
$25 000.
2 Beryl sells exercise equipment and is paid a commission of 10% on all sales.
Calculate Beryl’s earnings in a week where her sales total is:
a $2600 b $3270 c $5687.90.
3 Darren’s job is to sell CDs to music stores. If Darren sells CDs to the value of
$40 000, calculate his commission if it is paid at a rate of:
a 1% b 3% c 3.4%.
4 Linda is a car salesperson who is paid 1.5% commission. Calculate the amount of
money Linda earns in a week where her sales total $95 000.
5 Ken is an author and is paid a royalty on his book sales. The royalty is 12% of the
value of all sales of his book. Calculate the value of Ken’s royalty if the value of sales
totals $34 500.
6
Ursula is a computer software salesperson. Ursula’s sales total $105 000 and she is
paid a commission of 0.8%. How much does Ursula receive in commission?
A $105 B $840 C $8400 D $84 000
7
Asif is a sales representative for a hardware firm. Asif earns $870 commission on
sales of $17 400. What rate of commission does Asif receive?
A 0.05% B 0.5%
C 5% D 20%
8 A real estate agent charges
commission at the following rate:
• 5% on the first $75 000
• 2.5% on the balance of the sale
price.
Calculate the commission charged
on the sale of a property valued at
$250 000.
9 Gabrielle is a fashion sales
representative. Gabrielle is paid a
commission of 5% on the first
$3000 of sales each week and 10%
commission on the balance.
Calculate Gabrielle’s commission in
a week where her sales total $9500.
1C
WORKED
Example
7
SkillS
HEET 1.3
Converting
a percentage
into
a decimal
SkillS
HEET 1.4
Finding a
percentage of
a quantity
(money)
EXCE
LSpreadshe
et
Calculations
with
percentages
multiple choice
multiple choice
WORKED
Example
8

10 Using the sliding scale for commission shown in question 8, calculate the commission
on a property that sells for:
a $90 000 b $140 000 c $600 000.
11 Stanisa is a car salesman who is paid $250 per week plus a commission of 2% of any
sales he makes. Calculate Stanisa’s pay in a week where his sales total $35 000.
12 Daniel works as a sales representative for a car accessories firm. Daniel is paid $150
per week plus 4% of any sales. Calculate Daniel’s earnings in a week where his sales
total is:
a $6000 b $8500 c $12 475.
13
A group of sales representatives each have $10 000 in sales for a week. Who earns the
most money?
A Averil, who is paid a commission of 8%
B Bernard, who is paid $250 plus 6% commission
C Cathy, who is paid $350 plus 4% commission
D Darrell, who is paid $540 plus 2.5% commission
14 Fred and Gina sell life insurance. Fred is paid a commission of 8% and Gina is paid
$250 plus 5% commission.
a How much does Fred earn for a week in which his sales are $5000?
b How much does Gina earn for a week in which her sales total $5000?
c In another week Gina earns $650. What is the value of Gina’s sales?
d Fred wishes to earn $650 in a week. How much should his sales be?
15 Mario is a pay television salesman. Mario earns $500 per week plus 5% commission
on all sales above $5000. Calculate Mario’s pay in a week where his sales total $7500.
16 Neville is a door-to-door encyclopedia salesman. He is paid $300 per week plus
3% commission on all sales greater than $5000. Calculate Neville’s pay in a week
where his sales total is:
a $4000 b $6500 c $8560.
17
A firm employs five sales representatives. Which representative will earn the most in
a week where each of their sales totals $12 480?
A Peter, who receives a commission of 4%
B Richard, who receives $100 plus a commission of 3%
C Susan, who is paid $280 plus a commission of 1.8%
D Trevor, who is paid $300 plus a commission of 3.5% on all sales over $6000
18 Andrew and Bonito are sales representatives. Andrew is paid $300 plus a commission
of 2.5% on all sales. Bonito is paid $250 plus a 3.5% commission on all sales over
$3000.
a Calculate Andrew’s commission in a week where his sales total $6500.
b Calculate Bonito’s commission in a week where his sales total $6500.
c Who will earn the most money in a week where both Andrew and Bonito make
$16 000 in sales?
WORKED
Example
9
multiple choice
WORKED
Example
10
multiple choice
Work
SHEET 1.1

Payment by piece
Payment by piece, or piecework
refers to payment for the amount of
work completed. It is commonly
paid for jobs such as car detailing
and letterbox delivery.
The amount earned is calculated
by multiplying the rate of payment
by the number of pieces of work
completed.
In some cases, piecework is paid for multiples, rather than for single units. For
example, for letterbox deliveries you may be paid per 1000 deliveries made.
There are also examples where you will be asked to compare payment by piece with
other methods of earning income, in particular, wages.
Len has a job washing cars in a car yard. He is paid $2.25 per car washed. Calculate what
Len earns in an afternoon where he washes 24 cars.
THINK WRITE
Multiply the pay rate by the number of cars
detailed.
Pay = $2.25 × 24
Pay = $54.00
11WORKEDExample
Holly is delivering brochures to letterboxes in her local area. She is paid $23.00 per thou-
sand brochures delivered. Calculate what Holly will earn for a delivery of 3500 brochures.
THINK WRITE
Divide 3500 by 1000 to calculate the
number of thousand brochures
delivered.
3500 ÷ 1000 = 3.5
Multiply 3.5 by $23.00 to calculate
what Holly is paid.
Holly’s pay = 3.5 × $23.00
Holly’s pay = $80.50
1
2
12WORKEDExample
A person delivering to a letterbox is paid for piecework.

Payment by piece
1 Julia works after school at a car yard detailing cars. If Julia is paid $10.85 per car,
calculate what she will earn in an afternoon when she details 7 cars.
2 A group of four friends take a job picking fruit over summer. They are paid $4.50 per
basket of fruit picked. Calculate the earnings of each person in the group if:
a Ryan picked 23 baskets b Summer picked 21 baskets
c Seth picked 19 baskets d Taylor picked 18 baskets.
3 Natalie advertises that she will do ironing for $12.50 per basket. Calculate Natalie’s
earnings for doing 14 baskets of ironing.
4 Matthew charges $15 to mow a lawn. Calculate Matthew’s earnings in a week if he
mows 9 lawns.
5 Dean works as a house cleaner. He charges $46.50 to clean a house. If Dean cleans
7 houses, calculate his earnings.
6 Barbara delivers pamphlets to local letterboxes. She is paid $21.80 per thousand
pamphlets delivered. Calculate what Barbara will be paid for delivering 15 000
pamphlets.
Tristan has a job picking apples. He is paid $4.40 per basket.
a Calculate Tristan’s pay for picking 21 baskets of apples in one day.
b If it takes Tristan 8 hours to pick these apples, calculate the equivalent hourly rate of
pay he has earned.
THINK WRITE
a Multiply 21 (the number of baskets) by
$4.40 (the pay per basket).
a Pay = 21 × $4.40
Pay = $92.40
b Divide $92.40 (total pay) by 8 (number
of hours worked).
b Hourly rate = $92.40 ÷ 8
Hourly rate = $11.55
13WORKEDExample
1. Payment by piece is payment to an employee for the amount of work
completed.
2. To calculate the amount to be paid, multiply the number of units of work
completed by the amount to be paid per unit.
3. Be careful when pay is calculated for completing 100 or 1000 units of work.
You will need to ﬁrst divide by this amount.
4. Remember your work on other methods of payment. You will need it to
compare payment by piece with them.
remember
1D
WORKED
Example
11
WORKED
Example
12

7 A local business employs four people to deliver advertising to letterboxes. They are
paid $18.40 per 1000 deliveries. Calculate the amount each person is paid.
a Jim makes 5000 deliveries. b Georgia makes 7500 deliveries.
c Nicholas makes 4750 deliveries. d Claire makes 6200 deliveries.
8 Raul works in a factory assembling toys. Raul is paid $19.25 per 100 toys assembled.
Calculate what Raul is paid in a day where he assembles:
a 300 toys b 650 toys c 540 toys.
9 Carolina works as a bicycle courier. She charges $5.70 per kilometre for her
deliveries. Calculate Carolina’s earnings for a 4 km delivery.
10 Keith is a taxi owner/driver. He is paid $3.00 plus $1.60 per kilometre. Calculate the
amount Keith will earn for a journey of:
a 5 km b 15.5 km c 10.2 km.
11 Denise works as a fruit picker. She is paid $4.20 for every basket of fruit picked.
a Calculate the amount Denise will earn in a day during which she picks 32 baskets
of fruit.
b If it takes Denise 8 hours to pick the fruit, calculate the equivalent hourly rate of pay.
12 Charlie works in a car yard as a detailer. Charlie is paid $11.60 per car.
a What will Charlie earn in an afternoon during which he details 15 cars?
b If it takes Charlie 8 hours to detail the cars, calculate his hourly rate of pay.
c If Charlie could ﬁnish in 6 hours, calculate the hourly rate of pay he would earn.
1 Kim works a 37-hour week at a rate of $12.32 per hour. Calculate her weekly wage.
2 Viet works 35 hours a week at an hourly rate of $9.89. Calculate Viet’s weekly wage.
3 Samantha receives an annual salary of $38 500 and is paid weekly. Calculate
Samantha’s weekly pay.
4 Tom receives an annual salary of $86 000 and is paid fortnightly. Calculate Tom’s
fortnightly pay.
5 Celine is paid $1246.40 per fortnight. Calculate her annual salary.
6 Mick is paid 7% commission on all sales he makes. Calculate his commission for a
week in which his sales total $6960.
7 Christine is paid $250 per week plus 2.5% commission on all sales. Calculate
Christine’s pay for a week in which her sales total $12 800.
8 Jason has a job picking fruit and is paid $4.85 per basket. Calculate Jason’s pay for a
day in which he picks 43 baskets of fruit.
9 Julia has a job delivering pamphlets to letterboxes and is paid $13.40 per 1000
pamphlets delivered. Calculate Julia’s pay for delivering 4500 pamphlets.
10 Cameron is an author who receives a royalty of 8% of the value of sales of his book.
Calculate Cameron’s royalty for book sales totalling $23 000.
WORKED
Example
13
2

Working overtime
Overtime is paid when a wage earner works more than the regular hours each week.
When an employee works overtime a higher rate is paid. This higher rate of pay is
called a penalty rate. The rate is normally calculated at either:
time and a half, which means that the person is paid 1 times the usual rate of pay,
or
double time, which means that the person is paid twice the normal rate of pay.
A person may also be paid these overtime rates for working at unfavourable times,
such as at night or during weekends.
To calculate the hourly rate earned when working overtime we multiply the normal
hourly rate by the overtime factor, which is 1 for time and a half and 2 for double time.
To calculate the pay for a period of time worked at time and a half or double time, we
multiply the normal pay rate by the overtime factor (either 1 or 2) and then by the
number of hours worked at that overtime rate.
When we calculate the total pay for a week that involves overtime, we need to calculate
the normal pay and then add the amount earned for any overtime.
1
2
---
1
2
---
Gustavo is paid $9.78 per hour in his
job as a childcare worker. Calculate
Gustavo’s hourly rate when he is
being paid for overtime at time and
a half.
THINK WRITE
Multiply $9.78 (the normal hourly rate) by
1 (the overtime factor for time and a half).
Time and a half rate = $9.78 × 1
Time and a half rate = $14.671
2
---
1
2
---
14WORKEDExample
1
2
---
Adrian works as a shop assistant and his normal rate of pay is $12.84 per hour. Calculate
the amount Adrian earns for 6 hours work on Saturday, when he is paid time and a half.
THINK WRITE
Multiply $12.84 (the normal pay rate) by
1 (the overtime factor) and by 6 (hours
worked at time and a half).
Pay = $12.84 × 1 × 6
Pay = $115.561
2
---
1
2
---
15WORKEDExample

Some examples will have more than one overtime rate to consider and some will
require you to work out how many hours have been worked at each rate.
Natasha works as a waitress and is paid $11.80 per hour for a 38-hour week. Calculate
Natasha’s pay in a week where she works 5 hours at time and a half in addition to her
regular hours.
THINK WRITE
Calculate Natasha’s normal pay. Normal pay = $11.80 × 38
= $448.40
Calculate Natasha’s pay for 5 hours at
time and a half.
Time and a half = $11.80 × 1 × 5
= $88.50
Add the normal pay and the time and a
half pay together.
Total pay = $448.40 + $88.50
= $536.90
1
2
1
2
---
3
16WORKEDExample
Graeme is employed as a car assembly worker and is paid
$10.40 per hour for a 36-hour week. If Graeme works
overtime, the ﬁrst 6 hours are paid at time and a half and
the remainder at double time. Calculate Graeme’s pay in
a week where he works 45 hours.
THINK WRITE
Calculate the number of hours
overtime Graeme worked.
Overtime = 45 − 36
Overtime = 9 hours
Of these nine hours, calculate
how much was at time and a
half and how much was at
double time.
Time and a half = 6 hours
Double time = 3 hours
Calculate Graeme’s normal pay. Normal pay = $10.40 × 36
Normal pay = $374.40
Calculate what Graeme is paid
for 6 hours at time and a half.
Time and a half = $10.40 × 1 × 6
Time and a half = $93.60
Calculate what Graeme is paid
for 3 hours at double time.
Double time = $10.40 × 2 × 3
Double time = $62.40
Calculate Graeme’s total pay by
adding the time and a half and
double time payments to his
normal pay.
Total pay = $374.40 + $93.60 + $62.40
Total pay = $530.40
1
2
3
4
1
2
---
5
6
17WORKEDExample

Working overtime
1 Reece works in a restaurant and is paid a normal hourly rate of $11.30. Calculate the
amount Reece earns each hour when he is being paid time and a half.
2 Carmen works as a waitress and is paid $11.42 per hour. Calculate Carmen’s rate
per hour on a Sunday when she is paid double time.
3 Gareth works as a train driver and is normally paid $11.48 per hour. For working on
public holidays he is paid double time and a half (overtime factor = 2 ). Calculate
Gareth’s hourly rate of pay on a public holiday.
4 Ben works in a hotel and is paid $11.88 per hour. Calculate the total amount Ben will
earn for an 8-hour shift on Saturday when he is paid at time and a half.
5 Taylor works as an usher at a concert venue. She is normally paid $13.10 per hour.
Calculate Taylor’s pay for 6 hours on Sunday when she is paid double time.
7
Ernie works as a chef and is paid $9.95 per hour. What will Ernie’s hourly rate be
when he is paid time and a half for overtime?
A $11.45 B $14.92 C $14.93 D $19.90
Name
Ordinary
rate
Overtime
rate
Hours
worked Pay
A. Nguyen $8.90 Time and a half 4
M. Donnell $9.35 Double time 6
F. Milosevic $11.56 Time and a half 7
J. Carides $13.86 Time and a half 6.5
Y. Robinson $22.60 Double time 5.5
1. Overtime is paid when you work more than your normal working hours in a
week, and you receive a higher rate of pay for the extra hours.
2. Overtime can be paid at:
(a) time and a half — 1 times the normal hourly rate
(b) double time — twice the normal hourly rate.
3. To calculate the hourly rate when working overtime, multiply the normal
hourly rate by the overtime factor.
4. To calculate the pay that is received for overtime, multiply the normal hourly
rate by the overtime factor by the number of hours worked at that overtime rate.
5. To calculate the total pay for a week when overtime has been worked, calculate
the normal pay and the pay for each overtime rate separately, and add them.
1
2
---
remember
1E
WORKED
Example
14
SkillS
HEET
1.5
Multiplying
a quantity
(money) by a
decimal
SkillS
HEET
1.6
Adding
periods
of time
SkillS
HEET
1.7
Multiplying
and dividing
a quantity
by a
fraction
1
2
---
WORKED
Example
15
multiple choice

8
Stephanie works in a shop and is paid $9.40 per hour. Calculate how much more
Stephanie will earn in 8 hours work at time and a half than she would at ordinary
rates.
A $37.60 B $75.20 C $112.80 D $188.00
9
Eric works on the wharves unloading containers and is paid $14.20 per hour.
Calculate the number of hours at time and a half that Eric will have to work to earn
the same amount of money that he will earn in 9 hours at ordinary rates.
A 4.5 hours B 6 hours C 10.5 hours D 13.5 hours
10 Rick works 37 hours at ordinary time each week and receives $12.64 per hour.
Calculate Rick’s pay in a week where, in addition to his normal hours, he works
4 hours overtime at time and a half.
11 Kirsty works 36 hours each week at a pay rate of $16.40 per hour. Calculate Kirsty’s
pay in a week where, in addition to her ordinary hours, she works 4 hours on Sunday,
when she is paid double time.
12 Grant works as a courier and is paid $13.25 per hour for a 35-hour working week.
Calculate Grant’s pay for a week where he works 4 hours at time and a half and 2 hours
at double time in addition to his regular hours.
14
Jenny is a casual worker at a motel. The normal rate of pay is $10.40 per hour. Jenny
works 8 hours on Saturday for which she is paid time and a half. On Sunday she
works 6 hours for which she is paid double time. Jenny’s pay is equivalent to how
many hours work at the normal rate of pay?
A 14 B 21 C 24 D 28
15
Patricia works a 35-hour week and is paid $14.15 per hour. Any overtime that Patricia
does is paid at time and a half. Patricia wants to work enough overtime so that she
earns more than $600 each week. What is the minimum number of hours that Patricia
will need to work to earn this amount of money?
A 40 B 41 C 42 D 43
Name
Ordinary
rate
Normal
hours
Time and a
half hours
Double time
hours Total pay
W. Clark $8.60 38.5 4 —
A. Hurst $9.85 37.5 — 6.5
S. Gannon $14.50 38.5 5 2.5
G. Dymock $16.23 37.5 4 1.5
D. Colley $24.90 36.5 6 8.5
multiple choice
multiple choice
WORKED
Example
16
multiple choice
multiple choice

16 Steven works on a car assembly line and is paid $12.40 for a 36-hour working week.
The first 4 hours overtime he works each week is paid at time and a half with the rest
paid at double time. Calculate Steven’s earnings for a week in which he works 43 hours.
17 Kate works as a computer technician and is paid $18.56 per hour for a 38-hour working
week. For the first 4 hours overtime each week Kate is paid time and a half and the
rest is paid at double time. Calculate Kate’s pay in a week where she works:
a 38 hours b 41 hours c 45 hours.
18 Zac works in a supermarket. He is paid at an ordinary rate of $8.85 per hour. If Zac
works more than 8 hours on any one day the first 2 hours are paid at time and a half
and the rest at double time. Calculate Zac’s pay if the hours worked each day are:
Monday — 8 hours Tuesday — 9 hours Wednesday — 12 hours
Thursday — 7 hours Friday — 10.5 hours.
1. Load the spreadsheet Wages_1 that you started earlier in this chapter and edit it with
the following information. Alternatively, access the spreadsheet Wages_2 from the
Maths Quest General Mathematics Preliminary Course CD-ROM.
2. In cell G7 write the formula =C7*D7 + C7*1.5*E7 + C7*2*F7. This formula will
calculate the gross wage for Frederick Astini. (You should get $526.40.)
3. Highlight cells G7 to G11 and choose the Fill Down option to copy this formula to
the rest of this column. (Your answers should show $526.40, $442.40, $537.60,
$481.60 and $644.00.)
4. Check the functioning of your spreadsheet by changing the hours worked by
Frederick Astini to 38 normal hours, 3 hours at time and a half and 4 hours at double
time. You should now have $554.40 in cell G7. Now change the hours for the other
employees and notice the gross pay changing. Now change the hourly rate of pay for
each employee.
5. Use the Save As option to save this spreadsheet under the name Wages_2. (This
will mean that you have copies of both version 1 and 2 of the spreadsheet.)
WORKED
Example
17
Computer ApplicationComputer Application Wages2
E
XCELSpread
sheet
Wages_2

Fixed incomes
Many people rely on government allowances for an income. These allowances include
the youth allowance, pensions and other welfare benefits.
Investigating government payments
Youth allowance
1 What is the youth allowance?
2 How much is paid per week for the youth allowance?
3 What conditions are placed on receipt of the youth allowance?
4 What will be the total received by a person after one year of receiving the
youth allowance?
5 Find out the average weekly income for an 18-year-old person. Compare this
with a person who receives the youth allowance.
Unemployment benefits
6 What is the difference between unemployment benefits and the youth
allowance?
7 How much is paid per week for the unemployment benefit for a:
a single person?
b single person with children?
c married person?
8 Do you have to work to receive the unemployment benefit?
9 What conditions are placed on a person receiving unemployment benefits?
(For example, must they show that they are looking for work.)
10 Compare the amount received by a person on unemployment benefits with the
average weekly income for an adult in Australia.
Pensions
11 Name three different types of
pension that are paid by the
government.
12 What are the conditions for
receiving each of these
pensions?
13 How much is received per
week for each of these
pensions?
14 Does the amount received
vary according to marital
status and the number of
dependants?

Additions to and deductions from
gross pay
Although we may calculate a person’s pay, this is not the amount that is actually
received. The amount that we calculate, based on their wage or salary, is called gross
pay or gross wage. From your gross pay, several deductions may be made for items
such as tax, union fees, private health insurance, superannuation and so on. The amount
left after these deductions have been taken out is called the net pay and it is this
amount that you actually receive.
To calculate an employee’s net pay we subtract any deductions from the gross pay.
In some cases, you will be required to calculate the size of a deduction based on either
an annual amount or a percentage.
Robert’s gross pay is $643.60 per week. Robert has deductions for tax of $144.46, super-
annuation of $57.92 and union fees of $11.40. Calculate Robert’s net pay.
THINK WRITE
From $643.60 (gross pay) subtract
$144.46 (tax), $57.92 (superannuation)
and $11.40 (union fees).
Net pay = $643.60 − $144.46 − $57.92 − $11.40
Net pay = $429.82
18WORKEDExample
Bruce is a shop assistant and he has his union fees deducted from his pay each week. If the
annual union fee is $324.60, calculate the size of Bruce’s weekly union deduction.
THINK WRITE
Divide $324.60 (the annual union fee)
by 52.
Weekly deduction = $324.60 ÷ 52
Round the answer off to the nearest
cent.
Weekly deduction = $6.24
1
2
19WORKEDExample
Charissa is a salary earner and her gross fortnightly salary is $1320. Charissa pays 9% of
her gross pay each fortnight in superannuation. Calculate how much is deducted from
Charissa’s pay each fortnight for superannuation.
THINK WRITE
Calculate 9% of $1320 (gross pay). Superannuation = 9% of $1320
Superannuation = 9 ÷ 100 × $1320
Superannuation = $118.80
20WORKEDExample

When employees take annual leave, they may receive an annual leave loading. When
on holidays, such employees are paid an extra 17 % of their gross pay for up to
4 weeks.
1
2
---
Russell is a newspaper printer and is paid
$14.75 per hour for a 36-hour working
week.
a Calculate Russell’s pay for a
normal working week.
b Calculate Russell’s total pay for
his 4 weeks annual leave if he
receives a 17 % annual leave
loading on the 4 weeks pay.
THINK WRITE
a Multiply $14.75 (hourly rate) by
36 (hours worked).
a Normal pay = $14.75 × 36
Normal pay = $531.00
b Multiply $531.00 (weekly pay)
by 4 to ﬁnd his normal pay for
4 weeks.
b Normal 4 weeks pay = $531.00 × 4
= $2124.00
Calculate the annual leave
loading by ﬁnding 17 % of
$1692.
Annual leave loading = 17 % of $2124.00
= 17 ÷ 100 × $2124.00
= $371.70
Add $371.10 (annual leave
loading) to $2124 (normal
4 weeks pay).
Total holiday pay = $2124.00 + $371.70
= $2495.70
1
2
---
1
2
1
2
---
1
2
---
1
2
---
3
21WORKEDExample
1. Gross pay refers to pay before any deductions are made.
2. Net pay refers to the pay received after deductions have been taken out.
Net pay = gross pay − deductions
3. Some deductions are calculated on an annual basis and then taken out in equal
weekly or fortnightly amounts.
4. Some deductions are calculated as a percentage of gross earnings.
5. When employees take their annual leave a loading is often paid. This means
that they are paid an extra 17 % of their gross pay.1
2
---
remember

Additions to and deductions
from gross pay
1 Trevor is a tiler and his gross pay is $532.75 per week. His weekly deductions are
$106.20 for tax, $47.95 for superannuation and $17.70 for health fund contribu-
tions. Calculate Trevor’s net pay each week.
3 David works in a mine and is paid a wage of $15.75
per hour for a 36-hour working week. His deductions
are $118.02 for tax, $32.50 for health insurance,
$51.03 for superannuation and $5.00 for the miner’s
social club. Calculate David’s net pay.
4 Belinda is on an annual salary of $65 500. Belinda is
paid fortnightly.
a Calculate Belinda’s fortnightly pay.
b If Belinda has fortnightly deductions of $834.92
for tax, $226.73 for superannuation and $23.50
as a contribution to a professional organisation,
calculate Belinda’s net pay.
5 Lars works as a train driver and is a member of
the union. If Lars’ union fees are $394.00 per
year and Lars has his fees deducted from his pay
weekly, calculate the size of Lars’ weekly
deduction.
6 Yasmin is a salary earner who is paid
fortnightly. Yasmin has her fees for private
health insurance deducted from her pay fortnightly. If the
annual premium for Yasmin’s health cover is $1456.50, calculate the amount
that needs to be deducted from Yasmin’s pay each fortnight.
7 Dorothy is paid a wage of $13.45 per hour for a 38-hour working week.
a Calculate Dorothy’s gross weekly pay.
b Dorothy pays union fees of $265.60 per annum. Calculate the amount that should
be deducted from her pay each week for union fees.
c Dorothy has $98.73 deducted from her pay each week for tax and union fees.
Calculate Dorothy’s net pay.
Gross pay Deductions Net pay
$345.00 $89.45
$563.68 $165.40
$765.90 $231.85
$1175.60 $429.56
$2500.00 $765.40
1F
SkillS
HEET
1.4
Finding a
percentage
of a
quantity
(money)
SkillS
HEET
1.8
Expressing
one
quantity as a
percentage
of another
SkillS
HEET
1.9
Increasing
a quantity
by a
percentage
WORKED
Example
18
WORKED
Example
19

8 Patrick is on an annual salary of $56 000 and is paid fortnightly.
a Calculate Patrick’s gross fortnightly pay.
b Patrick pays fortnightly into a private health fund for which the annual premium is
$1165.75. Calculate the fortnightly payment.
c Patrick has his health fund payment and tax (total $660.60) deducted from his fort-
nightly pay. Calculate Patrick’s net fortnightly pay.
9 Sabrina earns a weekly wage of $623.50. She puts 9% of this wage into a
superannuation fund. Calculate the amount that Sabrina pays in superannuation.
10 Arthur earns a gross fortnightly salary of $1520.50. He pays 11% of his gross salary
in superannuation. Calculate the amount that Arthur has deducted from his salary each
fortnight for superannuation.
11 Rex is paid $11.12 per hour for a 38-hour working week.
a Calculate Rex’s gross weekly wage.
b Rex pays 10.5% of his gross weekly wage in superannuation. Calculate Rex’s
weekly superannuation contribution.
c Rex pays tax of $68.18 as well as his superannuation contribution. Calculate Rex’s
weekly net wage.
12 Raylene is on an annual salary of $75 000 and is paid fortnightly.
a Calculate Raylene’s gross fortnightly salary.
b Raylene pays 12.75% of her gross salary in superannuation. Calculate the amount
that is deducted from Raylene’s salary each fortnight for superannuation.
c Raylene has union fees of $486.00 per annum and private health insurance of
$1323.70 per annum deducted from her pay fortnightly. Calculate the amount of
the deduction made for both union fees and health insurance.
d If Raylene pays $1009.22 in fortnightly tax, as well as the above deductions, calcu-
late her net weekly pay.
13 Liang-Yi earns $13.60 per hour for a 38-hour working week.
a Calculate the amount Liang-Yi will earn in a normal working week.
b Calculate the total amount Liang-Yi will receive for his 4 weeks annual leave if he
receives a 17 % holiday loading.
14 Paula is paid an annual salary of $45 800.
a Calculate Paula’s gross weekly salary.
b Calculate the total amount Paula will receive for her 4 weeks annual leave if she is
paid a 17 % holiday loading.
15 Leon is paid $12.95 per hour for a 36-hour working week.
a Calculate Leon’s weekly wage.
b Leon takes one week’s holiday for which he is given a 17 % loading. Calculate
the holiday loading.
c If Leon pays $83.24 in tax, calculate his net pay for his week’s holiday.
16 Scott is paid an annual salary of $68 500.
a Calculate Scott’s salary for a 4-week period.
b Calculate how much holiday loading Scott will receive for this 4-week period if it
is paid at 17 %.
c Scott pays $1250 per annum in private health insurance, which is deducted from
his gross salary. Calculate how much health insurance Scott must pay for a 4-week
period.
d If Scott pays $1779.92 in tax for this 4 weeks, calculate his net pay for the 4-week
holiday.
WORKED
Example
20
WORKED
Example
21
1
2
---
1
2
---
1
2
---
1
2
---

1. Load your spreadsheet Wages_2 and add the Deductions and Net Pay
columns. Alternatively, accesss the spreadsheet Wages_3 from the Maths Quest
General Mathematics Preliminary Course CD-ROM.
2. In cell I7 write the formula =G7 − H7. This formula will calculate Net Pay by sub-
tracting Deductions from Gross Pay.
3. Your spreadsheet will now calculate both a person’s Gross Pay and Net Pay. Save
this as Wages_3. (You should now have three versions of the spreadsheet saved.)
4. Now clear all the data from the columns Pay Rate, Normal Hours, Time and a half
Hours, Double Time Hours and Deductions. You should then have a spreadsheet set
up with no data and $ - (as can be seen below) where there are formulas.
When a spreadsheet is in this form it is called a template. The spreadsheet is now
ready to accept new data and make new calculations. Save this version as Wages
template. Alternatively, download the Wages template from the Maths Quest General
Mathematics Preliminary Course CD-ROM.
Computer ApplicationComputer Application Wages template3
E
XCELSpread
sheet
Wages_3
E
XCELSpread
sheet
Wages
template

Costs of banking
Once we have earned money, we use a bank or similar ﬁnancial institution to look after
it until we need it. When we deposit money in the bank the bank pays interest on that
account. However, for many accounts where we need instant access to our money, the
interest paid is very low and there may be fees associated with using the account.
Examining bank fees and taxes
Find three bank accounts into which your pay could be deposited electronically.
Answer the following questions about them.
1 What is the interest rate payable on the account?
2 Is there a minimum balance that must be maintained in the account?
3 What are the features of this account? (For example, do you get a cheque book?)
4 Is there a monthly management fee on the account?
5 How many free transactions are you allowed each month? What are the charges
for exceeding this number of transactions?
6 Are the transaction fees applied differently to deposits and withdrawals? Are
they levied differently for over-the-counter and automatic teller and EFTPOS
transactions?

1 Wendy works 37 hours per week at a rate of $12.74 per hour. Calculate Wendy’s
weekly wage.
2 David is paid an annual salary of $43 240. Calculate David’s fortnightly pay.
3 Rebecca is paid a commission of 7.2% of the value of all sales she makes. Calculate
Rebecca’s pay in a week where her sales total $5700.
4 Veronica works assembling radios. She is paid $5.23 for every radio assembled.
Calculate Veronica’s pay in a week where she assembles 45 radios.
5 Christy is paid $34.50 per 1000 letterbox deliveries. Calculate what Christy is paid for
2200 deliveries.
6 Matthew is paid $12.68 per hour at ordinary rates. Calculate what Matthew earns per
hour in overtime when he is paid at time and a half.
7 Calculate Norman’s earnings for a 6-hour shift at double time when his ordinary rate
of pay is $8.45 per hour.
8 Darren is a bank teller who is paid $9.80 per hour. Calculate what Darren will earn in
a week where he works 37 hours at ordinary rates as well as 5 hours at time and a
half.
9 Zelko’s gross wage is $459.50 per week. He has deductions of $80.93 for tax, $13.80
for superannuation and $11.25 for union fees. Calculate Zelko’s net wage.
10 Calculate what Melissa will receive for 4 weeks holiday pay if her normal pay is
$512.40 per week and she is paid a 17 % holiday loading.
Budgeting
Once we have earned money we need to allocate the money to cover our expenses;
otherwise, we may spend more than we earn! Allocating money to cover expenses is
called making a budget. A budget is divided into two parts: income and expenditure. A
budget is balanced when income and expenditure are equal.
Consider the budget below, drawn up for Tanya, who earns a net wage of $700.
Income Expenditure
Wages $700 Rent
Groceries
Bills
Car loan
Car running costs
Entertainment
Credit card
Savings
$150
$100
$100
$75
$50
$60
$50
$115
Total $700 Total $700
3
1
2
---
1
2
---

When designing a budget, it is important to look for all your expenses and set money
aside for them. For example, electricity bills arrive every three months and money
should be set aside each week so that when the bill does arrive you have the money to
pay for it. The amount set aside should be based on the normal amount of the bill over
a year, with that amount divided into weekly or fortnightly amounts.
For bills such as electricity and telephone, an extra amount should be allowed, as you
do not know the exact amount of the bill until it arrives. Such an allowance covers the
possibilities of a price rise or increased usage. This is not necessary for bills such as
council rates or insurance, as these are known in advance.
Some bills are calculated over different lengths of time, so the simplest way to develop
a budget is to calculate all bills over a year.
Ben receives four electricity bills each year. For the previous year they were for $136, $187,
$169 and $105. How much should Ben budget for electricity bills out of each week’s pay?
We should allow an extra 10% to cover the possibility of price increases or extra usage.
THINK WRITE
Calculate the total of the previous years
bills.
Annual total = $136 + $187 + $169 + $105
Annual total = $597
To calculate the weekly amount, divide
$597 by 52.
Weekly amount = $597 ÷ 52
Weekly amount = $11.48
Increase $11.48 by 10%. 110% of $11.48 = $12.62
Make a practical approximation of the
answer.
Ben should budget $12.50 per week to cover
the electricity.
1
2
3
4
22WORKEDExample
Marlene has the following bills.
Electricity $110 every 2 months
Telephone $95 per quarter
Car insurance $254 every 6 months
Rates $1250 per year
Calculate the total amount that Marlene should budget for all of these bills each fortnight,
allowing for an extra 10% to cover possible increases.
THINK WRITE
Calculate the total annual amount for
electricity.
Electricity = $110 × 6
Electricity = $660
telephone.
Telephone = $95 × 4
Telephone = $380
car insurance.
Car insurance = $254 × 2
Car insurance = $508
rates.
Rates = $1250
1
2
3
4
23WORKEDExample

To bring a budget into balance, any money that is not spent can be saved. The amount
saved can be calculated by subtracting the expenses to which we are committed from
the total earnings.
To do work on budgeting you will need to be able to interpret the information on
various household bills.
THINK WRITE
Find the annual total for all of these
bills.
Total = $660 + $380 + $508 + $1250
Total = $2798
Increase $2798 by 10%. 110% of $2798 = 110 ÷ 100 × $2798
110% of $2798 = $3077.80
Divide $3077.80 by 26. Fortnightly allowance = $3077.80 ÷ 26
Fortnightly allowance = $118.38
Round off and give a written answer. Marlene should allow about $118 per fortnight
to cover her bills.
5
6
7
8
Peter earns $950 per fortnight. He allows $110 per fortnight for his bills, $250 per fort-
night for groceries, $70 for car running costs and $80 per fortnight for entertainment.
Peter also has a mortgage for which the payment is $600 per month.
a Calculate the amount Peter should allocate each fortnight for his mortgage.
b Calculate the amount of money Peter can save each fortnight.
c Draw up a budget for Peter, showing his income and expenditure.
THINK WRITE
a Calculate the annual
mortgage amount.
a Annual mortgage = $600 × 12
Annual mortgage = $7200
Calculate the fortnightly
amount by dividing by 26.
Fortnightly amount = $7200 ÷ 26
Fortnightly amount = $276.92
b Calculate total expenses. b Total expenses = $276.92 + $110 + $250 + $70 + $80
Total expenses = $786.92
Calculate savings by
subtracting all expenses
from $950.
Savings = $950 − $786.92
Savings = $163.08
c Draw up a budget by listing
income and expenses in two
columns.
c
1
2
1
2
Income Expenditure
Wages $950 Mortgage
Bills
Groceries
Car
Savings
$276.92
$110.00
$250.00
$70.00
$163.08
Total $950 Total $950.00
24WORKEDExample

Look at the extract from a sample telephone bill below.
a What is the total of the bill?
b For what period are the call charges?
c How much of the bill is for service and equipment?
THINK WRITE
a Look in the box labelled ‘Total amount
payable’.
a The total of the bill is $154.10.
b Look at the dates following ‘Local
Calls’.
b The calls were for the period 5 Jan to 4 Apr.
c Look at the amount next to ‘Service &
Equipment’.
c The cost for service and equipment was
$51.45.
25WORKEDExample

Budgeting
1 Vesna gets her telephone bill quarterly. Last year her four bills were $89.50, $103.40,
$110.30 and $95.00. Calculate the amount that Vesna should budget for her telephone
bill each week, allowing approximately 10% to cover price increases or extra usage.
2 Christopher pays $1360 each year in council rates. Calculate how much he should
budget for each fortnight for council rates.
3 Isabelle pays $34.65 per month in car insurance. Calculate the amount that she should
budget each week for car insurance.
4 Tristan’s mortgage repayments are $750 per month. Calculate the amount that Tristan
should budget for each fortnight to cover his mortgage bill.
5 Mr and Mrs Banks have the following bills.
Electricity $130 every quarter
Car insurance $35 per month
House insurance $29.50 per month
Council rates $1100 per year
Calculate the amount that Mr and Mrs Banks should budget for each week, to pay all
these bills, allowing an extra 10% for extra usage or price increases.
6 Mr and Mrs Duric have the following bills.
Car insurance $287 every 6 months
Home contents insurance $365 per year
Private health insurance $1200 per year
Rent $180 per week
Calculate the total amount that Mr and Mrs Duric must budget for each fortnight, to
cover all these bills.
7 Neville earns $685 per week. His expenses are $100 for rent, $90 for groceries, $75
for bills, $70 in car running costs, $60 in entertainment and $50 for miscellaneous
expenses.
a Calculate the amount that Neville can save each week.
b Present the above information in the form of a budget for Neville.
1. A budget is a statement of income and expenditure.
2. A budget is in balance when income and expenditure are equal.
3. When preparing a budget, you should calculate weekly or fortnightly amounts
based on annual expenditure.
4. Any unspent money should be set aside as savings to bring a budget into
balance.
5. To manage a budget, you will need to be able to read a variety of household
bills.
remember
1G
WORKED
Example
22
SkillS
HEET
1.9
Increasing
a quantity
by a
percentage
E
XCELSpread
sheet
Budgets
WORKED
Example
23
WORKED
Example
24

8 Petria has the following bills.
Electricity $120 every quarter
Telephone $80 every quarter
Council rates $800 per annum
Water rates $700 per annum
Insurance $70 per month
a Calculate the amount that Petria must budget each fortnight for the above bills.
b Petria has a mortgage with a monthly repayment of $900. Calculate the amount
that Petria must budget each fortnight for her mortgage.
c Petria has a net fortnightly pay of $1345. If Petria budgets $250 per fortnight for
groceries, $80 for entertainment, $30 for medical expenses and $70 for car running
costs, calculate the amount that Petria can save each fortnight.
d Prepare the above information in a budget for Petria.
9 Look at the extract from a sample telephone bill below.
a What is the total of the bill?
b For what period are the local calls charged?
c What is the charge for international calls?
d If four of these bills are received each year, what amount should be budgeted per
week to pay them?
WORKED
Example
25

10 Look at the extracts from a sample electricity bill below.
a What is the amount due for this bill?
b What was the amount charged for off-peak use on this
bill?
c How many days does this bill cover?
d How many kWh of power were used under the
Domestic heading?
e What is the present reading of the domestic meter?
f What was the previous reading of the off-peak meter?

11 Look at the extracts from a sample gas bill below.
a What is the amount due for this bill?
b How many days does this bill cover?
c What is the cost per MJ on this bill?
d What is the daily gas consumption in
MJ for this household?
AGL Retail Energy Pty Ltd, ACN 074 839 464
PO Box 944, North Sydney NSW 2059
Invoice Number 00001
Date of Issue 21 / 09 / 07
Customer Number
MR BILL SAMPLE
787 SAMPLE RD
SAMPLEVILLE VIC 3149
03A
Account Enquiries 131 606
Gas faults and emergencies 24hrs 131 808
24 Hour Emergency (Gasfitters, Electricians) 131 909
Sales 131 707
Callers OutsideVictoria 1800 645 221
Payment Due
Total Due
10 / 10 / 07
$143.75
This Bill
$143.75
Balance
$0.00
Payments Received
$55.92
Last Bill
$55.92
Gas Charge See over for details 143.75
Total Due $143.75
$
Supply Address: 787 SAMPLE RD, SAMPLEVILLE
Details
Average MJ
Per Day
Average Cost
Per Day
Gas Consumption:
Meter Current Previous Units Megajoules
Type Number Date Reading Date Reading Consumed Consumed
Gas MS666421 / 09 / 07 1874 11 / 07 / 07 1578 296 11593 MJ1
1 - To convert Gas Units to megajoules, multiply the Units by 39.166666
Consumption Charge: Tariff - General Domestic Rate
Total for 72 days was 11593 MJ, charged at 1.2400¢ per MJ
Total Gas Charge = $143.75
This Bill
Same Bill LastYear
$2.00 $1.50161 123

12 Look at the extract from the sample bill for council rates below.
a What is the amount owed in council rates?
b What is the rateable value of the property?
c What is the domestic waste charge?
d The rates can be paid in how many instalments of what amount?
BLUE MOUNTAINS CITY COUNCIL
GREAT WESTERN HIGHWAY, KATOOMBA
P.O. Box 189, Katoomba, N.S.W., 2780
Phone: (STD 047) 82 0777 DX: 8305 Katoomba
RATE ENQUIRIES DIRECT (047) 82 0538
Office and Cashier’s Hours: Monday to Friday 8.30 a.m. to 5.00 p.m.
RATES AND
CHARGES NOTICE
FOR PERIOD
1 JULY, 2007 TO 30 JUNE, 2008
RATE NOTICE Section 546 Local Government Act, 1993.
As the owner, holder, tenant, or other person liable to pay rates and charges in
respect of the below-mentioned land (or the agent to any such person) you are
hereby notified that such land has been rated by Council as shown hereunder.
• SHOULD THE ADDRESS
SHOWN ON THIS NOTICE
BE INCORRECT, PLEASE
ADVISE COUNCIL
DIRECT IN WRITING
• ACCRUAL OF INTEREST
INTEREST ACCRUES ON
RATES AND CHARGES
THAT REMAIN UNPAID
AFTERTHE DUE DATE.
INTEREST ACCRUES
ON A DAILY BASIS.
INTEREST DOES NOT
ACCRUE ON
INSTALMENTS NOT
YET DUE. INTEREST
RATE 10.5% PER
ANNUM.
• FOR IMPORTANT
INFORMATION
AND PAYMENT
METHODS
PLEASE SEE
REVERSE
DESCRIPTION AND SITUATION OF LAND RATED
GENERAL MANAGER
BILLING NUMBER
246810
PARTICULARS OF RATES AND CHARGES CENTS IN $ AMOUNT
1st INSTALMENT 2nd INSTALMENT 3rd INSTALMENT 4th INSTALMENT
POSTING DATE
29/07/07
FIRST INSTALMENT OR FULL AMOUNT
DUE DATE
31/08/07
RATEABLE VALUE
BASE DATE 1791
Domestic 251.90 251.90 251.90 $1007.70
31/08/07 30/11/07 28/02/08 31/05/08
Residential Faulconbridge 1.018000 90000 916.20
Domestic Waste Charge 91.50 1 91.50
Teller’s Stamp
Teller’s Stamp
PLEASE DEDUCT ANY PAYMENTS MADE SINCE
22/7/07FOR PAYMENT BY QUARTERLY INSTALMENTS PAY ABOVE AMOUNTS BY DUE DATES.
FOR
PAYMENT
IN FULL
PAY THIS
AMOUNT
J CITIZEN
10 BROWN ST
SMITHVILLE NSW 2222
Work
SHEET 1.2

Methods of payment
• A salary is a ﬁxed amount paid to an employee to do a job. This is usually based on
an annual amount divided into weekly or fortnightly instalments.
• A wage is an amount paid to an employee according to an hourly rate. The weekly
wage is the hourly rate multiplied by the hours worked.
• Commission or royalties are payments based on a percentage of sales.
• Payment by piece is payment to an employee according to the amount of work
completed.
Overtime
• Overtime is paid when the employee works more than the regular hours each week.
Usually the employee will be paid at either:
time and a half — 1 times the normal hourly rate, or
double time — twice the normal hourly rate.
Additions and deductions
• Gross pay is the pay the employee receives before any deductions are taken out.
• Deductions are made from gross pay for tax, superannuation, union fees and so on.
• The amount left from gross pay after deductions are taken out is called net pay.
• Employees receive an extra 17 % when they take their annual leave. This is called
the annual leave loading.
Budgeting
• A budget is a list of income and expenses.
• Budgets are used to allocate money to various purposes and to ensure that
expenditure does not exceed income.
• If income and expenses are equal the budget is said to be balanced.
summary
1
2
---
1
2
---

1 Carole earns a salary of $39 600 per year and is paid weekly. Calculate her weekly pay.
2 Neil earns a salary of $67 400 per year and is paid fortnightly. Calculate his fortnightly pay.
3 Lainie earns a salary of $1326 per month. Calculate her annual salary.
4 Paul earns a salary of $51 000 per annum and works an average of 44 hours per week.
Calculate the hourly rate to which Paul’s annual salary is equivalent.
5 Calculate the weekly wage of each of the following people.
a Sandra, who works 36 hours at $14.50 per hour
b Darren, who works 38 hours at $15.65 per hour
c Melissa, who works 43 hours at $13.68 per hour
6 Bartenders earn a standard rate of $12.30 per hour. Casual bartenders receive a casual rate of
$13.80 per hour.
a Kevin is a full-time bartender who works a 36-hour week. Calculate his weekly wage.
b Len is a casual bartender who works 16 hours a week. Calculate Len’s weekly wage.
7 Charlotte works 36 hours for a wage of $410.40. Calculate her hourly rate of pay.
8 Brian earns $11.83 per hour. Calculate the number of hours that Brian would need to work
in a week if he wanted to earn $500.
9 Renee is a furniture salesperson who is paid 8% commission on all her sales. Calculate
Renee’s pay in a week where her sales total $4940.
10 Daryl is a car salesman who is paid $275 per week plus 1.5% commission on all sales.
Calculate Daryl’s pay in a week where his sales total $34 900.
11 Felicity sells cosmetics and is paid $150 per week plus 15% commission on all sales in
excess of $1000. Calculate Felicity’s commission in a week where her sales total $3560.
12 Hong has an after-school job detailing cars. Hong is paid $11.75 for every car that he
details. Calculate what Hong is paid for detailing 29 cars.
13 Svetlana delivers brochures to the local neighbourhood and is paid $17.50 for every
1000 brochures delivered. Calculate what Svetlana will earn for delivering 5600 brochures.
14 Beatrice earns $14.20 per hour. Calculate what she will earn per hour:
a on Saturdays, when she is paid time and a half
b on Sundays, when she is paid double time.
1A
CHAPTER
review
1A
1A
1A
1B
1B
1B
1B
1C
1C
1C
1D
1D
1E

15 Nicholas is a storeman who is paid a normal rate of $10.90 per hour. Calculate what
Nicholas will earn for:
a 6 hours work at time and a half
b 5 hours work at double time.
16 A photographic chemicals ﬁrm pays its factory workers $9.70 per hour. Calculate what each
of the following employees earns in a week where:
a Chao-ping works 38 normal hours
b Elizabeth works 38 normal hours and 4 hours at time and a half
c Phillip works 38 normal hours and 3 hours double time
d Charlie works 38 normal hours, 4 hours time and a half and 3 hours double time.
17 Eddie works as a shop assistant and is paid an ordinary rate of $10.54 per hour for a 36-hour
working week. Eddie is paid time and a half for the ﬁrst 4 hours overtime worked and
double time for any hours beyond that. Calculate Eddy’s wage in a week where he works
47 hours.
18 Marella works as a seamstress and receives a
gross wage of $439.00 per week. From her
pay, $73.85 is deducted for tax, $4.80 for
union fees, $39.51 for superannuation and
$9.20 for health insurance. Calculate
Marella’s net wage.
19 Anne works as a shop assistant. Her annual
union fees are $210.60. Anne has her union
fees deducted from her pay weekly. Calculate
the size of Anne’s weekly deduction.
20 Harold earns a salary of $48 250 per annum
and is paid fortnightly.
a Calculate Harold’s fortnightly pay.
b Harold pays 9.5% of his gross fortnightly
pay into a superannuation fund. Calculate
the size of Harold’s fortnightly
superannuation contribution.
21 Lance is paid $14.86 per hour and works
38 hours at normal time and 3 hours overtime
for which he is paid time and a half.
a Calculate Lance’s gross weekly pay.
b Lance has his private health cover deducted from his gross pay. The annual contribution
is $689.40. Calculate the amount deducted weekly from Lance’s pay.
c Lance pays 11.5% of his gross pay into superannuation. Calculate the amount of Lance’s
d If Lance also pays $140.30 in tax, calculate Lance’s net wage.
22 Ruth has a net income of $700 per week. She has expenses of $190 for her mortgage, $90
for her bills, $80 for entertainment, $50 for car running costs, $125 for groceries and $30 for
medical needs. Calculate the amount that Ruth can allocate for savings in her budget.
1E
1E
1E
1F
1F
1F
1G

23 Amy has to budget for the following bills.
Insurance $62.50 per month
Rates $1050 per year
Calculate the amount that Amy should budget for each week to pay all of these bills.
Practice examination questions
1
Which of the following is the highest salary?
A $961.48 per week B $1923.12 per fortnight
C $4165.00 per month D $50 000 per annum
2
Simone works as a ﬂorist and receives a normal hourly rate of $13.60. Simone’s pay for a
Saturday night, when she works 6 hours at a rate of time and a half, is:
A $20.40 B $81.60 C $122.40 D $163.20
3
Noel sells computer software and receives a $250 per week retainer plus a commission of 5%
of all sales over $10 000. In a week where Noel’s sales reach $13 460, he is paid a total of:
A $17 B $423 C $673 D $923
1G
multiple choice
multiple choice
multiple choice

4
Janelle works a 38-hour week at a rate of $14.50 per hour. When Janelle takes her 4 weeks
annual leave she is paid a loading of 17 %. Janelle’s weekly wage, when she takes her leave,
is:
A $551 B $647.43
C $2204 D $2589.70
5 Ken works as a pest inspector. Ken is paid a wage of $15.40 per hour.
a If Ken works a normal 36-hour week, calculate his wage.
b Calculate Ken’s wage for a week if, in addition to his normal hours, he works 3 hours at
time and a half and 2 hours at double time.
c Ken receives an allowance of 79c per hour for working in conﬁned spaces. Calculate Ken’s
wage in a week if he works his normal 36 hours, but 23 of those hours are spent working
in conﬁned spaces.
d Calculate the total amount which Ken will receive for his 4 weeks annual leave if he is paid
an annual leave loading of 17 %.
6 Danielle is a preschool teacher who receives a salary of $47 600 per annum.
a Calculate the amount that she will receive each fortnight.
b Danielle pays 9% of her gross salary in superannuation. Calculate her fortnightly
c If Danielle also has $485.38 in tax, $45.80 for health insurance and $15.60 in union dues
deducted from her pay, calculate her net fortnightly pay.
multiple choice
1
2
---
1
2
---
testtest
CHAPTER
yourselfyourself
1

In this chapter
2A Units of measurement
2B Relative error
2C Signiﬁcant ﬁgures
2D Rates
2E Percentage change
2F Using ratios
syllabusreference
Measurement 1
• Units of measurement
2
Units of
measurement
5_61_05706_NSW GM PC - 02 Page 45 Thursday, August 16, 2007 2:29 PM

READY?
areyou
Are you ready?
Try the questions below. If you have difﬁculty with any of them, extra help can be
obtained by completing the matching SkillSHEET. Either click on the SkillSHEET icon
next to the question on the Maths Quest Preliminary Course CD-ROM or ask your
teacher for a copy.
Conversion of units
1 Complete each of the following conversions.
a 5 m = ___ cm b 6.2 km = ___ m c 8500 mm = ___ m
d 2000 g = ___ kg e 6.25 t = ___ kg f 750 mL = ___ L
Converting units of time
2 Complete each of the following conversions.
a 48 hours = ___ days b 4 years = ___ weeks c 8 hours = ___ min
Writing one quantity as a percentage of another
3 In each of the following write the ﬁrst quantity as a percentage of the second. Give your answers
correct to 1 decimal place.
a 1 cm; 2 m b 0.5 m; 15 m c 5 min; 9 hours
Rounding to a given number of decimal places
4 Round each of the following correct to the number of decimal places indicated in the brackets.
a 2.186 486 [4] b 0.001 563 4 [3]
c 48.8094 [2] d 118.3468 [1]
Increase or decrease by a percentage
5 Calculate the following.
a $750 increased by 12% b $2500 decreased by 5%
c 3 kg increased by 7.5% d 1.25 L decreased by 12.5%
Simplifying ratios
6 Simplify each of the following ratios.
a 48 : 20 b 1.5 m : 45 cm c 0.2 : 0.65 d :
2.1
2.2
2.3
2.4
2.5
2.6
1
4
---
1
6
---
5_61_05706_NSW GM PC - 02 Page 46 Thursday, August 16, 2007 2:29 PM

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