smc-1126-10-Wages

v1 Financial Maths, STD2 F1 2004 HSC 27b

Jack is paid at these rates:

\begin{array}{|l|} \hline \text{Weekday rate} & \text{$\$$15 per hour}\\ \text{Saturday rate} & \text{Time-and-a-half}\\ \text{Sunday rate} & \text{Double time}\\ \hline \end{array}

His time sheet for last week is:

\begin{array}{|l|l|l|l|} \hline & \textit{Start} & \textit{Finish} & \textit{Unpaid break}\\ \hline \text{Friday} & \text{9.00 am} & \text{4.00 pm} & \text{1 hour} \\ \text{Saturday} & \text{9.00 am} & \text{4.00 pm} & \text{1 hour} \\ \text{Sunday} & \text{9.00 am} & \text{1.00 pm} & \text{30 minutes} \\ \hline \end{array}

Calculate Jack's gross pay for last week. (3 marks)
--- 6 WORK AREA LINES (style=lined) ---
Jack decides not to work on Sundays. He wants to keep his weekly gross pay the same. How many extra hours at the weekday rate must he work? (1 mark)
--- 2 WORK AREA LINES (style=lined) ---

Show Answers Only

$\$330$
$\text{7 extra hours}$

Show Worked Solution

i.	$\text{Pay(Fri)}$	$=6 \ \text {hours } \times 15.00$
		$=\$90.00$
	$\text{Pay(Sat)}$	$=6 \ \text {hours } \times 1.5 \times 15.00$
		$=\$135.00$
	$\text{Pay(Sun)}$	$=3.5 \ \text {hours } \times 2 \times 15.00 $
		$=\$105.00$

$\therefore \text{Gross pay }$	$=90+135+105$
	$=\$330$

ii. $\text{Pay on Sun}=\$105$

$\text{Weekly equivalent hours}$	$=\dfrac{105}{15}$
	$=7 \ \text{hours}$

$\therefore \ \text{He will have to work 7 extra hours on a weekday}$

v1 Financial Maths, STD2 F1 2018 HSC 8 MC

A gardener charges $12 per hour, or part thereof, for doing yard work.

What does the gardener charge for working from 8 am until 4.20 pm on a particular day?

$105
$108
$110
$120

Show Answers Only

`text(B)`

Show Worked Solution

`text(8 am – 3:20 pm)`	`= 8\ text(hrs 20 mins)`

`text(S)text(ince part of an hour is charged as a full hour,)`

`:.\ text(Charge)`	`= 9 xx 12`
	`= $108`

`=>\ text(B)`

v1 Financial Maths, STD2 F1 2013 HSC 11 MC

An enterprise agreement has the following annual salary arrangements:

Rowan's employer pays 5% more than the enterprise agreement. He is on Step 2 and receives an allowance for Leader 1.

What is Rowan's gross monthly pay?

$3575.50
$3730.00
$3937.50
$4150.00

Show Answers Only

`C`

Show Worked Solution

♦ Mean mark 46%

`text(Gross annual pay)`	`=(40\ 000+5000)xx1.05`
	`=$47\ 250`

`:.\ text(Gross monthly pay)`	`=(47\ 250)/12`
	`=$3937.50`

`=>\ C`

v1 Financial Maths, STD2 F1 2007 HSC 3 MC

Dan is about to go on holidays for four weeks. His weekly salary is $375 and his holiday loading is 20% of four weeks pay.

What is Dan's total pay for the four weeks holiday?

$400
$1250
$1800
$2150

Show Answers Only

`C`

Show Worked Solution

`text(Salary)\ text{(4 weeks)}`	`= 4 xx 375`
	`= $1500`

`text(Holiday loading)`	`= 1500 xx 20%`
	`= $300`

`:.\ text(Total pay)`	`= 1500+300`
	`= $1800`

`=> C`

v1 Financial Maths, STD2 F1 2008 HSC 7 MC

Maya’s regular wage is $20 per hour. One week, she worked 9 hours at double time.

How many hours would Maya need to work at time-and-a-half to earn the same amount?

Show Answers Only

`C`

Show Worked Solution

`text(Amount earned at double time)`

`= 9 xx 2 xx 20`

`= $360`

`text(Time-and-a-half rate)`	`= 1.5 xx 20`
	`= $30 text(/hr)`

`:.\ text(# Hours at time-and-a-half)`

`= 360 / 30`

`= 12\ text(hrs)`

`=> C`

v1 Financial Maths, STD1 F1 2021 HSC 12

A karate school runs a holiday program and charges $150 per student.

The costs of running the program are:

Karate instructor: $110 per hour

Hall hire: $52 per hour plus 10% GST.

The program runs for two hours a day for five days.

What profit does the karate school make if 20 students pay for the program? (3 marks)

--- 6 WORK AREA LINES (style=lined) ---

Show Answers Only

`$1328`

Show Worked Solution

`text(Revenue) = 20 xx 150 = $3000`

`text(Cost per hour)`	`= 110+(52 xx 1.1)`
	`= 110+57.20`
	`= $167.20`

`text(Total cost)`	`= 2 xx 5 xx 167.20`
	`= $1672`

`:.\ text(Profit)`	`= 3000-1672`
	`= $1328`

Financial Maths, STD1 F1 2024 HSC 27

Zazu works a 38-hour week and is paid at an hourly rate of $45. Any overtime hours worked are paid at time-and-a-half.

In a particular week, Zazu worked the regular 38 hours and some overtime hours. In that week Zazu earned $2790.

How many hours of overtime did Zazu work in that week? (3 marks)

--- 6 WORK AREA LINES (style=lined) ---

Show Answers Only

$\text{16 hours of overtime}$

Show Worked Solution

$\text {Let X = overtime hours}$

	$\text{Total pay}$	$=(38 \times 45)+\Big(X \times \dfrac{3}{2}\times 45\Big) $
	$2790$	$=1710+\dfrac{135}{2}X$
	$\dfrac{135}{2}X$	$=1080$
	$X$	$=\dfrac{1080 \times 2}{135}$
		$=16 \text{ hours of overtime}$

Financial Maths, STD1 F1 2023 HSC 22

The hours worked last week by Rose are shown. Her normal rate of pay per hour is $24.05.

\begin{array} {|l|l|}
\hline
\rule{0pt}{2.5ex} \text{Monday to Friday (normal rate)} \rule[-1ex]{0pt}{0pt} & \text{8:30 am – 12:30 pm} \\
\hline
\rule{0pt}{2.5ex} \text{Saturday (time-and-a-half)} \rule[-1ex]{0pt}{0pt} & \text{9:00 am – 11:30 am} \\
\hline\rule{0pt}{2.5ex} \text{Sunday (double time)} \rule[-1ex]{0pt}{0pt} & \text{9:00 am – noon} \\
\hline
\end{array}

How much did Rose earn last week? (4 marks)

--- 6 WORK AREA LINES (style=lined) ---

Show Answers Only

$$745.55$

Show Worked Solution

$\text{Normal Pay}$	$=5\times 4\times $24.05$	$=$481.00$
$\text{Time-and-a-half}$	$=2.5\times 1.5\times $24.05$	$=$90.19$
$\text{Double time}$	$=2\times 3\times $24.05$	$=$144.55$
	$\text{TOTAL}$	$=$715.49$

Financial Maths, STD1 F1 2022 HSC 7 MC

Tian is paid $20.45 per hour, as well as a meal allowance of $16.20 per day.

What are Tian's total earnings if she works 9 hours per day for 5 days?

$329.85
$936.45
$1001.25
$1649.25

Show Answers Only

`C`

Show Worked Solution

`text{Earnings (5 days)}`	`=5 xx [(9 xx 20.45) + 16.20]`
	`=5 xx 200.25`
	`=$1001.25`

`=>C`

Financial Maths, STD1 F1 2021 HSC 12

A dance school runs a holiday program and charges $150 per student.

The costs of running the program are:

Dance teacher: $110 per hour

Room hire: $52 per hour plus 10% GST.

The program goes for two hours a day for five days.

What profit does the dance school make if 20 students pay for the program? (3 marks)

--- 6 WORK AREA LINES (style=lined) ---

Show Answers Only

`$1328`

Show Worked Solution

`text(Revenue) = 20 xx 150 = $3000`

`text(C)text(ost per hour)`	`= 110 + (52 + \text{GST})`
	`= 110 + 52 xx 1.1`
	`= $167.20`

`text(Total cost)`	`= 2 xx 5 xx 167.20`
	`= $1672`

`:.\ text(Profit)`	`= 3000 – 1672`
	`= $1328`

Financial Maths, STD1 F1 2019 HSC 26

Scott decided to have a shed built at his home. He agreed to the following costs:

Materials

– Timber	$5400
– Roof	$1800
– Nails	$160
– Paint	$375

$70 per hour for the builder when working Monday to Friday
$30 per hour for the labourer when working Monday to Friday
Builder and labourer paid time-and-a-half when working on Saturday.

It took six days to build the shed. The builder and labourer both worked from 8 am until 4 pm each day from Monday to Friday. On each of these days, they both took a 1 hour unpaid lunch break at 12 noon.

The builder and labourer also both worked 4 hours on Saturday, without a break, to finish the job.

What was the total cost to build the shed? (4 marks)

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Show Answers Only

`$11\ 835`

Show Worked Solution

`text(Material cost)`	`= 5400 + 1800 + 160 + 375`
	`= $7735`

`text(Labour cost:)`

`text{Hours per weekday = 8 am to 4 pm (less 1 hour) = 7}`

`text(Builder cost)`	`= 5 xx 7 xx 70 + 4 xx 1.5 xx 70`
	`= $2870`

`text(Labourer cost)`	`= 5 xx 7 xx 30 + 4 xx 1.5 xx 30`
	`= $1230`

`:.\ text(Total cost)`	`= 7735 + 2870 + 1230`
	`= $11\ 835`

Financial Maths, STD1 F1 2019 HSC 11

Julie earns $28 per hour. She is also paid an $8 travel allowance per shift.

How much will she earn from a 4-hour shift? (2 marks)

Show Answers Only

`$120`

Show Worked Solution

`text(Shift earnings)`	`=4xx28+8`
	`=$120`

Financial Maths, STD2 F1 2019 HSC 7 MC

Julia earns $28 per hour. Her hourly pay rate increases by 2%.

How much will she earn for a 4-hour shift with this increase?

$2.24
$28.56
$112
$114.24

Show Answers Only

`D`

Show Worked Solution

`text(Hourly rate)`	`= 28 xx 1.02`
	`= $28.56`

`:.\ text(Shift earnings)`	`= 4 xx 28.56`
	`= $114.24`

`=> D`

Financial Maths, STD2 F1 2018 HSC 8 MC

A nanny charges $15 per hour, or part thereof, for looking after a child.

What does the nanny charge for looking after a child from 8 am until 3.20 pm on a particular day?

$105
$108
$110
$120

Show Answers Only

`text(D)`

Show Worked Solution

`text(8 am – 3:20 pm)`	`= 7\ text(hrs 20 mins)`

`text(S)text(ince part of an hour is charged as a full hour,)`

`:.\ text(Charge)`	`= 8 xx 15`
	`= $120`

`=>\ text(D)`

Financial Maths, STD2 F1 2017 HSC 6 MC

Tom earns a weekly wage of $1025. He also receives an additional allowance of $87.50 per day when handling toxic substances.

What is Tom’s income in a fortnight in which he handles toxic substances on 5 separate days?

$1112.50
$1462.50
$2225.00
$2487.50

Show Answers Only

`D`

Show Worked Solution

`text(Fortnightly wage)`	`= 2 xx 1025`
	`= $2050`

`text(Allowances)`	`= 5 xx 87.50`
	`= $437.50`

`:.\ text(Income)`	`= 2050 + 437.50`
	`= $2487.50`

`=>D`

Financial Maths, STD2 F1 2016 HSC 26e

Jenny earns a yearly salary of $63 752. Her annual leave loading is 17.5% of four weeks pay.

Calculate her total pay for her four weeks of annual leave. (3 marks)

--- 6 WORK AREA LINES (style=lined) ---

Show Answers Only

`$5762.20`

Show Worked Solution

`text(4 weeks’ normal pay)`

`= 4/52 xx 63\ 752`

`= $4904`

`:.\ text(Annual leave pay)`

`= 4904(1 + 17.5/100)`

`= $5762.20`

Financial Maths, STD2 F1 2016 HSC 20 MC

Isabella works a 35-hour week and is paid at an hourly rate of $18. Any overtime hours worked are paid at time-and-a-half. In a particular week, she earned $1008.

How many hours in total did Isabella work in this week to earn this amount?

37.3
42
49
56

Show Answers Only

`=> C`

Show Worked Solution

`text(Let)\ \ X=\ text(number of extra hours worked.)`

`text(Total wage)`	`= 35 xx 18 + X xx 27`
`1008`	`= 630 + 27X`
`27X`	`=378`
`X`	`=14`

`:.\ text(Total hours worked)\ =35+14=49`

`=> C`

Financial Maths, STD2 F1 2004 HSC 27b

David is paid at these rates:

His time sheet for last week is:

Calculate David’s gross pay for last week. (3 marks)

--- 6 WORK AREA LINES (style=lined) ---
David decides not to work on Saturdays. He wants to keep his weekly gross pay the same. How many extra hours at the weekday rate must he work? (1 mark)

--- 2 WORK AREA LINES (style=lined) ---

Show Answers Only

`$414.00`
`text(9 extra hours)`

Show Worked Solution

i. `text{Pay (Fri)}`	`= text(4 hours) xx 18.00`
	`= $72.00`
`text{Pay (Sat)}`	`= 6\ text(hours) xx 1.5 xx 18.00`
	`= $162.00`
`text{Pay (Sun)}`	`= 5\ text(hours) xx 2 xx 18.00`
	`= $180.00`

`:.\ text(Gross pay)`	`= 72 + 162 + 180`
	`= $414.00`

ii. `text(Pay on Sat) = $162.00`

`text(Weekly equivalent hours)`

`= 162/18`

`= 9\ text(hours)`

`:.\ text(He will have to work 9 extra hours on)`

`text(a weekday for the same gross pay)`

Financial Maths, STD2 F1 2004 HSC 20 MC

Stan worked for 24 hours as shown on his pay slip.

What was his hourly rate of pay?

$11.20
$12.13
$14.56
$18.20

Show Answers Only

`A`

Show Worked Solution

`text(Let)\ X = text(normal time rate)`

`20X + (4 xx 1.5X)`	`= $291.20`
`26X`	`= $291.20`
`X`	`= $11.20`

`:.\ text(Hourly rate of pay = $11.20)`

`=> A`

Financial Maths, STD2 F1 2007 HSC 3 MC

Joe is about to go on holidays for four weeks. His weekly salary is $280 and his holiday loading is 17.5% of four weeks pay.

What is Joe’s total pay for the four weeks holiday?

$196
$329
$1169
$1316

Show Answers Only

`D`

Show Worked Solution

`text(Salary)\ text{(4 weeks)}`	`= 4 xx 280`
	`= $1120`

`text(Holiday loading)`	`= 1120 xx 17.5%`
	`= $196`

`:.\ text(Total pay)`	`= 1120 + 196`
	`= $1316`

`=> D`

Financial Maths, STD2 F1 2008 HSC 7 MC

Luke’s normal rate of pay is $15 per hour. Last week he was paid for 12 hours, at time-and-a-half.

How many hours would Luke need to work this week, at double time, to earn the same amount?

Show Answers Only

`D`

Show Worked Solution

`text(Amount earned last week)`

`= 12 xx 1.5 xx 15`

`= $270`

`text(Double time rate)`	`= 2 xx 15`
	`= $30 text(/hr)`

`:.\ text(# Hours at double time)`

`= 270/30`

`= 9\ text(hrs)`

`=> D`

Financial Maths, STD2 F1 2011 HSC 19 MC

Simon is a mechanic who receives a normal rate of pay of $22.35 per hour for a 40-hour
week.

When he is needed for emergency call-outs he is paid a special allowance of $150 for that
week. Additionally, every time he is called out to an emergency he is paid for a minimum
of 4 hours at double time.

In the week beginning 2 February, 2011 Simon worked 40 hours normal time and was
needed for emergency call-outs. His emergency call-out log book for the week is shown.

What was Simon’s total pay for that week?

$1189.28
$1296.30
$1334.55
$1446.30

Show Answers Only

`D`

Show Worked Solution

♦ Mean mark 41%
COMMENT: To reduce errors, calculate each element of pay separately in your working and then add up the total, as per the Worked Solution.

`text(Normal pay)`	`=40xx22.35`
	`=894.00`

`text(Special Allowance)= 150.00`

`text(Emergency Calls)`	`= (5xx2xx22.35)+(4xx2xx22.35)`
	`=223.50+178.80`
	`=402.30`

`text(Total Weekly Pay)`	`=894.00+150.00+402.30`
	`=1446.30`

`=> D`

Financial Maths, STD2 F1 2010 HSC 23a

This advertisement appeared in a newspaper

What is the maximum possible salary per annum for this civil engineer, correct to the nearest dollar? (2 marks)

--- 4 WORK AREA LINES (style=lined) ---

Show Answers Only

`$86\ 396`

Show Worked Solution

`text(Base wage)=1586.70\ text(pw)`

`text(Max weekly base)`	`=$1586.70+(text{3.5%}\ xx 1586.70)`
	`=1586.70+55.53`
	`=1642.23\ text((nearest cent))`

`:.\ text(Max annual base)`	`=1642.23xx52`
	`=85\ 395.96`
	`=$85\ 396\ text{(nearest dollar)}`

Financial Maths, STD2 F1 2009 HSC 10 MC

Billy worked for 35 hours at the normal hourly rate of pay and for five hours at double time. He earned $561.60 in total for this work.

What was the normal hourly rate of pay?

$7.02
$12.48
$14.04
$16.05

Show Answers Only

`B`

Show Worked Solution

`text(Let hourly rate) = $X\ text(per hour)`

`35X + 5(2X)`	`= 561.60`
`45X`	`=561.60`
`X`	`= 561.60/45`
	`= $12.48`

`=> B`

Financial Maths, STD2 F1 2012 HSC 29d

Su-Lin pays a monthly contribution of 5% of her salary into a superannuation fund. Her salary is `$81\ 600` per annum.

What is the amount of Su-Lin’s monthly contribution? (2 marks)

Show Answers Only

`$340`

Show Worked Solution

`text(Annual super cont.)`	`=5 text(%) xx 81\ 600`
	`= $4080`

`:.\ text(Monthly contribution)`	`= 4080/12`
	`= $340`

Financial Maths, STD2 F1 2012 HSC 18 MC

Jo qualifies for both Rent Assistance and Youth Allowance and receives a fortnightly payment from the government.

Rent Assistance is $119.40 per fortnight.

The maximum Youth Allowance is $402.70 per fortnight. It is reduced by 50 cents in the dollar for any income earned over $236 per fortnight.

Jo earns $300 per fortnight from a part-time job.

What is the total payment Jo receives each fortnight from the government?

$370.70
$372.10
$458.60
$490.10

Show Answers Only

`D`

Show Worked Solution

`text(Rent assistance)\ = $119.40`

`text(Youth allowance)`	`= 402.70\ text(less 50c per dollar)\ \ (text(income) > $236)`
	`= 402.70-0.5(300-236)`
	`= 402.70-32`
	`= $370.70`

`:.\ text{Total Payment}`	`=119.40 + 370.70`
	`=$490.10`

`=> D`

Financial Maths, STD2 F1 2013 HSC 11 MC

An enterprise agreement has the following annual salary arrangements:

George's employer pays 6% more than the enterprise agreement. He is on Step 3 and receives an allowance for Leader 2.

What is George's gross monthly pay?

$4375.00
$4412.50
$4600.00
$4637.50

Show Answers Only

`D`

Show Worked Solution

♦ Mean mark 46%

`text(Gross annual pay)`	`=(45\ 000+7500)xx1.06`
	`=$55\ 650`

`:.\ text(Gross monthly pay)`	`=(55\ 650)/12`
	`=$4637.50`

`=>\ D`

Financial Maths, STD2 F1 2013 HSC 3 MC

Luke's normal rate of pay is $24.80 per hour. In one week he worked 14 hours at the normal rate, 4 hours at time-and-a-half, and 3 .5 hours at double time. He was also paid a wet weather allowance of $50 for the week.

What was his pay for the week?

$583.20
$620.40
$669.60
$719.60

Show Answers Only

`D`

Show Worked Solution

`text(Pay)`	`=(14xx24.80)+(4xx1.5xx24.80)+(3.5xx2xx24.80)+50`
	`=347.20+148.80+173.60+50`
	`=$719.60`

`=>D`

i.	\(\text{Pay(Fri)}\)	\(=6 \ \text {hours } \times 15.00\)
		\(=\$90.00\)
	\(\text{Pay(Sat)}\)	\(=6 \ \text {hours } \times 1.5 \times 15.00\)
		\(=\$135.00\)
	\(\text{Pay(Sun)}\)	\(=3.5 \ \text {hours } \times 2 \times 15.00 \)
		\(=\$105.00\)

	\(\text{Total pay}\)	\(=(38 \times 45)+\Big(X \times \dfrac{3}{2}\times 45\Big) \)
	\(2790\)	\(=1710+\dfrac{135}{2}X\)
	\(\dfrac{135}{2}X\)	\(=1080\)
	\(X\)	\(=\dfrac{1080 \times 2}{135}\)
		\(=16 \text{ hours of overtime}\)

\(\text{Normal Pay}\)	\(=5\times 4\times $24.05\)	\(=$481.00\)
\(\text{Time-and-a-half}\)	\(=2.5\times 1.5\times $24.05\)	\(=$90.19\)
\(\text{Double time}\)	\(=2\times 3\times $24.05\)	\(=$144.55\)
	\(\text{TOTAL}\)	\(=$715.49\)

\(\therefore \text{Gross pay }\)	\(=90+135+105\)
	\(=\$330\)

\(\text{Weekly equivalent hours}\)	\(=\dfrac{105}{15}\)
	\(=7 \ \text{hours}\)