New Century Maths 11
Mathematics General
Preliminary course (Pathway 2)
Worked Solutions
Chapter 4
SkillCheck
1 a $17.60 × 5 = $88
b $3.10 × 1.5 = $4.65
c $0.35 × 1400 = $490
2 a $17.60 × 34 ÷ 100 = $14 473.12
b $153 000 ÷ 52.18 = $2932.1579 …
≈ $2932.16
c $85 629 × 1.5 ÷ 100 = $1284.435 ≈ $1284.44
Hours worked per week = 10.5 × 5 = 52.5
Weekly pay = $18.45 × 52.5
= $968.625 ≈ $968.63
2 Normal pay = 5 × 9 × $20.50 = $922.50
Time-and-a-half pay = 5 × 1.5 × $20.50
= $153.75
Weekly pay = $922.50 + $153.75 = $1076.25
3 $120 000 ÷ 52.18 ≈ $2299.73 so B
4 $523.30 × 52 = $27 211.60 so A
5 a $211.35 × 26 = $54 999.10
b $54 999.10 ÷ 52.18 = $1057.675 ≈ $1057.68
c $211.35 ÷ 2 ÷ 38 = $27.833 … ≈ $27.83
3
6 Normal pay = 36 × $17.44 = $627.84
2360
100%  6.451...  6%
36 580
4 Start with the brackets, then do the
Time-and-a-half pay = 10 × 1.5 × $17.44
= $261.60
multiplication and finally the addition.
Total pay = $627.84 + $261.60 = $889.44
58 000  0.45  (250 000  180 000)
 58 000  0.45  70 000
 58 000  31 500
 89 500
Exercise 4-01
1 Hours worked per day = 10.5
7 a $682.40 × 52 = $35 484.80
b $35 484.80 ÷ 12 = $2957.0666 … ≈ $2957.07
8 Time-and-a-half pay = 9 × 1.5 × $17.54
= $236.79
1
Double pay = 9 × 2 × $17.54 = $315.72
Weekly pay = $640.50 + $109.80 + $219.60
= $969.90
Total pay = $236.79 + $315.72 = $552.51
9 Day Normal
Hours
Overtime
11 a $145 239 ÷ 52.18 × 2
= $5566.845… ≈ $5566.85
Hours
Mon
6
0
Tues
6
0
Wed
7
0
Thurs
8
2
Fri
8
4
Sat
0
8
Sun
0
6
Total
35
20
b $145 239 ÷ 12 = $1057.675 ≈ $12 103.25
c $145 239 ÷ 52.18 = $2783.4227 …
≈ $2783.42
12 a $83 215 ÷ 12 = $6934.5833 … ≈ $6934.58
b $83 215 ÷ 52.18 × 2
= $3189.5362 … ≈ $3189.54
c A law clerk would work a 5 day week which
Normal pay = 35 × 9 × $23.10 = $808.50
is equivalent to a 10 day fortnight.
Time-and-a-half pay = 20 × 1.5 × $23.10
$3189.5362 … ÷ 10 = $318.95362 … ≈ $318.95
= $693.00
13 a Weekly pay = $104 235 ÷ 52.18
= $1997.6044 …
Weekly pay = $808.50 + $693.00 = $1501.50
10 She worked 9 hours a day for 5 days, 45 hours.
Hourly rate = $1997.6044 … ÷ 42 ≈ $47.56
This will be 35 h normal, 4 h time-and-a-half and
b Calculate $83 215 ÷ 52.18 × 2 or 2 ×
6 h double pay.
$1997.6044 …
Normal pay = 35 × $18.30 = $640.50
2 × $1997.6044 = $3995.2088 … ≈ $3995.21
Time-and-a-half pay = 4 × 1.5 × $18.30 = $109.80
Double pay = 6 × 2 × $18.30 = $219.60
c $104 235 ÷ 12 = $8686.25
14
Day
Normal hours Overtime hours
2
Tues
7.5
0
Carlos: $3460 × 12 ÷ 52.18 = $795.707 …
Wed
7.5
0
Dimitri: 31 600 ÷ 52.18 = $605.5960 …
Fri
4.0
4.5
Answer: C (Carlos)
Sun
7.5
1.0
Total
26.5
5.5
Note: there is no need to round the answers, and
other rates e.g. per month could be chosen.
Normal pay = 26.5 × $16.28 = $431.42
Time-and-a-half pay = 5.5 × 1.5 × $16.28 =
18 a He works for 8.5 hours per day.
Hourly rate = $163.22 ÷ 8.5
$134.31
= $19.2023 … ≈ $19.20
Weekly pay = $431.42 + $134.31= $565.73
b Weekly pay = 6 × $163.22 = $979.32
15 Normal pay = 33 × $16.72 = $551.76
c Yearly pay = $979.32 × 52 ≈ $50 924.64
Overtime (2½×) pay = 6 × 2.5 × $16.72
19
Day
Normal hours
1
9.0
0
2
8.0
0
3
9.0
1.0
4
9.0
5.0
5
9.0
3.5
Total
44.0
9.5
Overtime hours
= $250.80
Total pay = $551.76 + $250.80 = $802.56
16 a He works for 9.5 hours per day.
Daily pay = 9.5 × $22.18 = $210.71
b Weekly pay = 5 × $210.71= $1053.55
c Yearly pay = $1053.55 × 52 = $54 784.60
Monthly pay = $54 784.60 ÷ 12 ≈ $4565.38
17 Convert all to the same kind of rate (weekly)
Ali: 35 × $18.70 = $654.50
Boun: $580
Normal pay = 44 × $28.10 = $1236.40
Time-and-a-half pay = 9.5 × 1.5 × $28.10
≈ $400.43
Weekly pay = $1236.40 + $400.43 = $1636.83
20 4 hours time-and-a-half = 6 hours normal rate.
3
Equivalent normal hours = 32 + 6 = 38 hours.
6 a First $18 000 = 5% of $85 000 = $4250
Hourly rate = $719.20 ÷ 38
Next $60 000 = 3% of $60 000 = $1800
= $18.9263… ≈ $18.93
Exercise 4-02
Remaining: $242 000 – $85 000 – $60 000
= $97 400
1 a 31 × $3.30 = $102.30 so A.
The rest = 2.5% of $97 400 = $2435
2 a 60 ÷ 12 = 12 lots of 5 min.
Commission = $4250 + $1800 + $2435 = $8485
14 × 12 = 168 envelopes
b 2.5 × 168 × $0.065 = $27.30
3 5 × 18 × $0.75 = $67.50 so D
b First $18 000 = 5% of $85 000 = $4250
Next $60 000 = 3% of $60 000 = $1800
Remaining: $310 000 – $85 000 – $60 000
4 a Share value = 350 × $4.30 = $1505
= $165 000
Commission = 2% of $1505 = $30.10
The rest = 2.5% of $165 000 = $4125
b 2% of value = $135
Value = $135 ÷ 2% = $135 ÷ 0.02 = $6750
Commission = $4250 + $1800 + $4125
= $10 175
5 Commission:
7 434 × $0.47 = $203.98
First $18 000 = 4% of $18 000 = $720
8 Value of sales = 8400 × $8.95 = $75 180
The rest = 2.5% of ($270 000 – $18 000)
Earnings = 1.8% of $75 180 = $1353.24
= 2.5% of $252 000
9 a Value of sales = 1 245 000 × $39.50
= $6300
Retainer: $320
Total earnings = $320 + $6300 + $720 = $7340
= $49 177 500
b Royalties = 1.5% of $49 177 500 =
$737 662.50
4
10 a 1329 × $0.11 = $146.19
b $91.31 ÷ $0.11 = 821
20 a First $3 000 = 4.8% of $3000 = $144
Next $3000 = 6% of $3000 = $180
11 Number of cars = 2.5 × 6 = 15
Remaining: $8758 – $3000 – $3000 = $2758
Earnings = 15 of $5.24 = $78.60
The rest = 7.5% of $2758 = $206.85
12 8% of value = $62.72
Commission = $144 + $180 + $206.85 = $530.85
Value = $62.72 ÷ 8% = $62.72 ÷ 0.08 = $784
13 Value of sales = 34 700 × $32.95 = $1 143 365
Exercise 4-03
Earnings = 13% of $1 143 365= $148 637.45
1 Note that there are a variety of different possible
14 5 × 7.5 × $12.40 = $465
15 5% of value = $83.90
Value = $83.90 ÷ 5% = $83.90 ÷ 0.05 = $1678
2024
 100% = 8.8%
16
23 000
17 15.5 cents = $0.155
214.21 ÷ 0.155 = 1382 newspapers
18 a 114 × $1.05 = $119.70
b 223.65 ÷ 1.05 = 213 gifts
19 500 ÷ 8.40 = 59.52 …
To earn over $500 she must test more than 59
answers to each part of this question.
a roof tiler
b nurse
c airline steward
d steelworker
e scientist in Antarctica
f scaffolder
g army officer
h miner
2 Per day: 10 × $24.15 + %25.10 = $266.60
Total: 5 × $266.60 = $1333
brands of food, i.e. 60 or more.
3 4 weeks’ pay = $68 275 ÷ 52.18 × 12
5
= $5076.208…
Loading = 17.5% of $5076.208… ≈ $915.92
Weekly wage = 6 × $148.16 = $888.96
b 4 weeks’ wage = 4 × 6 × $124.30 = $2983.20
4 $419.70 + 60% of $419.70 = $671.52
Loading = 17.5% of $2983.20 = $522.06
5 a Miner earns $28.42 + $9.97 = $38.39 for 7.5
10 Hourly rate = $32.56 + $7.49 = $40.05
hours, 5 days per week.
Weekly income = 5 × 7.5 × $38.39 = $1439.63
Weekly wage = 9.5 × 5 × $40.05 ≈ $1902.38
11 Permanent staff:
Bonus = 17.5% of (4 × $632.58)
b Yearly income = 52 × $1439.625 =
= $442.806 ≈ $442.81
$74 860.50
Difference = $442.81 – $272 = $170.81
6 $83 204 ÷ 52.18 × 2 + 2 × $177.35 = $3543.81
12 Hourly rate = $18.14 + $5.10 = $23.24
7 Monthly salary = $53 045 ÷ 12 = $4420.4166 …
7.00 a.m. to 3.00 p.m. is 8 hours.
Bonus = 15% of $4420.4166… = $663.0625 =
Weekly wage = 8 × 5 × $23.24 = $929.60
$663.06
8 Consider weekly amounts.
Wage = 5 × 10 × $17.90 = $895
Allowance = 5 × $23.40 = $117
Total weekly pay = $895 + $117 = $1012
9 a In this case it is easier to work out the rate per
13 Wage = 5 × 9 × $15.23 = $685.35
Allowance = 2 × 9 × $4.60 = $82.80
Total weekly pay = $685.35+ $82.80= $768.15
14 Commission = 3.5% of $943 658 = $33 028.03
Allowance = $128.40
day and multiply by 6.
Retainer = $510
Per day: $124.30 + $12.25 + $8.40 + $3.21
Total earnings = $33 028.03 + $128.40 + $510
= $148.16
= $33 666.73
6
15 4 weeks pay = 4 × 35 × $18.20 = $2548
Loading = 17.5% of $2548 = $445.90
16 17.5% × 4 × wage = $403.12
c Dell is not eligible for the aged pension as she is
under 65 years old. ($0)
2 They live in the same house and many costs
(e.g. rates) are shared.
Wage = $403.12 ÷ 4 ÷ 0.175
3 a i See the first row, $453.30 fortnightly.
= $575.8857… ≈ $575.89
ii $453.30 × 26 = $11 785.80
iii $11 785.80 ÷ 12 = $982.15
Exercise 4-04
b $409 × 26 ÷ 2 = $5317
1 a Use the tables on page 161 for ‘Single’
c More. This is fair as they have no partner to
Calculate her fortnightly income.
$850 ÷ 52.18 × 2 = $32.579 … < $138
She gets the full payment of $569.80
b Use the tables on page 161 for ‘A couple’.
share costs.
4 She is under 25 so use the youth allowance
table. She is single with a child (counts as
children) so she receives the maximum allowance
of $486.60, so C.
Combined fortnightly income = $144 × 2 = $288.
5 a Assuming there are two parents, $409.00.
Add $24.60 to the threshold for the dependent
b The second category, so $490.40.
child.
c She is single, so $569.80
Threshold = $240 + $24.60 = 264.60
d Separated due to illness, so $490.40 per
Payment is reduced by 40c for every dollar they
fortnight.
earn above $264.60.
This excess = $288 – $264.60 = $23.40
Income = 2 × $475.90 – 0.4 × $23.40 = $942.44
i For a year, $490.40 × 26 = $12 750.40
ii For a week, $490.40 ÷ 2 = $245.20
7
6 Use the ABSTUDY table. He is single, no
c $875.32 – $245.09 – $30.76 – $86.11
children (top section) and 18–20 years, at home so
= $513.36
he gets $244.40, which is option A.
7 a Jill is partnered, and assuming no children, it
4 a $635.25 – tax – $26.11 – $7.90 = $429.07
Tax = $635.25 – $26.11 – $7.90 – $429.07
would be $371.40.
= $172.17
b Brett is partnered with dependent child(ren),
and 21 years and over, so $409.00
b
172.17
 100% = 27.1027…% ≈ 27.10%
635.25
c
26.11
 100% = 4.1101…% ≈ 4.11%
635.25
c Maude is partnered, no children, and 21 years
(and over), so $409.00
d Dee is single, no children, and under 16, at
home, so $203.30
5 a Tax = 27.5% of $638.20
= $175.505 ≈ $175.51
b Superannuation = 8% of $638.20
Exercise 4-05
= $51.056 ≈ $51.06
1 $827.25 – $244.04 – $64.83 – $18.20 – $26.15
= $474.03 so C.
d $638.20 – $248.51 = $389.69
2 a $945.30 – $235.90 – $55.17 – $24.78 – $17.50
= $611.95
b
c $175.51 + $51.06 + $7.10 + $14.84 = $248.51
6 a 22% of tax = $135.52
Tax = $135.52 ÷ 22% = $135.52 ÷ 0.22 = $616.00
185.92
 100% = 24.955…% ≈ 25%
629.60
3 a Gross weekly pay = $45 674 ÷ 52.18
= $875.3162 …
≈ $875.32
b 10% of $616.00 = $61.60
c $616.00 – $135.52 – $61.60 – $4.70 = $414.18
7 a $54 251 ÷ 52.18 × 2 = $2079.3790 ≈ $2079.38
b $2079.38 – $307.26 – $145.60 – $27.14
b Tax = 28% of $875.3162 … ≈ $245.09
8
= $1599.38
c
307.26
100% = 14.7765…% ≈ 14.8%
2079.38
8 a 39 × $19.38 = $755.82
Net wage = $923.64 – $334.51 = $589.13
11 Other Deductions, total deductions:
$71.60 + $16.22 + $43.55 + $24.80 = $151.21
Pay period 14.3.11–27.3.11 is two weeks.
b 25% of $755.82= $188.955 ≈ $188.96
Gross pay = $87 026 ÷ 52.18 × 2 ≈ $3335.61
c $755.82 – $188.96 – $17.40 = $549.46
Tax = 31% of $3335.51 = $1034.04
9 a Gross: $108 275 ÷ 12 ≈ $9022.92
Net pay = $3335.51 – $1034.04 – $151.21
Net: $9022.92 – $4330 – 1080.50 – 107.54
= $3504.88
b
= $2149.36
Exercise 4-06
4330
 100% = 47.988…% ≈ 48%
9022.92
1 Income is money you receive; expenses are
payments or other money you spend.
c
3504.88
 100% = 38.844…% ≈ 38.8%
9022.92
a expense
b income
c expense
d expense
e income
f expense
g expense
h expense
i income
j expense
k income
l expense
m income
n income
o expense
10 Normal pay = 35 × $21.48 = $751.80
Time-and-a-half pay = 4 × 1.5 × $21.48 = $128.88
Double time pay = 1× 2 × $21.48 = $42.96
Gross wage = $751.80 + $128.88 + $42.96
= $923.64
Tax = 25% of $923.64 = $230.91
Deductions = $230.91 + $60.65 + $18.15 + $24.80
2 a $537.00 – $185.70 = $351.30
b Total expenses = total income = $537.00
$537.00 – $160 – $56 – $124 – $25 – $58 – $60
= $54
= $334.51
9
c Note that there may be other ways such as
spending less on entertainment or increasing the
amount of casual work.
For a spreadsheet, enter all the data for the
individual items. Use SUM( … ) for income total,
3 a $615.40 – $40 – $138 – $52 – $36 – $20 – $60
and make expenses total equal to income total.
– $85 – $65 – $8 = $111.40
Savings will equal total expenses minus sum of
bills. Use SUM so if the spreadsheet starts with
b 52 × $111.40 = $5792.80 so yes.
cell A1, then Income total is =sum(B2:B4) (in
c New price = 1.2 × $2200 = $2640 so yes.
cell B15)
4 a Enter the data as follows.
Income
Wages
Expenses total is =sum(B2:B4) (in cell D15)
Savings is =B15–sum(D2:D13) (in cell D14)
Expenses
$1901.77 Bills
P/T job
$289.53 School fees
Parent
$197.20 Entertainment
$105.30
$85.80
$295.00
allowance
Savings = $2388.5 – $1953.22 = $435.28
Enter this in the table.
Income
Health fund
Total:
b If using a table, add up expenses. $1953.22
Expenses
$53.40
Wages
Clothes
$132.00
P/T job
$289.53 School fees
Home maint
$184.00
Parent
$197.20 Entertainment
Groceries
$210.50
allowance
$1901.77 Bills
$105.30
$85.80
$295.00
Petrol
$85.40
Health fund
Fri takeaway
$46.00
Clothes
$132.00
Papers/mags
$26.00
Home maint
$184.00
$210.50
$53.40
Home loan
$545.60
Groceries
Car loan
$184.22
Petrol
$85.40
Savings
?
Fri takeaway
$46.00
$2388.50
Papers/mags
$26.00
$2388.50 Total:
10
Total:
Home loan
$545.60
Car loan
$184.22
Savings
$435.28
$2388.50 Total:
$2388.50
2 a $91 262 – $1810.15 = $89 451.85
Cents are not included in taxable income.
Taxable income = $89 451
b Use the fourth row in the table.
5 a What he earns, $551.40
Tax = $17 547 + 0.37 × ($89 451 – $80 000)
= $21 043.87
b $110 + $64 + $46 + 45.10 × 4 ÷ 52 + $12.80 ×
6 ÷ 52 + $45 + $42 × 12 ÷ 52 ≈ $279.64
c $551.40 – $279.64 = $271.76
c Levy = 1.5% of $89 451 = $1341.77
3 a $87 210 – $650.25 – $314.80 – $120.50
= $86 124.45
Exercise 4-07
Cents are not included in taxable income.
1 a Taxable income = $31 425 – $285 = $31 140
Taxable income = $86 124
Use the second row in the table.
b Use the fourth row in the table.
Tax = 0.19 × ($31 140 – $18 200) = $2458.60
b Taxable income = $131 412 – $1036 – $643
= $129 733
Use the fourth row in the table.
Tax = $17 547 + 0.37 × ($129 733 – $80 000)
= $35 948.21
c Taxable income is below $18 200, so no tax is
payable. ($0)
Tax = $17 547 + 0.37 × ($86 124 – $80 000)
= $19 812.88
c Levy = 1.5% of $86 124 = $1291.86
4 a 52 × $952.80 + $286.10 + $2050.96 +
$892.51
– $241.60 – $345.80 – $175.80 – $843.50
= $51 168.47
Cents are not included in taxable income.
Taxable income = $51 168
b Use the third row in the table.
Tax = $3572 + 0.325 × ($51 168 – $37 000)
= $8176.60
d Taxable income is below $18 200, so no tax is
c Levy = 1.5% of $51 168 = $767.52
payable. ($0)
5 a Use the first row in the table.
11
Tax = 0.325 × $37 850
= $12 301.25
Refund = $72 156 – $63 049.09 = $8386.91
b Use the second row in the table.
Tax = $26 000 + 0.37 × ($102 670 – $80 000)
= $34 387.90
4 a Use the last row in the table.
c Use the third row in the table.
Tax = $63 000 + 0.45 × ($203 500 – $180 000)
= $73 575
Exercise 4-08
Tax = $54 547 + 0.45 × ($278 639 – $180 000)
= $98 934.55
b Levy = 1.5% of $194 026 ≈ $4179.59
c Money owing: $98 934.55 + $4179.59
1 a 52 × $314.68 = $16 363.36
b 52 × ($1014.65 – $314.68) = $36 398.44
2 a 52 × $475.15 = $24 707.80
b Weekly wage = $73 489 ÷ 52.18 ≈ $1408.37
Pay = $1408.37 – $475.15 – $26.80 = $906.42
3 a Taxable income = $204 540 – $10 534
= $194 026
b Use the last row in the table.
Tax = $54 547 + 0.45 × ($194 026 – $180 000)
= $103 114.14
PAYG paid = $104 568 which is more than what’s
owing so he gets a refund.
Refund = $104 568 – $103 114.14 = $1453.86
5 a Gross income = 52 × $589.60 = $30 659.20
Weekly deductions = 52 × $38.25 = $1989
Total deductions = $1989 + $150 = $2139
Taxable income = $30 659.20 – $2139
= $28 520.20
= $60 858.70
c Levy = 1.5% of $194 026 = $2910.39
d Money owing: $60 858.70 + $2910.39
= $63 769.09
Round down to $28 520
b Use the second row in the table.
Tax = 0.19 × ($28 520 – $18 200)
= $1960.80
PAYG paid = $72 156 which is more than what’s
c Levy = 1.5% of $28 520 = $427.80
owing so she gets a refund.
d Money owing: $1960.80 + $427.80 = $2388.60
12
PAYG paid = 52 × $136.45 = $7095.40 which is
more than what’s owing, so she gets a refund
Refund = $7095.40 – $2388.60 = $4706.80
6 Use the second row in the table.
Tax = 0.19 × ($34 589 – $18 200)
= $3113.91
Medicare Levy = 1.5% of $34 589 ≈ $518.84
Total due: $3113.91+ $518.84 = $3632.75
PAYG paid is $7836 which is more than what’s
owing so he gets a refund.
Total due: $30 979.09 – $19 084 = $11 895.09
b Use the second row in the table.
Tax = $26 000 + 0.37 × ($98 534 – $80 000)
= $32 857.58
No Medicare Levy
PAYG = $5279 × 4 = $21 116
Total due: $32 857.58 – $21 116 = $11 741.58
c Use the last row in the table.
Tax = $63 000 + 0.45 × ($1 200 000 – $180 000)
= $522 000
Refund = $7836 – $3632.75 = $4203.25
No Medicare Levy
7 Use the last row in the table.
PAYG = $37 460 × 12 = $449 520
Tax = $54 547 + 0.45 × ($381 459 – $180 000)
Total due: $522 000 – $449 520 = $72 480
= $145 203.55
Exercise 4-09
Medicare Levy = 1.5% of $381 459 ≈ $5721.89
1 110% × $5.50 = $6.05 so C
Total due: $145 203.55 + $5721.89 = $150 925.44
2 121% × €1500 = €1815
Tax due = $150 925.44 – $138 639 = $12 286.44
3 107% × 3724 baht = 3985 baht
8 a Use the second row in the table.
4 110% of original price = $42 000
Tax = $26 000 + 0.37 × ($93 457 – $80 000)
= $30 979.09
No Medicare Levy
1% of original price = $42 000 ÷ 110 = $381.81
818…
PAYG = $734 × 26 = $19 084
13
Original price = $381.81 818 … × 100 ≈ $38 182
11 a 157 190 – 142 900 = 14 290 won
so A
b
5 110% of original price = $18.50
1% of original price = $18.50 ÷ 110
14 290
 100% = 10%
142 900
12 a €264 – €220 = €44
b
= $0.168 181…
Original price = $0.168 181… × 100 ≈ $16.82
13
44
 100% = 20%
220
224.10
100% = 18%
1245
6 117.5% of original price = £126.90
14 15% of original price = €31.17
1% of original price = £126.90 ÷ 117.5 = £1.08
1% of original price = €31.17 ÷ 15 = €2.078
Original price = £1.08 × 100 ≈ £108
Original price = €2.078× 100 ≈ €207.80
7 114% of original price = 53.01 rand
Selling price = €207.80 + €31.17 = €238.97
1% of original price = 53.01 ÷ 114 = 0.465 rand
15 115% of original price = $152.72
Original price = 0.465 × 100 ≈ 46.50 rand
1% of original price = $152.72 ÷ 115 = $1.328
8
1.24
 100% = 19.076 …% ≈ 19%
6.50
9 a €9.88 – €1.58 = €8.30
b
1.58
 100% = 19.036 …% ≈ 19%
8.30
10 a 15% of original price = $4.62
1% of original price = $4.62 ÷ 15 = $0.308
Original price = $0.308 × 100 ≈ $30.80
b Final price = $30.80 + $4.62 = $35.42
Original price = $1.328 × 100 ≈ $132.80
16 10% of original price = $2.83
1% of original price = $2.83 ÷ 10 = $0.283
Original price = $0.283 × 100 ≈ $28.30
Selling price = $28.30+ $2.83= $31.13
17 107% of original price = 4419 baht
1% of original price = 4419 ÷ 107
14
= 41.299 06 … baht
Original price = 4.1299 … × 100 ≈ 4130 baht
2 Find the cost of the GST on the vertical axis, go
across to the green line, then down to read the
answer from the horizontal scale.
18 $6.93 – $6.50 = $0.43
0.43
 100% = 6.6153 …% ≈ 6.62%
6.50
3 Find the taxable income on the horizontal axis,
19 5% of original price = $2.40
go up to the green line, then across to read the tax
1% of original price = $2.40 ÷ 5 = $0.48
payable from the vertical scale.
Original price = $0.48 × 100 ≈ $48.00
Selling price = $48.00+ $2.40= $50.40
0.57
 100% = 19%
20
3
Exercise 4-10
4 Find the tax payable on the vertical axis, go
across to the green line, then down to read the
taxable income from the horizontal scale.
Note that the answers can only be as accurate as
you can read from the graphs. If your answer is
slightly different from the one given in the
5 a Calculate the GST on $10, $100 and at least
textbook, you may wish to check with your
one cost between these values. Carefully plot the
teacher.
points and use a ruler to join and make a straight
1 Find the cost of the item on the horizontal axis,
line from the $10 point to the $100 point.
go up to the green line, then across to read the
GST from the vertical scale.
15
This may vary by $1 if rounded to the nearest
whole number.
6 a Calculate the VAT on £50, £500 and at least
one cost between these values. Carefully plot the
points and use a ruler to join and make a straight
line from the £50 point to the £500 point.
GST on $10 = 7% of $10 = $0.70
GST on $100 = 7% of $100 = $7.00
b i Note: In Singapore, the marked price is the
price before GST is added. Find the cost of the
item ($95) on the horizontal axis, go up to the line
you drew, then across to read the GST from the
vertical scale. $6.60–$6.70 is reasonable.
VAT on £50 = 20% of £50 = £10
ii Find the GST ($6.50) on the vertical axis, go
VAT on £500 = 20% of £500 = £100
across to the line you drew, then down to read the
b i Find the cost of the item (£65) on the
original cost of $93 from the horizontal scale.
horizontal axis, go up to the line you drew, then
Depending on the graph, answers between $90
across to read the VAT (£13) from the vertical
and $95 may be reasonable.
scale.
iii Find the GST ($3.40) on the vertical axis, go
ii Find the VAT (£18) on the vertical axis, go
across to the line you drew, then down to read the
across to the line you drew, then down to read the
original cost of about $48.60 from the horizontal
original cost of £90 from the horizontal scale.
scale. ($48 or $49 would be acceptable)
Selling price = $48.60 + $3.40 = $52.00
16
iii Find the VAT (£64) on the vertical axis, go
across to read tax payable of about $9000 ($9220)
across to the line you drew, then down to read the
from the vertical scale.
original cost of about £320 from the horizontal
scale.
Selling price = £320 + £64 = £384
7 a i 0.105 × $14 000 = $1470
ii $1470 + 0.175 × ($48 000 – $14 000)
= $7420
ii Find taxable income of $82 000 on the
horizontal axis, go up to the line you drew, then
across to read tax payable of about $18 000 from
the vertical scale.
d i Find tax payable of $5300 on the vertical
axis, go across to the line you drew, then down to
read taxable income of about $36 000 from the
iii $7420 + 0.30 × ($70 000 – $48 000)
horizontal scale.
= $14 020
ii Find tax payable of $16 700 on the vertical
iv $14 020 + 0.33 × ($90 000 – $70 000)
= $20 620
b Join the points (0, 0) to ($14 000, $1470) to
($48 000, $7420) to ($70 000, $14 020) to
axis, go across to the line you drew, then down to
read taxable income of about $78 000 from the
horizontal scale.
Sample HSC problem
($90 000, $20 620) with straight lines, extending
the last line past ($90 000, $20 620).
a 52 × $237.80 = $12 365.60
b 52 × $789.40 = $41 048.80
c $41 048.80 – $986.50 = $40 062.80
Round up to the nearest dollar, $40 063
d Use the third row to calculate income tax.
$3572 + 0.325 × ($40 062 – $37 000) = $4567.15
c i Find taxable income of $54 000 on the
Medicare levy = 0.015 × $40 062 = $600.93
horizontal axis, go up to the line you drew, then
17
e Refund = $12 365.60 – $4567.15 – $600.93
= $7197.52
She earns 2c more per cupcake selling them by the
dozen.
6 10% of (2537 × $45.95) = $11 657.515
Chapter Review
≈ $11 657.52
1 a 52 × $631.15 = $32 819.80
b 26 × $1548 = $40 248
7 Below ground = $39.65 + $9.84
= $49.49 per hour
c 12 × $3786 = $45 432
2 a $138 611 ÷ 52.18 = $2656.4009 …
≈ $2656.40
b $98 503 ÷ 52.18 × 2 = $3775.5078 …
≈ $3775.51
c $263 764 ÷ 12 = $21 980.333 … ≈ $21 980.33
3 Mon
7 h normal, 2 h overtime
Wed
4 h normal, 0 h overtime
Fri
1 h normal, 5 h overtime
Total 12 h normal, 7 h overtime
Pay = 12 × $25.70 + 1.5 × 7 × $25.70 = $578.25
Mon
5 h above, 0 h below, meal: $0
Wed
0 h above, 5 h below, meal: $0
Fri
3 h above, 4 h below, meal: $27.40
Sat
2 h above, 4 h below, meal: $27.40
Total 12 h above, 17 h below, meal: $54.80
Pay = 12 × $39.65 + 17 × $49.49 + $54.80
= $1371.93
8 4 weeks pay = $86 430 ÷ 52.18 × 4
= $6625.527 …
Leave this value in the calculator
17.5% × $6625.527… = $1159.467…≈ $1159.47
9 a Richard is under 25, so use the youth
allowance table in Example 9. Assume he is single
4 a 28 × $3.65 = $102.20
with no children. He’s 18 (and over) and living at
b $390.55 ÷ $3.65 = 107 buckets
home. This is the third row so he earns $244.40
5 $4.80 per dozen = $4.80 ÷ 12 = $0.40 per
per fortnight.
cupcake
$38 for 100 = $38 ÷ 100 = $0.38 per cupcake
b Use ABSTUDY for indigenous students. He is
single, and assuming no children, all over 21 who
18
are single with no children will earn $453.30 per
fortnight.
= $27 041.94
c 0.015 × $105 662 = $1584.93
c Alison is over 24 so she receives Austudy. As
she is single with a child (=’children’) she will
d PAYG = ($1424.30 ÷ 2) × 52.18
= $37 159.99
receive $486.60 per fortnight.
10 a 52 × $594.10 = $30 893.20
Refund = $37 159.99 – $27 041.87 – $1584.93
= $8533.19
b 2 × $594.10 = $1188.20
13 110% of original price = $1246
c $94 762 ÷ 52.18 × 2 = $3632.1195 …
1% of original price = $1246 ÷ 110
≈ $3632.12
= $11.327272 …
d $3632.12 – $1188.20 – (2 × $28.70)
The GST is 10% of the original price
= $2386.52
GST = $11.327272 …× 10 ≈ $113.27
11 a $1654 ÷ 2 + $1270 × 12 ÷ 52.18
= $827 + $292.0659 …
14 a 15% × 1262 = 189.30 pesos
b 19% × 235 = 44.65 new lei
≈ $1119.07
c 14% × 26 950 = 3773 rand
b Answers will vary, depending on the
amounts chosen for entertainment, clothes and
savings
c Note that other answers may be possible, e.g.
car pooling, cutting down on takeaway meals etc.
12 a $118 764 – $13 102.20 = $105 661.80
Rounding up gives $105 662.
b $17 547 + 0.37 × ($105 662 – $80 000)
15 a 115% of original price = 200 000 pesos
1% of orig. price = 200 000 ÷ 115
= $1739.13043…
100% of orig. price = 1739.13043… × 100
≈ 173 913.04 pesos
b 120% of original price = 171 400 forint
1% of orig. price = 171 400 ÷ 120
19
= 1428.333… forint
100% of orig. price = $1428.333… × 100
≈ $142 833.33… forint
16 a The VAT on 0 baht is 7% of 0 = 0 baht
ii Find the VAT (28 baht) on the vertical axis, go
across to the line you drew, then down to read the
original cost of 400 baht from the horizontal scale.
iii Find the VAT (16 baht) on the vertical axis, go
across to the line you drew, then down to read the
The VAT on 500 baht = 7% of 500 = 35 baht
Use a ruler to join (0, 0) to (500, 35) in a straight
line.
original cost of about 230 baht from the horizontal
scale.
Price = 230 + 16 = 246 baht
Note that if the 230 is only accurate to the nearest
10 baht, you can only say about 250 baht or 240250 baht.
17 a Find taxable income of $72 000 on the
horizontal axis, go up to the line you drew, then
across to read tax payable of just over $14 800
from the vertical scale. As the small scale goes up
$400 dollars at a time, the best answer would be
about $14 900. $15 000 is acceptable.
b Find tax payable of $14 000 on the vertical
axis. Go across to the line you drew, then down to
b i Find the cost of the item (250 baht) on the
read taxable income of about $69 000 from the
horizontal axis, go up to the line you drew, then
horizontal scale.
across to read the VAT (17.5 baht) from the
vertical scale. 17 or 18 baht may be reasonable,
depending on the graph.
20