Mathematics Standard • Year 11 • Module 3 • Lesson 5

Earning Money — Exam Practice

Build fluency in the core Earning Money calculations: wages, overtime, allowances, commission, piecework and leave loading — one component at a time.

Build · Skill Drill

1. Quick recall

Answer each question in the space provided. 1 mark each

Q1.1 Complete each conversion factor:

Weekly × ____ = Annual. Annual ÷ ____ = Fortnightly. Annual ÷ ____ = Monthly.

Q1.2 Write the multiplier used to find each overtime rate from the ordinary hourly rate.

Time-and-a-half: × ____________ Double time: × ____________

Q1.3 Write the formula for annual leave loading on a weekly wage W: Leave loading = ____________

Stuck? Revisit lesson § Formula Reference (Earning Money — Formula Summary panel).

2. Worked example — gross pay with overtime and allowance

Follow each line of working. Every step has a reason on the right.

Problem. Liam earns $28.40 per hour for a 38-hour week, plus 6 overtime hours at time-and-a-half, plus a $52 weekly tool allowance. Calculate his weekly gross pay.

Step 1 — Ordinary pay (base rate × ordinary hours).

Ordinary = $28.40 × 38 = $1,079.20

Reason: rate per hour multiplied by hours worked.

Step 2 — Overtime rate (base rate × 1.5).

r_OT = $28.40 × 1.5 = $42.60/hr

Reason: time-and-a-half means multiply the base rate by 1.5 first, then apply to overtime hours.

Step 3 — Overtime pay (OT rate × OT hours).

Overtime = $42.60 × 6 = $255.60

Reason: 6 hours at the time-and-a-half rate.

Step 4 — Sum every component for gross pay.

Gross = $1,079.20 + $255.60 + $52.00 = $1,386.80

Reason: ordinary + overtime + allowance, kept as a table to mirror HSC marking.

Conclusion. Liam's weekly gross pay is $1,386.80.

3. Faded example — fill in the missing steps

A worker earns $24.80 per hour for a 38-hour week, plus 4 hours of double-time on a public holiday, plus a $30 weekly uniform allowance. Calculate the weekly gross pay. Fill in each blank line. 4 marks

Step 1 — Ordinary pay:

Ordinary = $24.80 × 38 = $ ____________

Step 2 — Double-time rate: r_OT = $24.80 × ____ = $ ____________ /hr

Step 3 — Overtime pay: Overtime = $ __________ × 4 = $ ____________

Step 4 — Sum the components:

Gross = $ __________ + $ __________ + $ __________ = $ ____________

Conclusion. Weekly gross pay = $ ____________

Stuck? Revisit lesson § Worked Example 1 — Integrated Pay Slip.

4. Graduated practice — Earning Money calculations

Show your working in the space below each part. Keep all dollar amounts to 2 decimal places unless told otherwise.

Foundation — single-step conversions and rates (4 questions)

Q	Problem	Answer
4.1 1	An annual salary is $62,400. What is the weekly equivalent?
4.2 1	An annual salary is $78,000. What is the fortnightly equivalent?
4.3 1	The base rate is $22.40 per hour. What is the time-and-a-half rate?
4.4 1	The base rate is $19.60 per hour. What is the double-time rate?

Standard — typical HSC difficulty (6 questions)

Show at least one line of substitution and clearly label your final answer with units.

4.5 Sara is paid $26.80/hr for a 38-hour week. Calculate her weekly wage. 2 marks

4.6 A worker earns $23.50/hr for 38 ordinary hours plus 5 hours at time-and-a-half. Calculate the weekly gross pay. 2 marks

4.7 A salesperson earns a $600 weekly retainer plus 3% commission on all sales. This week sales were $18,000. Calculate the weekly earnings. 2 marks

4.8 A piecework employee is paid $1.80 per item. In a week they assemble 420 items. Calculate the weekly pay. 2 marks

4.9 A worker earning $1,120 per week takes 4 weeks of annual leave. Calculate the leave loading they receive (17.5%). 2 marks

4.10 A worker has gross weekly pay of $1,540 and total deductions of $362. Calculate their net pay. 2 marks

Extension — combine two components (2 questions)

4.11 Maria earns $29.40/hr for a 38-hour week, 4 hours at time-and-a-half on Saturday, and 3 hours at double-time on Sunday. She also receives a $45 weekly travel allowance. Calculate her weekly gross pay, then convert it to an annual figure. 3 marks

4.12 A salesperson earns a $750 fortnightly retainer plus tiered commission: 2% on the first $10,000 of sales and 4% on sales above $10,000. If fortnightly sales are $24,500, calculate the total fortnightly earnings. 3 marks

Stuck on 4.12? Split the sales into two slices — the first $10,000 and the remaining $14,500 — and apply each rate to its own slice.

5. Self-check the easy 3

Tick the first three once you've checked your method works.

For 4.1 ($62,400 / year) I divided by 52, not 12 or 26, to get the weekly amount.

For 4.3 ($22.40/hr) I multiplied the base rate by 1.5 first, before applying it to any number of hours.

For 4.4 ($19.60/hr) I multiplied by 2.0 (not 1.5) because double-time means the rate is doubled.

How did this worksheet feel?

Got it Partly Lost

What I'll revisit before next class:

Answers — Do not peek before attempting

Q1.1 — Conversion factors

Weekly × 52 = Annual. Annual ÷ 26 = Fortnightly. Annual ÷ 12 = Monthly.

Q1.2 — Overtime multipliers

Time-and-a-half: × 1.5. Double time: × 2.0.

Q1.3 — Leave loading formula

Leave loading = 0.175 × 4W (17.5% of 4 weeks' wages).

Q3 — Faded example (gross pay with double-time)

Step 1: Ordinary = $24.80 × 38 = $942.40.
Step 2: r_OT = $24.80 × 2.0 = $49.60/hr.
Step 3: Overtime = $49.60 × 4 = $198.40.
Step 4: Gross = $942.40 + $198.40 + $30.00 = $1,170.80.
Conclusion: Weekly gross pay = $1,170.80.

Q4.1 — Annual $62,400 → weekly

$62,400 ÷ 52 = $1,200.00 per week.

Q4.2 — Annual $78,000 → fortnightly

$78,000 ÷ 26 = $3,000.00 per fortnight.

Q4.3 — Time-and-a-half from $22.40

$22.40 × 1.5 = $33.60/hr.

Q4.4 — Double-time from $19.60

$19.60 × 2 = $39.20/hr.

Q4.5 — Sara's weekly wage

W = $26.80 × 38 = $1,018.40 per week.

Q4.6 — Ordinary + 5 hours at time-and-a-half

Ordinary = $23.50 × 38 = $893.00.
r_OT = $23.50 × 1.5 = $35.25/hr.
Overtime = $35.25 × 5 = $176.25.
Gross = $893.00 + $176.25 = $1,069.25.

Q4.7 — Retainer + commission

Commission = $18,000 × 0.03 = $540.
Earnings = $600 + $540 = $1,140.00.

Q4.8 — Piecework

Pay = 420 × $1.80 = $756.00.

Q4.9 — Leave loading on $1,120/week

Loading = 0.175 × (4 × $1,120) = 0.175 × $4,480 = $784.00. (Note: this is the loading only, not the leave pay plus loading.)

Q4.10 — Net pay

Net = Gross − Deductions = $1,540 − $362 = $1,178.00.

Q4.11 — Maria: weekly gross + annual

Ordinary = $29.40 × 38 = $1,117.20.
Sat (time-and-a-half): rate = $29.40 × 1.5 = $44.10; pay = $44.10 × 4 = $176.40.
Sun (double-time): rate = $29.40 × 2 = $58.80; pay = $58.80 × 3 = $176.40.
Allowance = $45.00.
Weekly gross = $1,117.20 + $176.40 + $176.40 + $45.00 = $1,515.00.
Annual = $1,515.00 × 52 = $78,780.00.

Q4.12 — Tiered commission

Tier 1: 2% × $10,000 = $200.00.
Tier 2: 4% × ($24,500 − $10,000) = 4% × $14,500 = $580.00.
Total commission = $200 + $580 = $780.
Fortnightly earnings = $750 + $780 = $1,530.00.
Common error: applying 4% to the full $24,500 gives $980 commission — wrong. Each rate applies only to its own slice.