Mathematics • Year 10 • Unit 1 • Lesson 1
Wages and Salaries in the Real World
Apply hourly wage and annual salary calculations to real Australian pay scenarios — comparing job offers, reading pay slips, checking award rates and avoiding the "fortnight ≠ ½ a month" trap. Then explain your method in your own words.
1. Word problems
Each problem uses the wage or salary formulas from Lesson 1: Gross Pay = Hours × Hourly Rate, or Annual Salary ÷ pay periods (52 weekly, 26 fortnightly, 12 monthly). Show your working — a final answer with no working only earns half marks.
1.1 — Casual hospitality shift. Mia is a casual barista paid at the 2025 Australian national minimum wage of $24.10 per hour. She works three shifts this week: 4 hours on Tuesday, 6 hours on Wednesday, and 7.5 hours on Saturday.
(a) Calculate Mia's total hours for the week.
(b) Calculate her gross weekly pay. 3 marks
1.2 — Two graduate job offers. Yusuf has two job offers after finishing TAFE:
- Job A: a wage of $34.00 per hour for a 38-hour week.
- Job B: a salary of $69,500 per year.
(a) Calculate the annual equivalent of Job A.
(b) Which job pays more per year, and by how much? 3 marks
1.3 — Reading a pay slip. Jordan's fortnightly pay slip from a Sydney supermarket shows:
- Hours worked: 64
- Hourly rate: $26.50
- PAYG tax: $312.40
- Superannuation (employer-paid, not deducted from take-home): $186.78
(a) Calculate Jordan's gross fortnightly pay.
(b) Calculate Jordan's net fortnightly pay. (Hint: super does not come out of net pay — it's paid on top.) 3 marks
1.4 — The "divide by 24" trap. Alex's mum has a salary of $93,600 per year. Alex tries to work out her mum's fortnightly pay by computing $93,600 ÷ 12 ÷ 2 = $3,900.
(a) What is the correct fortnightly pay?
(b) How much does Alex's incorrect method overstate the fortnight by? 3 marks
1.5 — Casual rate vs award. A 16-year-old retail worker is being paid $17.50 per hour. The applicable Fair Work award says junior workers of that age must be paid at least $19.40 per hour. They worked 14 hours last week.
(a) Calculate the gross weekly pay the worker actually received.
(b) Calculate the gross weekly pay they should have received under the award.
(c) How much underpayment is the worker owed? 3 marks
2. Explain your thinking
This question is about communication, not just numbers. Use full sentences. 4 marks
2.1 A friend tells you: "A salary is always better than a wage because you don't lose money when you take a day off." Using everything from Lesson 1, explain (i) what is correct about that statement, (ii) what is misleading or wrong, and (iii) what the friend should compare instead in order to decide which job actually pays more. Refer to the term "annual equivalent" somewhere in your answer.
How did this worksheet feel?
What I'll revisit before next class:
1.1 — Mia's casual barista shifts
(a) Total hours = 4 + 6 + 7.5 = 17.5 hours.
(b) Gross pay = 17.5 × $24.10 = $421.75.
Why this is just the wage formula: penalty rates for Saturday aren't applied here — that's a Lesson 2 extension.
1.2 — Yusuf's two job offers
(a) Job A annual = 38 × $34.00 × 52 = $1,292 × 52 = $67,184.
(b) Job B = $69,500. Difference = $69,500 − $67,184 = $2,316. Job B pays more, by $2,316 per year.
The salary "feels" smaller per hour but the annual total is what counts — exactly the lesson's warning.
1.3 — Jordan's pay slip
(a) Gross = 64 × $26.50 = $1,696.00 per fortnight.
(b) Net = $1,696.00 − $312.40 = $1,383.60 per fortnight.
Super of $186.78 is paid by the employer on top of gross pay — it does not reduce take-home (net) pay.
1.4 — The "divide by 24" trap
(a) Correct fortnightly pay = 93,600 ÷ 26 = $3,600.00.
(b) Alex's incorrect figure = $3,900. Overstatement = $3,900 − $3,600 = $300 per fortnight too high. Over a year that's $300 × 26 = $7,800 of "phantom" pay.
The lesson's misconception card calls this out directly: there are 26 fortnights in a year, not 24.
1.5 — Casual rate vs award
(a) Actual pay = 14 × $17.50 = $245.00.
(b) Award pay = 14 × $19.40 = $271.60.
(c) Underpayment owed = $271.60 − $245.00 = $26.60 for the week.
Award rates set by the Fair Work Commission are the legal minimum — being paid below them is wage theft.
2.1 — Explain your thinking (sample response)
(i) My friend is partly correct: a salaried worker is paid a fixed amount each pay period regardless of exact hours worked, so taking a personal day usually does not reduce that pay packet. (ii) They are wrong to assume a salary always means higher pay — the lesson clearly states wages and salaries are structures, not levels. A high hourly wage of $35 over a 38-hour week works out to $69,160 a year, which beats many entry-level salaries. (iii) To decide which job actually pays more, my friend should calculate the annual equivalent of each offer (hours × hourly rate × 52 for a wage; the salary figure itself for a salary) and compare those two totals directly.
Marking: 1 for naming what is correct (no pay drop on a day off), 1 for what is misleading (salary ≠ higher pay), 1 for using "annual equivalent", 1 for a clear full-sentence explanation.