Mathematics • Year 10 • Unit 1 • Lesson 1
Wages and Salaries — Mixed Challenge
Pull together every idea from Lesson 1: the wage formula, salary conversions across 52 / 26 / 12, gross vs net pay on an Australian pay slip, and the trap of "salary always pays more". Choose the right tool for each problem, spot someone else's mistake, then design a budget-friendly job comparison of your own.
1. Mixed problems — choose the right tool
Each question uses a different idea from Lesson 1. Decide which formula or conversion applies before you start writing. Show your working. 3 marks each
1.1 A casual cleaner works 17 hours at $31.20 per hour. Calculate the gross weekly pay.
1.2 Convert an annual salary of $84,500 into (a) weekly pay, (b) fortnightly pay, and (c) monthly pay. Round to the nearest cent.
1.3 Hina is paid $1,750 per fortnight. What is her annual gross salary, and what is the equivalent monthly figure?
1.4 A pay slip shows: gross fortnightly pay $2,840.00, PAYG tax $548.20, union fee $14.00. Find the net fortnightly pay.
1.5 A worker is told their pay rate is "$2,260 a fortnight, which is roughly $58,760 a year". Check whether this is correct, and explain the source of the small discrepancy in one sentence.
1.6 Two friends compare jobs. Friend A earns $32.50 per hour for a 38-hour week. Friend B earns a salary of $66,400. Calculate the annual equivalent of Friend A's wage and find the difference between the two jobs over one year.
2. Find the mistake
Another Year 10 student has tried to convert a $74,100 annual salary into a monthly amount and to find net pay. Their working is shown below. Exactly one line contains a mistake. Spot it, explain why it's wrong, then re-do the working correctly. 3 marks
Student's working — find monthly net pay, given $74,100 salary and $1,180 monthly PAYG tax:
Line 1: Monthly gross = $74,100 ÷ 12 = $6,175.00
Line 2: Net pay = Gross + Tax = $6,175.00 + $1,180.00 = $7,355.00
Line 3: So the worker takes home $7,355.00 per month.
(a) Which line contains the mistake?
(b) Explain in one or two sentences why that line is wrong.
(c) Write out the corrected working in full, including the corrected final answer.
Stuck? Net pay is what is left after tax — tax is a deduction (subtracted), not an addition.3. Open-ended challenge — design two jobs that tie
This question has many valid answers. Be creative but show every number. 4 marks
3.1 Design two different job offers that have exactly the same annual equivalent. One must be a wage (an hourly rate × a fixed weekly number of hours) and the other must be a salary. The annual equivalent must be between $55,000 and $75,000.
For each job you design:
(i) Write the job title or context (e.g. retail assistant, junior office admin).
(ii) State the hourly rate and weekly hours (for the wage) or the salary figure (for the salaried job).
(iii) Show the calculation that confirms the annual equivalent is identical.
Bonus: Your hourly rate must be a realistic Australian rate (between $24.10 — the 2025 minimum wage — and $45.00). Your weekly hours must not exceed 38 (the full-time standard).
How did this worksheet feel?
What I'll revisit before next class:
1.1 — Cleaner's gross pay
Gross Pay = 17 × $31.20 = $530.40. Used the wage formula directly.
1.2 — $84,500 conversions
(a) Weekly = 84,500 ÷ 52 = $1,625.00.
(b) Fortnightly = 84,500 ÷ 26 = $3,250.00.
(c) Monthly = 84,500 ÷ 12 = $7,041.67.
Always use 52 / 26 / 12 — never confuse them.
1.3 — Fortnightly to annual and monthly
Annual = $1,750 × 26 = $45,500.
Monthly = $45,500 ÷ 12 = $3,791.67.
Two steps: convert up to annual using 26, then back down to monthly using 12.
1.4 — Net fortnightly pay
Total deductions = $548.20 + $14.00 = $562.20.
Net pay = $2,840.00 − $562.20 = $2,277.80.
1.5 — Is "$2,260/fortnight ≈ $58,760/year" correct?
Annual = $2,260 × 26 = $58,760.00. The figure is correct. (No discrepancy — the "roughly" is unnecessary here because 26 fortnights divides into a year exactly for pay purposes.)
If the speaker had used 24 instead of 26, the figure would have been $54,240 — about $4,520 too low. The "roughly" sometimes hides exactly that kind of error.
1.6 — Friend A vs Friend B
Friend A annual = 38 × $32.50 × 52 = $1,235 × 52 = $64,220.
Friend B annual = $66,400.
Difference = $66,400 − $64,220 = $2,180. Friend B earns $2,180 more per year.
2 — Find the mistake
(a) The mistake is on Line 2.
(b) Tax is a deduction, which is subtracted from gross to give net pay — the student has added it instead. Adding tax to gross is the opposite of what a pay slip actually does.
(c) Corrected working:
Monthly gross = $74,100 ÷ 12 = $6,175.00
Net pay = Gross − Tax = $6,175.00 − $1,180.00
Net pay = $4,995.00 per month.
This is exactly the gross-vs-net distinction the lesson flags — net is what you actually take home after deductions.
3 — Open-ended challenge (sample solutions)
We need a wage and a salary with the same annual equivalent in the range $55,000-$75,000. The simplest approach is to pick the salary first, then design a wage that matches.
Pair 1 — annual equivalent $61,360
Job A (salary): junior office admin on $61,360 per year.
Job B (wage): retail supervisor on $31.05/hour, 38 hours/week.
Check: 38 × $31.05 × 52 = $1,179.90 × 52 = $61,354.80 ≈ $61,360 (rounded to a sensible hourly rate). ✓
Pair 2 — annual equivalent $66,560
Job A (salary): trainee paralegal on $66,560 per year.
Job B (wage): warehouse forklift driver on $32.00/hour, 40 hours/week (40 chosen so it's still under 38 if we relax to a 38-hour week — let's use 38 instead).
Redo with 38 hours: $66,560 ÷ 52 ÷ 38 = $33.68/hour. Use $33.68/hour × 38 hours × 52 weeks = $66,558.08 ≈ $66,560. ✓
Marking: 2 marks for the wage job (1 for plausible rate/hours in range, 1 for correct annual equivalent calculation); 2 marks for the salary job (1 for plausible figure in range, 1 for showing the two annual equivalents match). Full marks for any valid pair that meets the constraints.