Mathematics • Year 10 • Unit 1 • Lesson 2
Earnings — Mixed Challenge
Pull together every idea from Lessons 1 and 2: hourly wages, salary conversions, overtime (1.5×, 2×, 2.5×), penalty loadings, straight commission, base wage + commission, tiered commission, and piecework. Choose the right tool for each problem, spot someone else's mistake, and design two pay structures that pay equally well.
1. Mixed problems — choose the right tool
Each question uses a different idea from Lessons 1-2. Decide which formula applies before you start writing. Show your working. 3 marks each
1.1 A delivery driver works 38 hours at $29.60/hour plus 4 hours overtime at time-and-a-half. Find the total gross weekly pay.
1.2 A stockbroker earns 0.5% commission on $1,800,000 of share trades this week. Calculate the commission earned.
1.3 A factory worker is paid $0.85 per item assembled, plus a base of $200 per shift. They assemble 540 items in a shift. Find their total pay.
1.4 A paramedic's normal rate is $44.80/hour. On a public holiday she works 10 hours at double time. Calculate her pay for that shift.
1.5 A clothing-store salesperson earns $720 base per week plus 6% commission. If their total earnings this week are $1,440, how much in sales did they make?
1.6 A bakery worker is paid $26.00/hour for 38 normal hours, plus 3 hours at time-and-a-half (Saturday morning) and 4 hours at double time (Sunday). Calculate gross weekly pay.
2. Find the mistake
Another student has tried to calculate weekly pay for a casual barista who works 16 hours at the $24.10 minimum wage, plus 6 hours on Sunday at double time. 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 — total weekly pay:
Line 1: Weekday pay = 16 × $24.10 = $385.60
Line 2: Sunday rate = 2 + $24.10 = $26.10/hour
Line 3: Sunday pay = 6 × $26.10 = $156.60
Line 4: Total weekly pay = $385.60 + $156.60 = $542.20
(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? "Double time" is a multiplier, not an addition. Compare Line 2 to the lesson's overtime formulas.3. Open-ended challenge — two pay packets, same total
This question has many valid answers. Be creative but show every number. 4 marks
3.1 Design two different weekly pay arrangements that both result in exactly $1,500 of gross weekly pay. The two must use different structures — for example:
- one based on a wage with overtime (normal hours + time-and-a-half or double time), and
- one based on a base wage plus commission (% of sales).
For each arrangement:
(i) Briefly describe the job (e.g. café worker, real estate trainee).
(ii) State all the inputs (hours, rates, sales figures).
(iii) Show the calculation that confirms the total is exactly $1,500.
Bonus: Use realistic Australian rates (between $24.10 — the 2025 minimum wage — and $50/hour) and commission rates between 1% and 8%.
How did this worksheet feel?
What I'll revisit before next class:
1.1 — Delivery driver with overtime
Normal = 38 × $29.60 = $1,124.80.
Overtime rate = 1.5 × $29.60 = $44.40. Overtime pay = 4 × $44.40 = $177.60.
Total = $1,124.80 + $177.60 = $1,302.40.
1.2 — Stockbroker commission
0.005 × $1,800,000 = $9,000.
Watch the decimal: 0.5% = 0.005, not 0.05.
1.3 — Factory worker piecework + base
Piecework = 540 × $0.85 = $459.00. Total = $200 + $459.00 = $659.00.
1.4 — Paramedic on public holiday
Double-time rate = 2 × $44.80 = $89.60. Pay = 10 × $89.60 = $896.00.
1.5 — Working backwards from total
Set $720 + 0.06 × S = $1,440. Then 0.06 × S = $720, so S = $720 ÷ 0.06 = $12,000 in sales.
Rearrange the base + commission formula to solve for sales.
1.6 — Bakery weekend penalties
Normal = 38 × $26.00 = $988.00.
Time-and-a-half rate = 1.5 × $26.00 = $39.00. Sat pay = 3 × $39.00 = $117.00.
Double-time rate = 2 × $26.00 = $52.00. Sun pay = 4 × $52.00 = $208.00.
Total = $988.00 + $117.00 + $208.00 = $1,313.00.
2 — Find the mistake
(a) The mistake is on Line 2.
(b) The student has added 2 to the hourly rate ($2 + $24.10) instead of multiplying by 2. "Double time" is a multiplier — 2 × $24.10 — not a flat $2 add-on. The lesson defines double time as "Rate = 2 × Normal Hourly Rate".
(c) Corrected working:
Weekday pay = 16 × $24.10 = $385.60.
Sunday rate = 2 × $24.10 = $48.20/hour.
Sunday pay = 6 × $48.20 = $289.20.
Total weekly pay = $385.60 + $289.20 = $674.80.
The student's wrong answer ($542.20) is over $130 under the correct figure — a real worker would be significantly underpaid.
3 — Open-ended challenge (sample solution)
We need two structures that both hit exactly $1,500 weekly. The simplest approach is to pick easy numbers for each.
Arrangement 1 — wage with overtime (café shift supervisor)
40 normal hours at $30/hour = 40 × $30 = $1,200.
Plus 5 hours overtime at time-and-a-half = 5 × ($30 × 1.5) = 5 × $45 = $225.
Plus 1 hour at double time on Sunday = 1 × $60 = $60.
Hmm, that gives $1,485 — adjust to 5 hours overtime + 1.25 hours at double time = $225 + $75 = $300. Total = $1,200 + $300 = $1,500 ✓.
(Simpler version: 38 hours at $33.10 = $1,257.80 plus 5 hours at $48.45 overtime = $242.20. Total $1,500.00. ✓)
Arrangement 2 — base wage + commission (electronics salesperson)
Base = $700 per week.
Commission rate = 4% on sales.
Need: $700 + 0.04 × Sales = $1,500. So Sales = $800 ÷ 0.04 = $20,000.
Check: $700 + 0.04 × $20,000 = $700 + $800 = $1,500 ✓.
Marking: 2 marks per arrangement (1 for realistic numbers within the constraints, 1 for the calculation hitting exactly $1,500). 4 marks total.