Mathematics • Year 10 • Unit 1 • Lesson 2
Overtime & Commission in the Real World
Apply overtime multipliers, weekend penalty rates, straight commission and tiered commission to realistic Australian pay scenarios — Sunday retail shifts, public holiday nursing, real estate stings, and choosing between two pay structures. Then explain your method in your own words.
1. Word problems
Each problem uses one (or more) of the structures from Lesson 2: overtime multipliers (1.5×, 2×, 2.5×), penalty loadings, straight commission, base wage + commission, or piecework. Show your working — a final answer with no working only earns half marks.
1.1 — Apprentice plumber with weekend overtime. Felix is an apprentice plumber earning $26.40 per hour. This week he works 38 regular weekday hours, plus a 5-hour emergency call-out on Saturday at time-and-a-half.
(a) Calculate his normal weekday pay.
(b) Calculate his Saturday pay.
(c) Calculate his total gross pay for the week. 3 marks
1.2 — Public holiday nursing shift. A registered nurse earns a normal rate of $42.00 per hour. She works an 8-hour Christmas Day shift, paid at double time and a half.
(a) Calculate her hourly rate for that shift.
(b) Calculate her total pay for the 8-hour shift.
(c) How much extra does she earn compared with a normal weekday 8-hour shift? 3 marks
1.3 — Real estate commission. A Sydney real estate agent earns 1.8% commission on each property sold. This month they sold two houses: one for $1,250,000 and another for $890,000.
(a) Calculate the commission earned on each sale.
(b) Calculate the total commission for the month. 3 marks
1.4 — Sunday retail penalty rate. Under a retail award, a casual shop assistant earns a base rate of $24.10/hour. On Sundays they receive a 25% casual loading plus a 175% Sunday penalty rate — so the Sunday rate is $24.10 × 1.25 × 1.75.
(a) Calculate the assistant's Sunday hourly rate (to the nearest cent).
(b) Calculate the assistant's pay for a 6-hour Sunday shift. 3 marks
1.5 — Compare two pay structures. Hina is offered the same sales role under two different structures:
- Option A: a flat wage of $1,400 per week.
- Option B: a base of $800 per week plus 4% commission on sales.
(a) How much in sales would Hina need to make under Option B for the two options to pay the same?
(b) If a typical week is $20,000 in sales, which option pays more, and by how much? 3 marks
2. Explain your thinking
This question is about communication, not just numbers. Use full sentences. 4 marks
2.1 A classmate writes: "Tom worked 10 hours overtime at double time. His normal rate is $25, so his overtime pay is 10 × $25 × 2 + 10 × $25 = $750 because we have to include his normal pay too." In your own words, explain (i) what mistake your classmate has made, (ii) which rule from Lesson 2 they've confused, and (iii) what the correct overtime pay is for those 10 hours alone. Refer to the phrase "overtime is added to normal pay, not included in it" somewhere in your explanation.
How did this worksheet feel?
What I'll revisit before next class:
1.1 — Apprentice plumber
(a) Normal weekday = 38 × $26.40 = $1,003.20.
(b) Saturday rate = 1.5 × $26.40 = $39.60/hour. Saturday pay = 5 × $39.60 = $198.00.
(c) Total gross = $1,003.20 + $198.00 = $1,201.20.
1.2 — Public holiday nursing shift
(a) Holiday rate = 2.5 × $42.00 = $105.00/hour.
(b) Total = 8 × $105.00 = $840.00.
(c) Normal 8-hour pay = 8 × $42.00 = $336.00. Extra earned on Christmas Day = $840.00 − $336.00 = $504.00.
1.3 — Real estate commission
(a) Sale 1: 0.018 × $1,250,000 = $22,500. Sale 2: 0.018 × $890,000 = $16,020.
(b) Total = $22,500 + $16,020 = $38,520.
Real-world note: the lesson anchor mentions agents typically earn 1-3% commission — this sits in that band.
1.4 — Sunday retail penalty rate
(a) Sunday rate = $24.10 × 1.25 × 1.75 = $30.125 × 1.75 = $52.72/hour (to nearest cent).
(b) 6-hour shift pay = 6 × $52.72 = $316.32.
This is the exact General Retail Industry Award 2020 calculation quoted in the lesson's anchor box.
1.5 — Two pay structures compared
(a) Set $800 + 0.04 × S = $1,400. Then 0.04 × S = $600, so S = $600 ÷ 0.04 = $15,000 in sales would make the two equal.
(b) At $20,000 sales: Option B = $800 + 0.04 × $20,000 = $800 + $800 = $1,600. Option A = $1,400. Option B pays more, by $200/week at that level of sales.
Below $15,000 sales the flat wage wins; above $15,000 the commission structure wins.
2.1 — Explain your thinking (sample response)
My classmate has double-counted Tom's normal pay inside his overtime calculation. The double-time multiplier of 2 already is the overtime rate — they have then added another lot of normal pay on top, which is wrong. Lesson 2 makes this explicit: "penalty rates and overtime are added to normal pay, not included in it" — meaning the calculation for overtime hours is just hours × overtime rate, and any normal weekday pay is a separate, additional line on the pay slip. The correct overtime pay for the 10 hours alone is 10 × $25 × 2 = $500 (not $750). If Tom also worked normal weekday hours, those would be calculated separately and added to this $500.
Marking: 1 for naming the mistake (double-counting); 1 for identifying the rule from the lesson; 1 for the correct $500 figure; 1 for a clear, full-sentence explanation.