Mathematics Standard • Year 11 • Module 3 • Lesson 3
Commission, Piecework and Leave Loading
Apply commission, piecework and leave loading to realistic Australian work scenarios — identify the model, calculate, conclude.
Problem 1 — Real estate agent (tiered commission)
A real estate agent earns commission on a tiered structure on each property sold: 2% on the first $400,000 of the sale price, 2.5% on the portion between $400,000 and $800,000, and 3% on any amount above $800,000.
This month she sells a single property for $950,000.
Set up: What are we solving for?
(i) Calculate the commission earned in Tier 1 (first $400,000). 1 mark
(ii) Calculate the commission earned in Tier 2 (portion from $400,001 to $800,000). 1 mark
(iii) Calculate the total commission on the sale, and state in one sentence why she would earn LESS commission ($950,000 × 3% = $28,500) if 3% were simply applied to the full sale price. 3 marks
Stuck? Each tier rate applies only to the slice of sales in that tier.Problem 2 — Pickers: piecework vs hourly wage
A fruit-picking farm offers two payment options to its workers.
Option A: $24.80 per hour for an 8-hour shift.
Option B: Piecework at $1.95 per kg of fruit picked.
Set up: What are we solving for?
(i) Calculate the shift pay for a worker on Option A. 1 mark
(ii) Calculate how many kg of fruit an Option B worker must pick in the shift to match Option A's pay. 2 marks
(iii) A particular Option B worker picks 112 kg in the shift. Calculate their pay and state whether they earned more or less than the Option A worker. 2 marks
Stuck? Match Option A pay = $24.80 × 8, then divide by $1.95/kg.Problem 3 — Teacher's annual leave pay
A primary school teacher earns $1,485 per week in ordinary time. She is entitled to 4 weeks of paid annual leave, plus a 17.5% leave loading.
Set up: What are we solving for?
(i) Calculate her 4 weeks of leave pay (before loading). 1 mark
(ii) Calculate the leave loading. 1 mark
(iii) Calculate the total amount she is paid for her 4 weeks of leave. Then state in one sentence why this total is NOT simply 17.5% of her annual salary. 3 marks
Stuck? Revisit lesson § Worked Example 3 — Leave Loading.Problem 4 — Solar sales rep (retainer + threshold commission)
A solar panel salesperson earns a fortnightly retainer of $1,100 plus 3% commission on sales above a $5,000 fortnightly threshold. This fortnight she sold $42,800 of solar systems.
Set up: What are we solving for?
(i) State the sales amount that her commission applies to (the amount above the threshold). 1 mark
(ii) Calculate the commission earned. 1 mark
(iii) Calculate her total fortnightly earnings. Then state in one sentence what a common student error would give as the commission, and what total this would lead to. 3 marks
Stuck? Common error: applying 3% to the FULL $42,800 instead of the $37,800 above threshold.Problem 5 — Three workers, three pay models
Identify which payment model each worker is on, then calculate their weekly pay.
Pat: Paid $3.20 per cushion sewn; sewed 220 cushions this week.
Quinn: Retainer $480 plus 4% commission on $18,500 of sales this week.
Rae: Weekly wage $1,360; took her 4-week annual leave block this week and is paid leave + 17.5% loading for the four weeks.
Set up: What are we solving for?
(i) For each worker, state the pay model (piecework / commission with retainer / leave pay + loading). 1 mark
(ii) Calculate Pat's, Quinn's, and Rae's pay for the period described. 4 marks
(iii) Who received the largest payment for the period and by how much over the next-highest? 2 marks
Stuck? Identify the model from keywords ("per cushion", "retainer + %", "annual leave + 17.5%").How did this worksheet feel?
What I'll revisit before next class:
Problem 1 — Tiered commission on $950,000 sale
Set up. Split the sale into three tiers, apply each rate to its slice, sum.
(i) Tier 1 = $400,000 × 0.02 = $8,000.00.
(ii) Tier 2 = ($800,000 − $400,000) × 0.025 = $400,000 × 0.025 = $10,000.00.
(iii) Tier 3 = ($950,000 − $800,000) × 0.03 = $150,000 × 0.03 = $4,500.00.
Total commission = $8,000 + $10,000 + $4,500 = $22,500.00. Conclusion: applying 3% to the full $950,000 ($28,500) would overpay because the lower tiers only earn 2% and 2.5%, not 3% — tiered means each rate applies only to its slice.
Problem 2 — Piecework vs hourly
Set up. Compare an 8-hour shift's wage with a piecework rate per kg.
(i) Option A = $24.80 × 8 = $198.40.
(ii) Break-even kg = $198.40 ÷ $1.95 = 101.74... → must pick at least 102 kg to match. (We round UP because picking 101.74 is impossible and 101 kg falls short.)
(iii) 112 kg pay = 112 × $1.95 = $218.40. Difference = $218.40 − $198.40 = $20.00. The Option B worker earned $20.00 more than Option A.
Problem 3 — Teacher's annual leave
Set up. Calculate leave pay, loading, and total received.
(i) Leave pay = $1,485 × 4 = $5,940.00.
(ii) Loading = $5,940 × 0.175 = $1,039.50.
(iii) Total = $5,940 + $1,039.50 = $6,979.50. Why not 17.5% of annual: the loading applies only to 4 weeks' ordinary pay, not to the full 52-week salary — applying 17.5% to the annual salary would overstate the bonus by about 13×.
Problem 4 — Solar threshold commission
Set up. Subtract the $5,000 threshold, then apply 3%.
(i) Commission-eligible sales = $42,800 − $5,000 = $37,800.
(ii) Commission = $37,800 × 0.03 = $1,134.00.
(iii) Total = $1,100 + $1,134 = $2,234.00. Common error: applying 3% to the full $42,800 gives $1,284 commission and an incorrect total of $2,384 — $150 too high.
Problem 5 — Three pay models compared
Set up. Identify each model from the wording, then calculate.
(i) Pat = piecework. Quinn = retainer + commission. Rae = leave pay + 17.5% loading.
(ii) Pat = 220 × $3.20 = $704.00.
Quinn = $480 + ($18,500 × 0.04) = $480 + $740 = $1,220.00.
Rae = ($1,360 × 4) + ($1,360 × 4 × 0.175) = $5,440 + $952 = $6,392.00 for the 4-week block.
(iii) Rae received the largest payment ($6,392.00) — but it's for a 4-week block. Comparing only the weekly rate, Rae averaged $1,598/week, Quinn earned $1,220 in one week, Pat earned $704 in one week. Per week, Rae was highest by $378 over Quinn. (Acknowledge in your answer that Rae's figure covers 4 weeks; bare comparison of $6,392 vs $1,220 is unfair.)