Mathematics Standard • Year 11 • Module 3 • Lesson 5
Earning Money — Exam Practice
Apply the Earning Money toolkit to realistic workplace pay scenarios — decompose, calculate, conclude.
Problem 1 — Hospital orderly pay slip (multi-component)
Jordan works as a hospital orderly. His ordinary rate is $26.40 per hour. In a particular fortnight he worked 76 ordinary hours, 6 hours on Saturday at time-and-a-half, and 5 hours on a public holiday at double time. He also receives a meal allowance of $18.50 per week.
Set up: What are we solving for?
(i) Calculate Jordan's ordinary pay for the fortnight. 1 mark
(ii) Calculate Jordan's overtime pay for the fortnight (Saturday + public holiday). 2 marks
(iii) Calculate Jordan's total gross pay for the fortnight, including the meal allowance for both weeks. 2 marks
Stuck? Revisit lesson § Strategy for Multi-Component Pay Questions — list every component, calculate each separately, then sum.Problem 2 — Comparing two job offers (commission vs salary)
Priya is choosing between two retail jobs.
Job A: Salary of $58,500 per year.
Job B: Retainer of $720 per fortnight plus 4% commission on all sales. Priya expects to make $26,000 in sales per fortnight on average.
Set up: What are we solving for?
(i) Calculate Job B's expected fortnightly earnings (retainer + commission). 2 marks
(ii) Convert Job B's expected fortnightly earnings into an annual figure. 1 mark
(iii) Which job pays more annually, and by how much? State your conclusion clearly. 2 marks
Stuck? Revisit lesson § Comparing Earning Options — convert both jobs to the same unit (annual) before comparing.Problem 3 — Piecework break-even (factory)
A factory offers two pay options to its assembly workers.
Option A: $21.60 per hour for a 38-hour week.
Option B: $2.40 per component assembled.
Set up: What are we solving for?
(i) Calculate the weekly pay for a worker on Option A. 1 mark
(ii) Let n be the number of components a Worker on Option B must produce in a week to earn at least as much as Option A. Write an inequality in n and solve it. 2 marks
(iii) State the minimum whole number of components needed, and explain in one sentence why you rounded the way you did. 2 marks
Stuck? Revisit lesson § Worked Example 3 — Piecework Break-Even.Problem 4 — Annual leave pay (teacher)
Lena is a graduate teacher earning $1,250 per week. She is entitled to 4 weeks of paid annual leave, plus a 17.5% leave loading on her annual leave pay.
Set up: What are we solving for?
(i) Calculate Lena's 4 weeks of leave pay (before loading). 1 mark
(ii) Calculate the leave loading Lena receives. 1 mark
(iii) Calculate the total amount Lena is paid for her 4 weeks of annual leave. 2 marks
Stuck? Revisit lesson § Key Formulas — Leave loading = 0.175 × 4W.Problem 5 — Gross, net and a missing deduction (small-business payroll)
A small business owner is checking a payslip for one of her staff. The payslip shows:
Ordinary pay (38 hours @ $25.60): $972.80
Overtime (4 hours @ time-and-a-half): $ ____________ (you must calculate)
Tool allowance: $40.00
Total deductions (tax + super): $321.00
Net pay shown on payslip: $844.40
Set up: What are we solving for?
(i) Calculate the overtime pay that should appear on the payslip. 2 marks
(ii) Calculate the gross pay that should appear (ordinary + overtime + allowance). 1 mark
(iii) Using Gross − Deductions = Net, check whether the net pay shown on the payslip is correct. If not, state by how much it is wrong and which direction. 3 marks
Stuck? Revisit lesson § Reading the Question Before Writing Anything — gross vs net is the most common trap.How did this worksheet feel?
What I'll revisit before next class:
Problem 1 — Jordan's fortnightly pay slip
Set up. We are decomposing the fortnight into ordinary, Saturday overtime, public-holiday overtime and allowance, then summing for gross.
(i) Ordinary = $26.40 × 76 = $2,006.40.
(ii) Saturday rate: $26.40 × 1.5 = $39.60/hr; Saturday pay = $39.60 × 6 = $237.60.
Public-holiday rate: $26.40 × 2 = $52.80/hr; PH pay = $52.80 × 5 = $264.00.
Total overtime = $237.60 + $264.00 = $501.60.
(iii) Allowance for 2 weeks = $18.50 × 2 = $37.00.
Gross = $2,006.40 + $501.60 + $37.00 = $2,545.00 for the fortnight. (Common slip: forgetting to double the allowance for the fortnight.)
Problem 2 — Priya: commission vs salary
Set up. We are converting both job offers into annual pay so we can compare like with like, then stating which is higher and by how much.
(i) Commission = $26,000 × 0.04 = $1,040.
Fortnightly earnings (Job B) = $720 + $1,040 = $1,760.00.
(ii) Annual (Job B) = $1,760 × 26 = $45,760.00.
(iii) Job A annual = $58,500. Difference = $58,500 − $45,760 = $12,740. Job A pays more by $12,740 per year. (Conclusion sentence is essential — a bare number "$12,740" loses the conclusion mark.)
Problem 3 — Piecework break-even
Set up. We are finding the target weekly income from Option A, then solving an inequality for the number of pieces required under Option B to reach or exceed it.
(i) Option A weekly pay = $21.60 × 38 = $820.80.
(ii) Let n = number of components needed. Inequality: 2.40n ≥ 820.80. Dividing both sides by 2.40: n ≥ 820.80 ÷ 2.40 = 342.
(iii) Minimum = 342 components. Since 820.80 ÷ 2.40 = 342 exactly, 342 components meets the target precisely. (If the division had not been exact — e.g. 342.3 — we would round UP to 343, because "at least as much" means we cannot fall short.)
Problem 4 — Lena's annual leave pay
Set up. We are calculating the total Lena receives for 4 weeks of annual leave, which is the regular leave pay plus the 17.5% loading.
(i) Leave pay = $1,250 × 4 = $5,000.00.
(ii) Leave loading = 0.175 × $5,000 = $875.00.
(iii) Total = $5,000 + $875 = $5,875.00. (Common error: reporting only the loading $875 as the "total" — that's just the bonus on top, not the whole amount paid.)
Problem 5 — Payslip check
Set up. We are filling in the missing overtime line, computing the correct gross, then checking the stated net pay against Gross − Deductions.
(i) Overtime rate = $25.60 × 1.5 = $38.40/hr. Overtime pay = $38.40 × 4 = $153.60.
(ii) Gross = $972.80 + $153.60 + $40.00 = $1,166.40.
(iii) Expected net = $1,166.40 − $321.00 = $845.40. The payslip shows $844.40, which is $1.00 too low. Conclusion: the payslip is incorrect by $1.00 — the staff member has been underpaid by $1.00 this week.