Mathematics • Year 10 • Unit 1 • Lesson 3
Budgets & GST in the Real World
Apply budget design, the 50/30/20 rule and Australian GST (× 1.10 to add, ÷ 11 to extract) to realistic scenarios — a part-time worker's monthly plan, supermarket receipts, tradie invoices, and the "GST is 10% of the total" trap. Then explain your method in your own words.
1. Word problems
Each problem uses budget arithmetic (Savings = Income − Expenses, or the 50/30/20 rule) or GST (× 1.10 to add, ÷ 11 to extract) from Lesson 3. Show your working — a final answer with no working only earns half marks.
1.1 — A part-timer's monthly budget. Mia works part-time and earns $2,200 per month. Her essential expenses are $1,250 (rent share, groceries, transport, phone), and her discretionary expenses are $480 (streaming, eating out, hobbies).
(a) Calculate her total expenses and her monthly savings.
(b) Calculate her savings as a percentage of income.
(c) Does she meet ASIC's 20% savings target from the 50/30/20 rule? 3 marks
1.2 — Supermarket receipt. Ava's supermarket bill totals $74.80 including GST. Some of the items (fresh bread, milk, vegetables) are GST-free.
(a) If the GST charged on the receipt is shown as $2.20, how much of the $74.80 is for GST-free items?
(b) What is the pre-GST cost of the items that did attract GST? 3 marks
1.3 — Plumber's quote vs invoice. A plumber quotes a customer "$580 plus GST". The customer reads the quote as "$580 total" and only sets aside $580 for the job.
(a) Calculate the actual total the customer must pay.
(b) How much short will the customer be if they only have $580? 3 marks
1.4 — The "10% of the total" GST trap. A friend buys a $440 (GST-inclusive) bike helmet and says "the GST on that is $44 because GST is 10%". Calculate the actual GST on the price, and show that your friend's answer is wrong.
(a) Calculate the actual GST amount.
(b) Calculate the pre-GST price.
(c) Show that 10% of the pre-GST price equals your GST answer (not your friend's). 3 marks
1.5 — Apply the 50/30/20 rule. Devon earns $4,800 per month after tax. Devon currently spends $2,640 on needs, $1,800 on wants, and saves $360.
(a) Calculate Devon's actual percentage spend on needs, wants, and savings.
(b) Compare against the 50/30/20 rule and identify which category is most out of line.
(c) How much would Devon need to shift from wants to savings to meet the 20% savings target? 3 marks
2. Explain your thinking
This question is about communication, not just numbers. Use full sentences. 4 marks
2.1 Your cousin says: "GST is just 10% so I always multiply the shelf price by 0.10 to find the tax". In your own words, explain (i) why this method is wrong when applied to a shelf (GST-inclusive) price, (ii) which fraction or operation should be used instead, and (iii) demonstrate using a $33 shelf-priced book to show the correct GST amount. Refer to "10/110 = 1/11" somewhere in your explanation.
How did this worksheet feel?
What I'll revisit before next class:
1.1 — Mia's part-time budget
(a) Total expenses = $1,250 + $480 = $1,730. Savings = $2,200 − $1,730 = $470.
(b) Savings % = $470 ÷ $2,200 × 100 = 21.4%.
(c) Yes — she exceeds the 20% target by 1.4 percentage points. She's slightly ahead of the rule's recommendation.
1.2 — Supermarket receipt with GST-free items
(a) GST-able items total = $2.20 × 11 = $24.20. GST-free items = $74.80 − $24.20 = $50.60.
(b) Pre-GST cost of GST-able items = $24.20 − $2.20 = $22.00 (or $24.20 ÷ 1.10).
The lesson notes that fresh food is GST-free in Australia — this question shows why a receipt's GST line is much smaller than 1/11 of the total.
1.3 — Plumber's "plus GST" trap
(a) Total = $580 × 1.10 = $638.00.
(b) Shortfall = $638.00 − $580.00 = $58.00.
The customer needed an extra $58 — "plus GST" always means an additional 10% on top.
1.4 — The "10% of the total" GST trap
(a) Actual GST = $440 ÷ 11 = $40 (not $44 as the friend said).
(b) Pre-GST = $440 − $40 = $400 (or $440 ÷ 1.10).
(c) Check: 10% of $400 = 0.10 × $400 = $40 ✓ — this matches our GST from (a), confirming the friend's $44 is wrong.
The friend computed 10% of the GST-inclusive price; the rule says GST is 10% of the pre-GST price.
1.5 — Devon's 50/30/20 check
(a) Needs % = $2,640 ÷ $4,800 × 100 = 55%. Wants % = $1,800 ÷ $4,800 × 100 = 37.5%. Savings % = $360 ÷ $4,800 × 100 = 7.5%.
(b) The biggest gap is savings — 7.5% vs 20% target means Devon saves only about a third of the recommended amount. Wants is also 7.5pp over target.
(c) 20% of $4,800 = $960. Devon needs to add $960 − $360 = $600 from wants into savings, leaving $1,200 for wants (25%) and $960 for savings (20%).
2.1 — Explain your thinking (sample response)
My cousin's method is wrong when applied to a shelf price because the shelf price already includes the GST — multiplying by 0.10 gives 10% of the GST-inclusive total, which overstates the tax. The shelf price is 100% of the pre-GST price plus 10% GST = 110% of pre-GST, so the GST portion is 10/110 = 1/11 of the total. To extract GST from a GST-inclusive price, divide by 11 (or multiply by 1/11). For example, a $33 shelf-priced book has actual GST of $33 ÷ 11 = $3.00 — my cousin's method would give $3.30, which is too high.
Marking: 1 for naming the mistake; 1 for stating ÷ 11 (or × 1/11); 1 for using "10/110 = 1/11"; 1 for the correct $3 worked example.