Mathematics Standard • Year 11 • Module 3 • Lesson 9
GST, Budgeting and Household Expenses
Apply GST, household-budget and bill calculations to realistic Australian household and small-business scenarios.
Problem 1 — Tradie quoting a kitchen renovation
Selina, a small-business builder, is preparing a quote for a kitchen renovation. Her pre-GST costs are:
Labour 38 hours @ $72/hr (pre-GST) • Cabinetry materials $3,840 (pre-GST) • Plumbing subcontract $1,260 (pre-GST) • Disposal/skip $180 (pre-GST).
Set up: What are we solving for?
(i) Calculate the pre-GST total. 1 mark
(ii) Calculate the GST-inclusive total Selina must quote on the invoice. 1 mark
(iii) What is the GST amount Selina will collect from the client and remit to the ATO? 1 mark
Stuck? Pre-GST × 0.10 gives the GST amount directly; pre-GST × 1.10 gives the inclusive total.Problem 2 — Comparing two electricity providers
The O'Brien household uses 1,420 kWh of electricity per quarter (91 days). They are comparing two providers, both quoted pre-GST:
Provider X: Supply $1.18/day; flat usage rate of 29.4c/kWh.
Provider Y: Supply $0.92/day; first 800 kWh at 27.6c/kWh, remaining at 36.2c/kWh.
Set up: What are we solving for?
(i) Calculate the GST-inclusive quarterly bill under Provider X. 2 marks
(ii) Calculate the GST-inclusive quarterly bill under Provider Y. 2 marks
(iii) Which provider is cheaper, and by how much per quarter? State a clear conclusion sentence. 2 marks
Stuck? Use the same usage (1,420 kWh) and same period (91 days) for both providers. Add GST at the very end.Problem 3 — Family monthly budget with mixed time periods
The Nguyen family records the following finances. Income: combined fortnightly wages $4,820; rental income $1,640 per month. Expenses: mortgage $2,260 per month; weekly groceries $310; quarterly electricity $640 (GST-inclusive); car loan $186 per fortnight; phone/internet bundle $115 per month (GST-inclusive); annual home insurance $1,860 (GST-inclusive).
Set up: What are we solving for?
(i) Convert all income items to monthly and calculate total monthly income. 2 marks
(ii) Convert all expense items to monthly and calculate total monthly expenses. 2 marks
(iii) Calculate the monthly surplus or deficit, and then state the annual position. 2 marks
Stuck? Fortnightly × 26 ÷ 12 = monthly. Weekly × 52 ÷ 12 = monthly. Quarterly ÷ 3 = monthly. Annual ÷ 12 = monthly.Problem 4 — Reducing a deficit
The Singh family has a current monthly deficit of $185. Their major monthly expenses are: groceries $1,180, takeaway/dining $420, streaming subscriptions $54 (GST-inclusive), gym memberships $96 (GST-inclusive), and discretionary shopping $610. They want to reduce the deficit to zero by cutting from the four most discretionary categories listed (everything except groceries).
Set up: What are we solving for?
(i) Calculate the total monthly spend on the four discretionary categories (excluding groceries). 1 mark
(ii) By what percentage (to 1 d.p.) must they cut discretionary spending to eliminate the $185 monthly deficit? 2 marks
(iii) If they instead cancelled the streaming and gym subscriptions entirely, would this be enough to close the deficit? Justify with a calculation. 2 marks
Stuck on (ii)? Required cut ÷ total discretionary × 100 = percentage cut.Problem 5 — Reading a small-business invoice
Jess, a small-business owner, receives the following invoice from her supplier:
Stock items: $2,418.00 (pre-GST)
Delivery: $86.00 (pre-GST)
Insurance excess (GST-free): $120.00
Total payable: $2,876.40
Set up: What are we solving for?
(i) Calculate the GST that should be charged on stock + delivery (these are taxable items). 2 marks
(ii) Calculate the total that should appear on the invoice (stock + delivery + GST + GST-free excess). 2 marks
(iii) Compare with the printed total of $2,876.40. Is the invoice correct? If not, by how much is it wrong, and in which direction? 2 marks
Stuck? GST-free items do not attract GST — calculate GST only on the taxable lines, then add the GST-free line at the end.How did this worksheet feel?
What I'll revisit before next class:
Problem 1 — Selina's renovation quote
Set up. Sum the pre-GST line items, then either ×1.10 for inclusive or ×0.10 for the GST component.
(i) Labour = 38 × $72 = $2,736. Pre-GST total = $2,736 + $3,840 + $1,260 + $180 = $8,016.00.
(ii) GST-inclusive = $8,016 × 1.10 = $8,817.60.
(iii) GST to remit = $8,016 × 0.10 = $801.60 (or equivalently $8,817.60 ÷ 11 = $801.60). Both methods give the same answer.
Problem 2 — Electricity provider comparison
Set up. Calculate each provider's pre-GST bill for 1,420 kWh over 91 days, then add GST and compare.
(i) Provider X. Supply = $1.18 × 91 = $107.38. Usage = 1,420 × $0.294 = $417.48. Pre-GST = $524.86. GST-inclusive = $524.86 × 1.10 = $577.35 (to nearest cent).
(ii) Provider Y. Supply = $0.92 × 91 = $83.72. Tier 1 = 800 × $0.276 = $220.80. Tier 2 = (1,420 − 800) × $0.362 = 620 × $0.362 = $224.44. Pre-GST = $83.72 + $220.80 + $224.44 = $528.96. GST-inclusive = $528.96 × 1.10 = $581.86.
(iii) Difference = $581.86 − $577.35 = $4.51. Provider X is cheaper, by $4.51 per quarter. (The high Tier 2 rate at Provider Y wipes out the supply-charge saving.)
Problem 3 — Nguyen family budget
Set up. Convert all items to monthly, sum income and expenses, then take the difference.
(i) Monthly wages = $4,820 × 26 ÷ 12 ≈ $10,443.33. Rental income = $1,640. Total monthly income ≈ $12,083.33.
(ii) Mortgage $2,260. Groceries = $310 × 52 ÷ 12 ≈ $1,343.33. Electricity = $640 ÷ 3 ≈ $213.33. Car loan = $186 × 26 ÷ 12 = $403.00. Phone/internet $115. Insurance = $1,860 ÷ 12 = $155.
Total monthly expenses ≈ $2,260 + $1,343.33 + $213.33 + $403.00 + $115 + $155 = $4,489.66.
(iii) Monthly surplus = $12,083.33 − $4,489.66 = $7,593.67. Annual surplus = $7,593.67 × 12 ≈ $91,124. (Conclusion: the family runs a healthy monthly surplus of about $7,594, equating to roughly $91,124 per year.)
Problem 4 — Closing the deficit
Set up. Total the discretionary categories, then express the required $185 cut as a percentage of that total.
(i) Discretionary total = $420 + $54 + $96 + $610 = $1,180.00.
(ii) Required cut % = $185 ÷ $1,180 × 100 ≈ 15.7% across discretionary spending.
(iii) Cancelling streaming + gym saves $54 + $96 = $150 per month. Since $150 < $185, this is not enough to close the $185 deficit — they would still be $35 short each month.
Problem 5 — Invoice check
Set up. Apply GST only to the taxable lines (stock + delivery); the GST-free excess is added separately.
(i) Taxable subtotal = $2,418 + $86 = $2,504. GST = $2,504 × 0.10 = $250.40.
(ii) Correct invoice total = $2,418 + $86 + $250.40 + $120 = $2,874.40.
(iii) Printed $2,876.40 vs correct $2,874.40 → invoice is $2.00 too high — Jess has been over-charged by $2.00. (Common error: applying GST to the $120 insurance excess as well — that would give $2,886.40, even further off.)