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.)