Mathematics Standard • Year 11 • Module 3 • Lesson 9

GST, Budgeting and Household Expenses

Build fluency with the three GST directions (×1.10, ÷1.10, ÷11), budget surplus/deficit calculations, and utility bills with fixed supply + tiered usage charges.

Build · Skill Drill

1. Quick recall

Answer each question in the space provided. 1 mark each

Q1.1 Complete each GST calculation rule.

Add GST: pre-GST × ____________. Remove GST: inclusive ÷ ____________. GST component of inclusive price: inclusive ÷ ____________.

Q1.2 Write the formula for budget surplus or deficit.

Surplus/deficit = ____________ − ____________

Q1.3 Convert: $260 per month into a weekly figure (use 52 weeks ÷ 12 months). $ ____________ per week.

Stuck? Revisit lesson § Three GST Calculations at a Glance.

2. Worked example — quarterly electricity bill with tiered usage and GST

Follow each line of working. Every step has a reason on the right.

Problem. An NSW household receives a 91-day electricity bill. Supply charge $1.08 per day; usage — first 600 kWh at 29.4c/kWh, remaining at 35.8c/kWh. Total usage 820 kWh. Calculate the pre-GST total and the GST-inclusive total.

Step 1 — Fixed supply charge.

Supply = $1.08 × 91 = $98.28

Reason: daily charge × number of days — applies regardless of usage.

Step 2 — Tier 1 usage (first 600 kWh).

Tier 1 = 600 × $0.294 = $176.40

Step 3 — Tier 2 usage (remaining 220 kWh).

Tier 2 = (820 − 600) × $0.358 = 220 × $0.358 = $78.76

Reason: split usage at the bracket boundary, like tiered commission.

Step 4 — Pre-GST total.

Pre-GST total = $98.28 + $176.40 + $78.76 = $353.44

Step 5 — Add GST.

GST-inclusive = $353.44 × 1.10 = $388.78 (to nearest cent)

Reason: electricity attracts GST — add 10% in one step.

Conclusion. The quarterly bill is $388.78 (GST-inclusive).

3. Faded example — weekly student budget

A casual worker earns $480 per week and receives a $240 monthly allowance from home. Weekly expenses: rent $190, groceries $105, transport $46. Monthly phone $42. Annual insurance $520. Fill in each blank to calculate the weekly surplus or deficit. 4 marks

Step 1 — Convert monthly allowance to weekly:

Weekly allowance = $240 × 12 ÷ ____ = $ ____________

Step 2 — Total weekly income: $480 + $ ________ = $ ____________

Step 3 — Convert phone and insurance:

Weekly phone = $42 × 12 ÷ 52 ≈ $ ____________
Weekly insurance = $520 ÷ 52 = $ ____________

Step 4 — Total weekly expenses:

= $190 + $105 + $46 + $ ________ + $ ________ = $ ____________

Step 5 — Surplus or deficit: $ ________ − $ ________ = $ ____________ → ____________ (surplus / deficit)

Stuck? Revisit lesson § Worked Example 4 — Budget Comparison After Converting Time Periods.

4. Graduated practice — GST, budget and bills

Show your working below each part. Keep amounts to the nearest cent.

Foundation — single-step GST and time conversions (4 questions)

Q	Problem	Answer
4.1 1	A plumber's pre-GST quote is $480. What is the GST-inclusive price?
4.2 1	A laptop is advertised at $1,815 including GST. Find the pre-GST price.
4.3 1	A receipt shows a GST-inclusive total of $396. Find the GST component.
4.4 1	Convert $1,560 per year to a monthly amount.

Standard — typical HSC difficulty (6 questions)

Show at least one line of substitution and clearly label your final answer with units.

4.5 A plumber bills $620 (pre-GST) for labour plus $145 (pre-GST) for materials. Calculate the GST-inclusive total. 2 marks

4.6 A grocery receipt shows a $258.50 GST-inclusive total. The receipt notes that $128 of items were GST-free (fresh food). Calculate the GST component on the remaining $130.50. 2 marks

4.7 The Patel family has monthly income of $7,840 and monthly expenses of $6,210. Calculate their monthly surplus or deficit. 2 marks

4.8 An electricity bill (91 days) has a flat supply charge of $1.16/day and usage of 740 kWh charged at a flat 31.2c/kWh. Calculate the GST-inclusive total. 2 marks

4.9 Convert: rent $360 per week, phone $48 per month, insurance $640 per year — all into monthly figures. Then add to give total monthly expenses for these three items. 2 marks

4.10 A water bill has a fixed quarterly service charge of $84 and usage of 38 kL charged at $2.85 per kL (no GST on residential water). Calculate the total bill. 2 marks

Extension — multi-step combining concepts (2 questions)

4.11 A 91-day electricity bill has supply $0.96/day; tiered usage — first 500 kWh at 28.4c/kWh, remaining at 36.0c/kWh. Total usage 720 kWh. All prices pre-GST. Calculate the GST-inclusive bill total. 3 marks

4.12 A student has weekly income from casual work of $510 plus a monthly allowance of $300. Weekly expenses are rent $205, groceries $110, transport $54. Monthly phone $44 (GST-inclusive). Annual insurance $580 (GST-inclusive). Convert everything to weekly and calculate the weekly surplus or deficit, then state the annual figure. 3 marks

Stuck on 4.12? Convert monthly × 12 ÷ 52; annual ÷ 52. Keep GST-inclusive prices as given — the question asks for actual money paid.

5. Self-check the easy 3

Tick the first three once you've checked your method works.

For 4.1 I multiplied $480 by 1.10 (not 1.1 + 10) to get $528.

For 4.2 I divided $1,815 by 1.10 (not by 11) to get the pre-GST price $1,650.

For 4.3 I divided $396 by 11 (not by 1.10) to get the GST component $36.

How did this worksheet feel?

Got it Partly Lost

What I'll revisit before next class:

Answers — Do not peek before attempting

Q1.1 — GST rules

Add GST: × 1.10. Remove GST: ÷ 1.10. GST component of inclusive price: ÷ 11.

Q1.2 — Budget formula

Surplus/deficit = Total income − Total expenses.

Q1.3 — Time conversion

$260 × 12 ÷ 52 = $60.00 per week.

Q3 — Faded example (student weekly budget)

Step 1: Weekly allowance = $240 × 12 ÷ 52 = $55.38 (to nearest cent).
Step 2: Total weekly income = $480 + $55.38 = $535.38.
Step 3: Weekly phone = $42 × 12 ÷ 52 ≈ $9.69. Weekly insurance = $520 ÷ 52 = $10.00.
Step 4: Total weekly expenses = $190 + $105 + $46 + $9.69 + $10.00 = $360.69.
Step 5: $535.38 − $360.69 = $174.69 surplus per week.

Q4.1 — Pre-GST $480 → inclusive

$480 × 1.10 = $528.00.

Q4.2 — Inclusive $1,815 → pre-GST

$1,815 ÷ 1.10 = $1,650.00.

Q4.3 — GST component of $396

$396 ÷ 11 = $36.00.

Q4.4 — $1,560/year → monthly

$1,560 ÷ 12 = $130.00 per month.

Q4.5 — Plumber total with GST

Pre-GST total = $620 + $145 = $765. GST-inclusive = $765 × 1.10 = $841.50.

Q4.6 — GST on partial receipt

GST component on $130.50 of taxable items = $130.50 ÷ 11 = $11.86 (to nearest cent). (Note: GST-free fresh food carries no GST, so the calculation applies only to the taxable portion.)

Q4.7 — Patel surplus

$7,840 − $6,210 = $1,630.00 monthly surplus.

Q4.8 — Flat-rate electricity bill

Supply = $1.16 × 91 = $105.56. Usage = 740 × $0.312 = $230.88.
Pre-GST total = $336.44. GST-inclusive = $336.44 × 1.10 = $370.08 (to nearest cent).

Q4.9 — Convert and sum (monthly)

Monthly rent = $360 × 52 ÷ 12 = $1,560. Monthly phone = $48. Monthly insurance = $640 ÷ 12 ≈ $53.33.
Total = $1,560 + $48 + $53.33 = $1,661.33 per month.

Q4.10 — Water bill (no GST)

Usage = 38 × $2.85 = $108.30. Total = $84 + $108.30 = $192.30.

Q4.11 — Tiered electricity + GST

Supply = $0.96 × 91 = $87.36.
Tier 1 = 500 × $0.284 = $142.00.
Tier 2 = (720 − 500) × $0.36 = 220 × $0.36 = $79.20.
Pre-GST = $87.36 + $142.00 + $79.20 = $308.56.
GST-inclusive = $308.56 × 1.10 = $339.42 (to nearest cent).

Q4.12 — Student budget

Weekly allowance = $300 × 12 ÷ 52 ≈ $69.23. Total weekly income = $510 + $69.23 = $579.23.
Weekly phone = $44 × 12 ÷ 52 ≈ $10.15. Weekly insurance = $580 ÷ 52 ≈ $11.15.
Total weekly expenses = $205 + $110 + $54 + $10.15 + $11.15 = $390.30.
Weekly surplus = $579.23 − $390.30 = $188.93.
Annual surplus = $188.93 × 52 = $9,824.36.