Mathematics • Year 10 • Unit 1 • Lesson 3
Budgets & GST — Mixed Challenge
Pull together every idea from Lessons 1-3: pay (wages and salaries) feeding into a budget, the 50/30/20 rule, adding GST (× 1.10), and stripping GST (÷ 11). Choose the right tool for each problem, spot someone else's mistake, then design a balanced monthly budget yourself.
1. Mixed problems — choose the right tool
Each question uses a different idea from Lessons 1-3. Decide which formula applies before you start writing. Show your working. 3 marks each
1.1 A washing machine is priced at $935 including GST. Find the GST amount and the pre-GST price.
1.2 A graphic designer quotes a logo job at $1,250 plus GST. Find the GST-inclusive total.
1.3 A student earns $720 per month from a part-time job. Apply the 50/30/20 rule to find the dollar amounts for needs, wants and savings.
1.4 A worker has monthly income of $4,200 and spends $1,820 on needs and $1,540 on wants. Calculate the savings and savings percentage. State whether they meet the 20% target.
1.5 A tradie's invoice shows: total $2,640 including GST. The customer wants to know the pre-GST labour and the GST separately. Calculate both.
1.6 Marcus has an annual salary of $78,400 and monthly expenses of $5,200 (all-inclusive). Convert the salary to a monthly figure (Lesson 1), then calculate monthly savings and savings percentage.
2. Find the mistake
Another student has tried to find the GST charged on a $209 (GST-inclusive) Bluetooth speaker, and to write the speaker's pre-GST price. Their working is shown below. Exactly one line contains a mistake. Spot it, explain why it's wrong, then re-do the working correctly. 3 marks
Student's working — GST and pre-GST price for a $209 speaker:
Line 1: "$209 already includes 10% GST."
Line 2: GST = $209 × 0.10 = $20.90
Line 3: Pre-GST = $209 − $20.90 = $188.10
Line 4: Check: $188.10 × 1.10 = $206.91 ≈ $209 (close enough).
(a) Which line contains the mistake?
(b) Explain in one or two sentences why that line is wrong.
(c) Write out the corrected working in full, including the corrected GST and pre-GST values.
Stuck? The check in Line 4 should equal exactly $209 — the fact that it doesn't is a clue. Look at the operation in Line 2.3. Open-ended challenge — design your own monthly budget
This question has many valid answers. Be realistic, but show every number. 4 marks
3.1 Imagine you have just landed your first full-time job after Year 12. Your monthly take-home pay is $3,400. Design a monthly budget that satisfies all the following:
- Lists at least five categories (e.g. rent share, groceries, transport, phone, subscriptions, dining out, savings, etc.).
- Allocates between 45% and 55% of income to needs (essentials).
- Allocates between 25% and 35% of income to wants (discretionary).
- Saves at least 15% of income.
- All categories together must sum to exactly $3,400.
Present your budget as a table or list showing the category, the dollar amount, and the percentage of income.
How did this worksheet feel?
What I'll revisit before next class:
1.1 — Washing machine
GST = $935 ÷ 11 = $85. Pre-GST = $935 − $85 = $850 (or $935 ÷ 1.10).
1.2 — Graphic design quote
Total = $1,250 × 1.10 = $1,375.
1.3 — 50/30/20 on $720
Needs (50%) = $360. Wants (30%) = $216. Savings (20%) = $144. Check: $360 + $216 + $144 = $720 ✓.
1.4 — Savings check
Total expenses = $1,820 + $1,540 = $3,360. Savings = $4,200 − $3,360 = $840.
Savings % = $840 ÷ $4,200 × 100 = 20%. Yes, they exactly meet the 20% target.
1.5 — Pre-GST labour from total
GST = $2,640 ÷ 11 = $240. Pre-GST labour = $2,640 − $240 = $2,400 (or $2,640 ÷ 1.10).
1.6 — Marcus's monthly savings
Monthly salary = $78,400 ÷ 12 = $6,533.33 (Lesson 1).
Savings = $6,533.33 − $5,200 = $1,333.33.
Savings % = $1,333.33 ÷ $6,533.33 × 100 ≈ 20.4%. Just above the 20% target.
2 — Find the mistake
(a) The mistake is on Line 2.
(b) The student multiplied the GST-inclusive total by 0.10, but that gives 10% of an already-tax-inclusive figure. GST is 10% of the pre-GST price, which equals 1/11 of the inclusive total — so the correct operation is $209 ÷ 11.
(c) Corrected working:
Line 2 corrected: GST = $209 ÷ 11 = $19.00.
Line 3 corrected: Pre-GST = $209 − $19 = $190.00.
Line 4 check: $190 × 1.10 = $209 exactly ✓.
The student's check in Line 4 failed (got $206.91 not $209) — that mismatch was a clue something was wrong earlier.
3 — Open-ended challenge (sample budget)
Sample monthly budget — total income $3,400
Needs ($1,700 = 50%)
- Rent share: $1,100 (32.4%)
- Groceries: $400 (11.8%)
- Transport (Opal + petrol): $200 (5.9%)
Wants ($1,020 = 30%)
- Phone & data: $80 (2.4%)
- Streaming (Netflix + Spotify): $40 (1.2%)
- Dining out and coffee: $300 (8.8%)
- Gym membership: $80 (2.4%)
- Clothes & entertainment: $520 (15.3%)
Savings ($680 = 20%)
- Emergency fund: $400 (11.8%)
- Holiday fund: $280 (8.2%)
Check: $1,700 + $1,020 + $680 = $3,400 ✓.
Needs 50% (within 45-55%) ✓. Wants 30% (within 25-35%) ✓. Savings 20% (≥ 15%) ✓.
Marking: 1 for ≥ 5 categories with realistic amounts; 1 for needs in range; 1 for wants in range and savings ≥ 15%; 1 for amounts summing exactly to $3,400 with clear percentage column. Many valid budgets exist — the marker rewards realism and arithmetic accuracy, not a specific category mix.