Mathematics • Year 10 • Unit 1 • Lesson 3
Budgets & GST — Skill Drill
Build fluency with the three tools from Lesson 3: the budget balance (Savings = Income − Expenses), adding 10% GST (× 1.10), and stripping GST from a total (÷ 11). One step at a time — fully worked example, guided practice, then independent problems.
1. I do — fully worked example
Read every line. Each step has a short reason on the right so you can see why, not just what.
Problem. A new phone costs $1,099 including GST. Find the GST amount and the pre-GST (before-tax) price.
Step 1 — Spot the rule.
The shelf price ($1,099) already includes 10% GST → use ÷ 11 to extract the GST portion.
Reason: a GST-inclusive total is 110% of pre-GST. GST as a fraction of total is 10/110 = 1/11.
Step 2 — Divide the total by 11 to get the GST amount.
GST = $1,099 ÷ 11 = $99.91 (to nearest cent)
Reason: division by 11 gives the GST portion of any GST-inclusive total.
Step 3 — Subtract GST from the total to get the pre-GST price.
Pre-GST = $1,099 − $99.91 = $999.09
Reason: total = pre-GST + GST, so pre-GST = total − GST.
Step 4 — Check (alternative method).
Pre-GST = $1,099 ÷ 1.10 = $999.09 ✓
Reason: dividing the total by 1.10 strips off the 10% mark-up. Same answer.
Answer: GST = $99.91, pre-GST price = $999.09.
2. We do — fill in the missing steps
Same structure as Section 1, but with the working faded. Fill in each blank. 4 marks
Problem. Riley earns $2,400 per month. Essential expenses are $1,400 and discretionary expenses are $600. Find Riley's monthly savings and savings percentage.
Step 1 — Spot the rule: Savings = Income − ________________________.
Step 2 — Add the two expense categories:
Total expenses = $1,400 + $______ = $______
Step 3 — Apply the savings formula:
Savings = $2,400 − $______ = $______
Step 4 — Find savings as a percentage of income:
Savings % = $______ ÷ $2,400 × 100 = ______ %
Step 5 — Check against the 50/30/20 rule:
Is ______% close to the 20% savings target? Yes / No (circle one)
3. You do — independent practice
Show your working in the space under each problem. The first four are foundation (single step). The middle two are standard (two steps). The last two are extension (multi-step in syllabus).
Foundation — single step
3.1 A laptop costs $1,320 including GST. Find the GST amount. 1 mark
3.2 A tradesperson quotes $450 plus GST. Find the total amount the customer pays. 1 mark
3.3 A restaurant bill is $88 including GST. How much GST was charged? 1 mark
3.4 Income is $1,800 per month and total expenses are $1,550. Calculate the monthly savings. 1 mark
Standard — combine two steps
3.5 Tahlia earns $3,200 per month. Her essential expenses are $1,950 and discretionary expenses are $850. Calculate her monthly savings and savings percentage. 2 marks
3.6 A tablet is advertised as "$649 plus GST". Find the GST and the GST-inclusive total. 2 marks
Extension — push your thinking
3.7 Apply the 50/30/20 rule to a weekly income of $1,150. Find the dollar amount for needs, wants and savings. 3 marks
3.8 An electrician's invoice shows: parts $220 (pre-GST), labour $480 (pre-GST). Calculate the GST charged and the total amount owing. 2 marks
How did this worksheet feel?
What I'll revisit before next class:
Section 2 — We do (faded Riley's budget)
Step 1: Savings = Income − Total expenses.
Step 2: Total expenses = $1,400 + $600 = $2,000.
Step 3: Savings = $2,400 − $2,000 = $400.
Step 4: Savings % = $400 ÷ $2,400 × 100 = 16.7% (1 dp).
Step 5: No — 16.7% is below the 20% target. Riley is saving less than the rule recommends.
3.1 — Laptop GST
GST = $1,320 ÷ 11 = $120.
3.2 — Tradesperson's total
Total = $450 × 1.10 = $495.
3.3 — Restaurant GST
GST = $88 ÷ 11 = $8.00.
3.4 — Monthly savings
Savings = $1,800 − $1,550 = $250.
3.5 — Tahlia's budget
Total expenses = $1,950 + $850 = $2,800. Savings = $3,200 − $2,800 = $400.
Savings % = $400 ÷ $3,200 × 100 = 12.5%.
Below the 20% target — she could try to cut discretionary expenses.
3.6 — Tablet GST and total
GST = $649 × 0.10 = $64.90.
Total = $649 + $64.90 = $713.90 (or $649 × 1.10).
3.7 — 50/30/20 rule on $1,150
Needs (50%) = 0.50 × $1,150 = $575.
Wants (30%) = 0.30 × $1,150 = $345.
Savings (20%) = 0.20 × $1,150 = $230.
Check: $575 + $345 + $230 = $1,150 ✓.
3.8 — Electrician's invoice
Pre-GST subtotal = $220 + $480 = $700.
GST = $700 × 0.10 = $70.
Total owing = $700 + $70 = $770 (or $700 × 1.10).