Mathematics • Year 8 • Unit 1 • Lesson 20
Financial Maths — Synthesis and Review
Practise every skill from Unit 1 in one place: FDP conversion, percentage of a quantity, profit/loss, rates, ratios and GST. One worked example, one guided example with blanks, then eight independent problems mixed across the whole unit.
1. I do — fully worked example (multi-skill)
A single problem that uses THREE different skills from the unit: rate calculation, splitting a bill, and finding the GST component.
Problem. Three friends share a cafe order: 3 sandwiches at $8.50 each and 2 coffees at $4.20 each (prices are inc-GST). They split the bill equally. (a) Total bill? (b) Each person's share? (c) How much GST is in the total?
Step 1 — Add the sub-totals (rate × quantity).
3 × $8.50 = $25.50 (sandwiches)
2 × $4.20 = $8.40 (coffees)
Total = $25.50 + $8.40 = $33.90
Reason: each line is a rate (price per item) × quantity.
Step 2 — Split equally between 3 people.
$33.90 ÷ 3 = $11.30 per person
Reason: "equally" means divide by the number of people.
Step 3 — Find the GST hidden in an inc-GST total.
GST = total ÷ 11 = $33.90 ÷ 11 ≈ $3.08
Reason: an inc-GST price is 110% of the pre-GST price, so GST is 10/110 = 1/11 of the inc-GST total.
Answer: Total $33.90; each pays $11.30; GST ≈ $3.08.
2. We do — fill in the missing steps
Same shape as Section 1, but with the working faded. Fill in each blank. 4 marks
Problem. A jacket has cost price $80 and is marked up 40%. Then a 15% discount is offered at the till. (a) Find the final selling price. (b) Find the profit.
Step 1 — Markup multiplier: +40% means × ______
Step 2 — Apply markup:
$80 × ______ = $______ (retail price)
Step 3 — Discount multiplier: −15% means × ______
Step 4 — Apply discount:
$______ × ______ = $______ (final selling price)
Step 5 — Profit:
Profit = Selling price − Cost price = $______ − $80 = $______
3. You do — independent practice (mixed)
Show your working. The first four are foundation (one skill each). The middle two are standard (two skills combined). The last two are extension (three or four skills combined).
Foundation — single skill
3.1 Convert 3/4 to a percentage. 1 mark
3.2 Find 15% of $240. 1 mark
3.3 A 750 g bag of rice costs $3. Find the price per kg (the unit rate). 1 mark
3.4 A $77 inc-GST item — how much GST is in the price? (Use GST = inc-GST ÷ 11.) 1 mark
Standard — two skills combined
3.5 Split $315 in the ratio 4 : 5. Then express the larger share as a percentage of the total. 2 marks
3.6 A car bought for $15 000 is sold for $13 500. (a) Profit or loss in dollars? (b) Express the loss as a percentage of cost price. 2 marks
Extension — three or more skills combined
3.7 A $300 jacket gets a 30% discount, then a further 10% off the sale price. (a) Final price. (b) Total percentage saved on the original $300 price. 2 marks
3.8 Split $420 in the ratio 1 : 2 : 4. (a) Find each share. (b) The middle person uses their share to buy a $132 inc-GST item — how much GST did they pay? (c) How much money does the middle person have left? 2 marks
How did this worksheet feel?
What I'll revisit before next class:
Section 2 — We do (jacket $80, +40% / −15%)
Step 1: +40% → × 1.40.
Step 2: $80 × 1.40 = $112.
Step 3: −15% → × 0.85.
Step 4: $112 × 0.85 = $95.20.
Step 5: Profit = $95.20 − $80 = $15.20.
3.1 — 3/4 to %
3 ÷ 4 = 0.75 = 75%.
3.2 — 15% of $240
0.15 × $240 = $36. (Or: 10% of $240 = $24; 5% = $12; total $36.)
3.3 — $3 for 750 g
750 g = 0.75 kg. Unit rate = $3 ÷ 0.75 = $4 per kg.
3.4 — $77 inc-GST
GST = $77 ÷ 11 = $7.
3.5 — $315 in 4 : 5
Parts = 9; 1 part = $35. Shares: $140 and $175. Larger share = $175. As a % of total: 175/315 × 100 ≈ 55.6% (or exactly 5/9 = 55.6%).
3.6 — $15 000 → $13 500
(a) Loss = $15 000 − $13 500 = $1500 loss.
(b) % loss = 1500/15 000 × 100 = 10%.
3.7 — $300 jacket, −30% then −10%
(a) Final = $300 × 0.70 × 0.90 = $300 × 0.63 = $189.
(b) Total saved = $300 − $189 = $111. As % of $300: 111/300 × 100 = 37% off in total (NOT 40%).
3.8 — $420 in 1 : 2 : 4
(a) Parts = 7; 1 part = $60. Shares: $60, $120, $240. Check: 60 + 120 + 240 = $420 ✓.
(b) Middle person has $120, buys a $132 inc-GST item. Wait — they only have $120! The item is $132 inc-GST = $12 GST. The middle person can't afford it: shortfall is $132 − $120 = $12. (Interpret carefully: they need an extra $12 to buy it.)
(c) If they DID buy it: $120 − $132 = −$12 (overdrawn by $12). Strictly, they have $0 left and owe $12. (Accept either: "can't afford it / short by $12" OR "if they magically can, $0 left and $12 short".)