Mathematics • Year 8 • Unit 1 • Lesson 19
Multi-Step Financial Problems
Combine markups, discounts, GST and ratio splits into one calculation using multipliers. One worked example, one guided example with blanks, then eight independent problems from single markups to chained discounts.
1. I do — fully worked example
Multi-step problems are best solved with MULTIPLIERS, not by repeatedly working out "10% of …" and adding or subtracting.
Problem. A retailer buys stock for $600. They mark it up 40%, then offer loyalty members a 10% discount. What does a loyalty member pay?
Step 1 — Turn the markup into a multiplier.
+40% means × 1.40 (the original 100% PLUS 40%)
Reason: a 40% markup keeps the original $600 AND adds 40% on top — the multiplier is 1 + 0.40 = 1.40.
Step 2 — Apply the markup.
$600 × 1.40 = $840 (the retail price)
Reason: this is what a NON-loyalty customer would pay.
Step 3 — Turn the discount into a multiplier.
−10% off means × 0.90 (the original 100% MINUS 10%)
Reason: a 10% discount keeps 90% of the price — the multiplier is 1 − 0.10 = 0.90.
Step 4 — Apply the discount to the retail price.
$840 × 0.90 = $756
Reason: discount is taken off the RETAIL price, not the cost price.
Step 5 — Combined check.
600 × 1.40 × 0.90 = 600 × 1.26 = $756 ✓
Reason: you can also multiply both multipliers together first (1.26) and apply once.
Answer: Loyalty members pay $756.
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. An item costs $100. Apply +25% markup, then 20% off the retail price.
Step 1 — Markup multiplier: +25% means × ______
Step 2 — Apply markup:
$100 × ______ = $______ (retail price)
Step 3 — Discount multiplier: −20% means × ______
Step 4 — Apply discount:
$______ × ______ = $______ (sale price)
Combined check:
100 × ______ × ______ = $______
3. You do — independent practice
Show your working. The first four are foundation (single markup, discount or GST). The middle two are standard (two-step chains). The last two are extension (three-step chains or ratio splits with GST).
Foundation — single step
3.1 A $200 item is marked up 20%. New price? 1 mark
3.2 A $150 jacket is on sale at 30% off. Sale price? 1 mark
3.3 A $50 (exc-GST) book has 10% GST added at the till. Final price? 1 mark
3.4 A $220 inc-GST item. How much GST is in the price? (Hint: GST is 1/11 of the inc-GST total.) 1 mark
Standard — two-step chains
3.5 A $100 item gets +20% markup, then 20% off. Final price. (Tip: it is NOT $100!) 2 marks
3.6 A $50 item has +50% markup, then 20% off. Show your working using multipliers. 2 marks
Extension — three-step chains and ratio splits
3.7 A retailer buys a jacket at $80 cost. They mark up 75% for retail, then run a 30% sale, then add 10% GST. Find the customer's final price. 2 marks
3.8 A $240 restaurant bill (inc-GST) is split among 4 friends in the ratio 1 : 2 : 2 : 3. (a) How much GST is in the bill (= 1/11 of $240)? (b) How much does each friend pay? 2 marks
How did this worksheet feel?
What I'll revisit before next class:
Section 2 — We do (faded $100, +25% then −20%)
Step 1: +25% → × 1.25.
Step 2: $100 × 1.25 = $125.
Step 3: −20% → × 0.80.
Step 4: $125 × 0.80 = $100.
Combined check: 100 × 1.25 × 0.80 = $100.
3.1 — $200 + 20%
$200 × 1.20 = $240.
3.2 — $150 jacket, 30% off
$150 × 0.70 = $105.
3.3 — $50 + 10% GST
$50 × 1.10 = $55.
3.4 — $220 inc-GST, find the GST
GST = $220 ÷ 11 = $20.
3.5 — $100, +20% then −20%
$100 × 1.20 × 0.80 = $100 × 0.96 = $96. (NOT $100 — the discount is taken off the LARGER marked-up price.)
3.6 — $50, +50% then −20%
$50 × 1.50 × 0.80 = $50 × 1.20 = $60.
3.7 — $80 jacket, +75%, −30%, +10% GST
$80 × 1.75 × 0.70 × 1.10. Step by step: $80 × 1.75 = $140; $140 × 0.70 = $98; $98 × 1.10 = $107.80.
3.8 — $240 bill in 1 : 2 : 2 : 3
(a) GST = $240 ÷ 11 = $21.82 (to nearest cent).
(b) Total parts = 1 + 2 + 2 + 3 = 8. 1 part = $240 ÷ 8 = $30. Shares: $30, $60, $60, $90. Check: 30 + 60 + 60 + 90 = $240 ✓.