Mathematics • Year 10 • Unit 1 • Lesson 4
Discounts, Mark-ups & Best Buys, Skill Drill
Build fluency with the three retail tools from Lesson 4: single discount (Sale = Original × (1 − d)), mark-up (Selling = Cost × (1 + m)), and unit price (Total ÷ Quantity). 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 pair of running shoes originally costs $180. During a sale they are reduced by 25%. Find the sale price.
Step 1, Spot the rule.
A percentage off the original price → discount formula.
Reason: Sale Price = Original Price × (1 − discount as decimal). Or work out the discount amount and subtract.
Step 2, Convert the discount to a decimal.
25% = 25 ÷ 100 = 0.25
Reason: always work with decimals, not raw percentages, in the formula.
Step 3, Find the multiplier "what's left after the discount".
Remaining fraction = 1 − 0.25 = 0.75
Reason: if you take off 25%, then 75% remains. That's your multiplier.
Step 4, Multiply the original price by the remaining fraction.
Sale price = $180 × 0.75 = $135
Reason: this is the "one-step shortcut" instead of finding the discount and subtracting.
Step 5, Check by computing the discount amount and subtracting.
Discount = $180 × 0.25 = $45. Sale = $180 − $45 = $135 ✓
Reason: same answer, confirms our shortcut is right.
Answer: The sale price is $135.00.
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. Cereal A costs $5.40 for 450g. Cereal B costs $7.20 for 600g. Which cereal is the better buy?
Step 1, Spot the rule: different-sized packages → use ________________ price to compare fairly.
Step 2, Convert each weight to "per 100g" units:
A: 450g ÷ 100 = ______ units of 100g
B: 600g ÷ 100 = ______ units of 100g
Step 3, Calculate each unit price (price ÷ quantity in units):
A: $5.40 ÷ ______ = $______ per 100g
B: $7.20 ÷ ______ = $______ per 100g
Step 4, Compare. The better buy is the one with the lower unit price:
Cereal ______ is the better buy (or they are equal if the prices match).
Step 5, State the answer in a sentence:
________________________________________________________
3. You do, independent practice
Show your working in the space under each problem. The first four are foundation (single rule). The middle two are standard (two-step). The last two are extension (multi-step including successive discounts).
Foundation, single rule
3.1 A bike originally costs $480. It is reduced by 15%. Find the sale price. 1 mark
3.2 A shop buys headphones for $45 and marks them up by 80%. Find the selling price. 1 mark
3.3 A 2-litre bottle of detergent costs $8.40. Find the unit price per litre. 1 mark
3.4 A jacket marked $200 has a 35% discount applied. Find the discount amount in dollars. 1 mark
Standard, combine two ideas
3.5 A retailer buys a jacket for $60 and applies a 65% mark-up. Find the selling price. 2 marks
3.6 Detergent X costs $8.40 for 2 litres. Detergent Y costs $11.25 for 2.5 litres. Which is the better buy? 2 marks
Extension, push your thinking
3.7 A television originally priced at $1,200 is reduced by 20%, then a further 15% is taken off the sale price. Find the final price after both discounts. 3 marks
3.8 A retailer buys a phone for $480 cost price and wants a selling price of $720. What percentage mark-up has been applied? 2 marks
Section 2, We do (faded cereal comparison)
Step 1: use unit price.
Step 2: A: 450 ÷ 100 = 4.5 units. B: 600 ÷ 100 = 6 units.
Step 3: A: $5.40 ÷ 4.5 = $1.20 per 100g. B: $7.20 ÷ 6 = $1.20 per 100g.
Step 4: They are equal, neither is a strictly better buy on price alone.
Step 5: "Both cereals cost $1.20 per 100g, so they offer the same value per gram. Choice depends on storage, freshness or preference."
3.1, Bike discount
Sale = $480 × 0.85 = $408.00.
3.2, Headphones mark-up
Selling = $45 × 1.80 = $81.00.
3.3, Detergent unit price
$8.40 ÷ 2 = $4.20 per litre.
3.4, Discount amount
Discount = $200 × 0.35 = $70.
3.5, Jacket mark-up
Selling = $60 × (1 + 0.65) = $60 × 1.65 = $99.00.
3.6, Detergent best buy
X: $8.40 ÷ 2 = $4.20/L. Y: $11.25 ÷ 2.5 = $4.50/L.
Detergent X is the better buy at $4.20/L vs $4.50/L.
3.7, Successive discounts on a TV
After first discount: $1,200 × 0.80 = $960.
After second discount: $960 × 0.85 = $816.00.
Note: a single 35% discount would give $780. Successive discounts are not the same as adding the percentages, confirms the lesson's "Misconceptions" warning.
3.8, Mark-up percentage from prices
Mark-up amount = $720 − $480 = $240.
Mark-up % = ($240 ÷ $480) × 100 = 50%.
Check: $480 × 1.50 = $720 ✓.