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📖 Lesson 4 ⏱ ~30 min Year 10 · Unit 1 ⚡ +50 XP

Discounts, Mark-ups and Best Buys

Master the maths of shopping: percentage discounts, selling price mark-ups, and how to use unit pricing to spot the real bargain.

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Core learning
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Worksheet

Worksheet

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Warm-up
Think First
+5 XP each

Q1 · A jacket is priced at $120 with 30% off. What do you think the sale price will be?

Q2 · Two 20% discounts are applied one after another. Do you think this equals a single 40% discount?

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From the lesson
Intentions

Learning Intentions

Know

  • The formulas for percentage discount and percentage mark-up.
  • The method for calculating unit price to compare value.

Understand

  • How successive discounts differ from a single discount of the same total percentage.
  • Why unit pricing is fairer than comparing total package prices.

Can Do

  • Calculate sale prices after single and successive percentage discounts.
  • Compare products using unit pricing and identify the best buy.
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From the lesson
Success Criteria

Success Criteria

  • I can calculate a sale price after a percentage discount.
  • I can calculate the selling price after a percentage mark-up on cost price.
  • I can compare two or more products using unit pricing and justify the best buy.
  • I can identify the difference between a single discount and successive discounts.
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From the lesson
Key Terms

Key Terms

Discount — A reduction in the original price, usually expressed as a percentage.
Mark-up — An increase added to the cost price to determine the selling price.
Cost price — The price a retailer pays to buy an item from a supplier.
Selling price — The price a customer pays, including any mark-up.
Unit price — The price per standard unit (e.g. per 100g, per litre) used to compare value.
Successive discounts — Two or more discounts applied one after another, each to the already reduced price.
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From the lesson
Misconceptions

Common Mistakes to Avoid

Wrong: “Two successive 20% discounts equal a single 40% discount.” A 20% discount followed by another 20% discount on the reduced price gives a total reduction of 36%, not 40%.

Right: After a 20% discount, 80% remains. A second 20% discount takes 20% of that 80%, leaving 64%. The total discount is 36%.

Wrong: “A larger package is always better value.” Without checking the unit price, you cannot assume bigger is cheaper per unit.

Right: Always calculate the price per 100g, per litre, or per item to compare fairly. Australian supermarkets are legally required to display unit prices.

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Concept
Percentage Discounts and Mark-ups
+5 XP

Every time you see a sale sign or a business sets a price, someone has done a percentage calculation. Knowing how these work puts you in control as both a buyer and seller.

A discount reduces the original price. A mark-up increases the cost price to create a selling price. Both use percentage change.

Discount and Mark-up Formulas
$\text{Discount Amount} = \text{Original Price} \times \dfrac{\text{Discount \%}}{100}$
$\text{Sale Price} = \text{Original Price} - \text{Discount Amount}$
$\text{Sale Price} = \text{Original Price} \times \left(1 - \dfrac{\text{Discount \%}}{100}\right)$
$\text{Selling Price} = \text{Cost Price} \times \left(1 + \dfrac{\text{Mark-up \%}}{100}\right)$

When two discounts are applied one after another, we call them successive discounts. Each discount is calculated on the new, already-reduced price.

What to write in your book
  • Discount reduces the original price; mark-up increases the cost price to set a selling price.
  • Sale price = Original price × (1 - discount decimal).
  • Selling price = Cost price × (1 + mark-up decimal).
  • Successive discounts are applied one after another, each on the already reduced price.
A pair of shoes originally costs $180 and is reduced by 25%. What is the sale price?
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From the lesson
Worked Example 1
Worked Example 1 - Calculating a Sale Price
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Given: A pair of running shoes originally costs $\$180$. During a sale they are reduced by $25\%$.
2
Find: The sale price.
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Method: Discount = $180 \times 0.25 = 45$. Sale price = $180 - 45 = 135$. Alternatively: $180 \times 0.75 = 135$.
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Answer: The sale price is $\mathbf{\$135.00}$.
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From the lesson
Worked Example 2
Worked Example 2 - Successive Discounts
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Given: A television is reduced by $20\%$, then a further $15\%$ is taken off the sale price. The original price is $\$1{,}200$.
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Find: The final price.
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Method: After first discount: $1{,}200 \times 0.80 = 960$. After second discount: $960 \times 0.85 = 816$.
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Answer: The final price is $\mathbf{\$816.00}$. Note: a single $35\%$ discount would give $\$780$, which is different.
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From the lesson
Worked Example 3
Worked Example 3 - Mark-up on Cost Price
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Given: A retailer buys a jacket for $\$60$ and applies a $65\%$ mark-up.
2
Find: The selling price.
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Method: Selling price = $60 \times (1 + 0.65) = 60 \times 1.65 = 99$.
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Answer: The selling price is $\mathbf{\$99.00}$.
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Concept
Finding the Best Buy with Unit Pricing
+5 XP

Australian supermarkets must display the unit price on shelf labels. This lets you compare products of different sizes fairly.

Unit price is the cost per standard unit of measurement. Common units include per 100g, per litre, per kilogram, or per item.

Unit Price
$\text{Unit Price} = \dfrac{\text{Total Price}}{\text{Quantity in Standard Units}}$
Heads up

Real-World Anchor: In Australia, the Unit Pricing Code requires large supermarkets to display unit prices. This helps consumers compare a 375g jar of coffee ($12.50) with a 500g jar ($15.00). The unit prices are $3.33/100g and $3.00/100g - the larger jar is better value.

What to write in your book
  • Unit price is the cost per standard unit (e.g. per 100g or per litre).
  • Calculate unit price by dividing total price by quantity in standard units.
  • Australian supermarkets must display unit prices to help compare value.
  • The best buy is the item with the lowest unit price.
Detergent X costs $8.40 for 2 litres. Detergent Y costs $11.25 for 2.5 litres. Which is the better buy?
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From the lesson
Worked Example 4
Worked Example 4 - Comparing Unit Prices
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Given: Cereal A costs $\$5.40$ for 450g. Cereal B costs $\$7.20$ for 600g.
2
Find: Which cereal is the better buy?
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Method: Unit price A = $5.40 / 4.5 = $1.20 per 100g. Unit price B = $7.20 / 6 = $1.20 per 100g.
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Answer: Both cereals cost the same per 100g. The better buy depends on storage space and freshness needs.
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From the lesson
Interactive

Interactive: Discount & Unit Price Calculator

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From the lesson
Practice

Your Turn

Question 1: A bike is reduced by 15% from $480. What is the sale price?

Question 2: A shop buys headphones for $45 and marks them up by 80%. What is the selling price?

Question 3: Detergent X costs $8.40 for 2 litres. Detergent Y costs $11.25 for 2.5 litres. Which is the better buy?

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From the lesson
Revisit

Revisit Your Thinking

Look back at your Think First answer about the $120 jacket with 30% off. Was your initial answer correct? Use the formula to confirm the sale price, and explain why some people mistakenly subtract 30 from 120 instead of calculating 30% of 120.

Reflect
Revisit your thinking
reflect

Earlier you were asked: What was your first thought on this topic?

Now that you've worked through the lesson, write a fuller answer. What changed in your thinking?

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From the lesson
MCQ 1
MCQ2 marks

A sofa originally priced at $850 is reduced by 20%. What is the sale price?

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From the lesson
MCQ 2
MCQ2 marks

A retailer buys a watch for $80 and applies a 75% mark-up. What is the selling price?

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From the lesson
MCQ 3
MCQ2 marks

A dress is reduced by 30%, then by a further 20%. The original price is $200. What is the final price?

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From the lesson
MCQ 4
MCQ2 marks

Shampoo A costs $9.60 for 400mL. Shampoo B costs $13.50 for 600mL. Which is the better buy?

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From the lesson
MCQ 5
MCQ2 marks

If a store offers “Buy 2, get 1 free” on items priced at $15 each, what is the effective discount per item?

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From the lesson
SAQ 1
Short Answer3 marks

A sporting goods store buys tennis racquets for $45 each and applies a 90% mark-up. During a clearance, they reduce the selling price by 30%. Calculate the final price of a racquet.

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From the lesson
SAQ 2
Short Answer4 marks

A shop has two different sized bottles of olive oil. The 500mL bottle costs $6.80. The 750mL bottle costs $9.45.

(a) Calculate the unit price (per 100mL) for each bottle. (2 marks)

(b) Which bottle represents the better value? Justify your answer. (1 mark)

(c) If the 500mL bottle is reduced by 15%, recalculate its unit price and determine if it is now the better buy. (1 mark)

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From the lesson
SAQ 3
Short Answer5 marks

A retail chain purchases winter coats for $120 each. They apply a mark-up of 80% to set the selling price. During an end-of-season sale, all coats are reduced by 25%. A loyalty member receives a further 10% off the sale price.

(a) Calculate the original selling price before any discounts. (1 mark)

(b) Calculate the price after the 25% sale discount. (1 mark)

(c) Calculate the final price a loyalty member pays. (1 mark)

(d) Calculate the total percentage discount from the original selling price to the loyalty price. Give your answer to one decimal place. (2 marks)

R
Recap
Quick Review

Sale price

= Original × (1 - discount decimal)

Selling price

= Cost × (1 + mark-up decimal)

Successive discounts

Multiply remaining fractions, not add percentages

Unit price

= Total price / quantity in standard units

Best buy

The item with the lowest unit price

Mark-up

Added to cost price to create profit

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From the lesson
Real-Life Link

Real-Life Link

Australian consumer law requires supermarkets to display unit prices on shelf labels, making it easy to compare value. Next time you shop at Coles, Woolworths or Aldi, look for the small text showing "$X.XX per 100g". This simple maths skill can save you hundreds of dollars per year. Online retailers like Amazon also use percentage discounts heavily - understanding successive discounts helps you know whether "30% off, then an extra 20% off" is really a 50% saving (it is not).

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From the lesson
Game

Game Time!

Test your discount and unit pricing skills in an interactive challenge.

Play Discount Challenge
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From the lesson
Continue
Continue to Lesson 5: Simple Interest →
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