Discounts and Sale Prices

What you will learn

• Find the amount taken off and the sale price.
• Use a multiplier to do it in one step.
• Work backwards to the original price.

Before you start: you should be able to find a percentage of an amount. See Percentages.

The idea

A discount is a percentage taken off a price. With $25\%$ off you pay the other $75\%$.

Two ways to find the sale price

1. Amount off: find the discount and subtract it.
2. Multiplier: multiply the price by the percentage you still pay. A $15\%$ discount means you pay $85\%$, so multiply by $0.85$.

Comparing the prices

A bar chart makes the saving easy to see.

Working backwards

If you know the sale price, divide by the multiplier to find the original. Do not take the percentage off the sale price.

Worked examples

Example 1: Sale price

A jacket costs £$64$ and is reduced by $15\%$.

1. $15\%$ of $64 = 0.15 \times 64 = 9.60$.
2. $64 - 9.60 = 54.40$.
3. Check with a multiplier: $0.85 \times 64 = 54.40$.

Answer: £$54.40$

Example 2: Two discounts

A £$100$ coat is $20\%$ off, then a voucher gives $10\%$ off the new price.

1. After $20\%$ off: $100 \times 0.8 = 80$.
2. After $10\%$ off that: $80 \times 0.9 = 72$.

Answer: £$72$, which is $28\%$ off, not $30\%$.

Example 3: Find the original

A sale price is £$45$ after $25\%$ off. What was the original price?

1. You paid $75\%$, so $0.75 \times \text{original} = 45$.
2. $45 \div 0.75 = 60$.

Answer: £$60$

Watch out: taking $25\%$ off £$45$ gives £$33.75$, which is the wrong way round.

Why it matters

Sales, vouchers and student offers are all percentage discounts. Being able to work out the real price lets you compare deals and spot when “up to $50\%$ off” is not as good as it sounds.