Here is a sign in a shop.
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Is the sign correct? Give a reason for your answer.

The sign is incorrect because percentage discounts cannot be simply added together when they are applied sequentially. The second discount is calculated on the already reduced price, not the original price. Let's test this with an example price of £100. 1. **First discount (20%):** 20% of £100 is £20. The reduced price is £100 - £20 = £80. 2. **Second discount (10%):** This 10% is taken off the *reduced price* of £80. 10% of £80 is £8. The final price is £80 - £8 = £72. 3. **Total Saving:** The total amount saved is £100 - £72 = £28. A saving of £28 on an original price of £100 is a 28% saving. Alternatively, using multipliers: - A 20% discount means you pay 80% (multiplier of 0.8). - A 10% discount means you pay 90% (multiplier of 0.9). - The combined effect is 0.8 × 0.9 = 0.72. - Paying 72% of the original price means a saving of 100% - 72% = 28%. Since 28% is not equal to 30%, the sign is incorrect.