Starter Francesca used to earn £350 per week. Her pay rises to £363.13. Frank used to earn £320. His pay rises to £332.80. Who has had the greatest percentage increase? A car costs £9750 when new. 5 years later it is sold for £4500. What is the average percentage decrease each year?

Reverse Percentages 18/10/2019 Recognise when a question requires reverse percentage method (rise and fall) Use a reverse percentage method to find original price without a calculator Use a reverse percentage method to find original price with a calculator

Reverse Percentages (Non Calc) Examples Steve paid £54 for a pair of trainers that had been reduced by 40% in a sale. What was the original price? Joanne paid £63 for a hotel room which was 10% cheaper than the normal price. What was the normal price? 60% = £54 ÷ 6 ÷6 10% = £9 x 100 100% = £90 x 100

Reverse Percentages (Non Calc) Examples Chloe’s shopping cost £96. This was 20% more expensive than last week. How much did she spend last week? Darnell paid £66 for a train ticket this year. The price had risen by 10% from last year. What was the cost last year? 110% = £66 ÷ 11 ÷11 10% = £6 x 100 100% = £60 x 100

Practice: Non calculator Pablo paid £81 for a family ticket at Drayton Manor, which gave him 10% off the full price. What is the full price? A farmer notices the number of chickens born this year has risen by 20% to 360. How many were born last year? 90% = £81 10% = £9 100% = £90 120% = 360 10% = 30 100% = 300 Kat has noticed that the number of cars parked on her street has risen by 20% to 48. How many cars were parked on her street before? Louisa paid £120 for a prom dress, which had 20% off in a sale. What was the original price? 120% = £48 10% = £4 100% = £40 80% = £120 10% = £15 100% = £150

What’s different about these numbers? JD Sports15% discount Price now £80.75 What’s different about these numbers? Increase of12% to £44.80 Odeon Student 10% discount Price now £6.21 Increase18% to £41.30 Nandos NUS 20% discount Price now: £19.20

Original Amount = 100% value EXAMPLES (a) 85% = £43.90 1% = £0.5165 Jane paid £43.90 for a skirt that had been reduced by 15% in a sale. What was the original price? 85% = £43.90 ÷ 85 ÷ 85 Decrease of 15% 85% value 1% = £0.5165 x 100 x 100 100% = £51.65 Original Price (b) Junior received a 8% pay rise. His new salary is £19200. What was his original salary? 108% = £19200 ÷ 108 ÷ 108 Increase of 8% 108% value 1% = £177.78 x 100 x 100 100% = £17778 Original Salary 7

Find the original price. Be careful with increases and decreases! JD Sports15% discount Price now £80.75 Find the original price. Be careful with increases and decreases! Increase of12% to £44.80 Odeon Student 10% discount Price now £6.21 Increase18% to £41.30 Nandos NUS 20% discount Price now: £19.20

JD Sports 15% discount Price now £80.75 100% – 15% = 85% 85% = £80.75 1% = £0.95 100% = £95.00 CHECK!

112 % = £44.80 1% = £0.40 100% = £40 Increase fare12% to £44.80 CHECK!

Odeon Student 10% discount 100% – 10% = 90% 90% = £6.21 1% = £0.069 100% = £6.90 Odeon Student 10% discount Price now £6.21 CHECK!

Increase 18% to £41.30 118 % = £41.30 1% = £0.35 100% = £35.00 CHECK!

100% – 20% = 80% 80% = £19.20 1% = £0.24 100% = £24.00 Nandos NUS 20% discount Price now: £19.20 CHECK!

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