T Madas T Madas Marcus bought a shirt

Marcus bought a shirt and a pair of trousers in the July sales. The shirt costs normally £ 18 but it was 20% off in the sales. The trousers cost normally £ 25 but it was 10% off in the sales. How much did he have to pay for the two items? 10% of £ 18 is £ 1. 80 20% of £ 18 is £ 3. 60 10% of £ 25 is £ 2. 50 £ 18 – £ 3. 60 = £ 14. 40 £ 25 – £ 2. 50 = £ 22. 50 14. 40 + 22. 50 £ 36. 90 © T Madas

Ann is a gorilla that weighs 185 kg. Her mate, Ben weighs 18% more than Ann. How many kg does Ben weigh? Ann Find 18% of 185 Ben 185 ÷ 100 = 1. 85 x 18 = 33. 3 185 kg 185 + 33. 3 = 218. 3 kg +18% © T Madas

600 people were asked for their preferred take-away food. The results were summarised in a table: Food 1. 2. Percentage Decimal Fraction Pizza 45% 0. 45 Chinese 22% 0. 22 Indian 8% 0. 08 Other 25% 0. 25 45 9 = 100 20 22 11 100 = 50 8 2 = 100 25 25 1 = 100 4 Complete the table. Work out how many people preferred an Indian take-away. 8% 8 out of 100 16 out of 200 24 out of 300. . . . 48 out of 600 © T Madas

A student achieved 53 marks on an A-Level paper in Mathematics, which is marked out of 75 marks. What was the percentage mark of this student? x 100 ta ge en rc ec D Pe im al Pa rt al on ti ac Fr in Pa w rt or ds Pa rt 53 = 53 ÷ 75 ≈ 0. 7067 = 70. 67% 75 53 out of 75 © T Madas

The Northgate School has 1750 students and 408 of them belong to the Sixth Form. What percentage of Northgate students are Sixth Formers? x 100 ta ge en rc Pe im ec D ac ti on al al Pa Pa rt rt 408 = 408 ÷ 1750 ≈ 0. 2331 = 23. 31% 1750 Fr in Pa w rt or ds 408 out of 1750 © T Madas

Bethany got 56 marks out of 70 marks in the recent Maths test. What was her percentage mark? ÷ 7 56 out of 70 x 10 56 8 80 = = = 80% 70÷ 7 10 x 10 100 © T Madas

Martina hit 51 out of the 60 targets in a riffle shooting competition. What was her percentage success rate? ÷ 3 51 out of 60 x 5 51 = 17 = 85 60÷ 3 20 x 5 100 = 85% © T Madas

Which out of: … 20% of £ 150 or 150% of £ 20 … … is the largest? 20% of £ 150: £ 15 x 2 = £ 30 150% of £ 20: £ 20 + £ 10 = £ 30 100% 50% © T Madas

Jacob got a student loan of £ 800, and he spent £ 240 of that amount on a new game console. What percentage of his loan did he spend on the console? ÷ 8 240 out of 800 240 = 30% 800÷ 8 100 ÷ 10 240 out of 800 ÷ 4 x 5 240 24 6 30 = = 30% 800÷ 10 80 ÷ 4 20 x 5 100 © T Madas

In Café-Luca a cup of coffee costs £ 1. 60. The diagram below shows how this cost is distributed, among different people. Work out what percentage of the cost of a cup of a coffee goes to the retailer. other 40 p retailer 64 p wholesaler 28 p processor 20 p grower 8 p ÷ 8 64 out of 160 x 5 64 8 40 = = = 40% 160÷ 8 20 x 5 100 © T Madas

The table below shows which foreign language did pupils prefer to learn. ch n e 1. Which language did 10% of the girls prefer? Fr n a m 2. Which language did 45% of the boys prefer? Ger an i l a 3. Which language was equally preferred by boys and girls? It Language Boys Girls French 3 15% 1 10% German 9 45% 3 30% Italian 4 20% 2 20% Spanish 4 20% 4 40% TOTAL 20 10 x 10 1 10 = 10% x 10 100 x 5 3 20 = 15% x 5 100 x 5 9 20 = 45% x 5 100 x 5 4 20 = 20% x 5 100 © T Madas

Riaz got the following marks in his end of year exams: • English: 37 50 • Science: 17 25 • Maths: 17 20 • History: 21 30 Change these marks into percentages English: x 2 37 50 = 74% x 2 Science: x 4 17 25 = x 4 100 68 = 68% 100 x 5 Maths: 17 = 85% 20 x 5 Science: 100 ÷ 3 x 10 21 7 = 30 10 = 70% 100 © T Madas

Eve asked some students in her school whether they own an i. Pod, and presented her results in the table below: Number of Students % of Students Yes 60 30% No 154 70% These figures cannot be correct. If the mistake is in the number of students, complete the following 2 tables of information. Number of Students % of Students Yes 60 30% No 140 70% Number of Students % of Students Yes 66 30% No 154 70% 60 : 30% 20 : 10% 140 : 70% 154 : 70% 22 : 10% 66 : 30% © T Madas

Jon asked some students in his school whether they own an i. Pod, and presented his results in the table below: Number of Students % of Students Yes 80 30% No 170 70% These figures cannot be correct. If the mistake is in the percentages, complete the following table of information. Number of Students % of Students Yes 80 32% No 170 68% ÷ 10 80 out of 250 x 4 80 8 32 = = = 32% 250÷ 10 25 x 4 100 © T Madas

Look at the table of information about A level passes in 2006. Number of students Percentage gained grade A English Mathematics 84000 48000 27% 35% How many more students gained grade A in English than in Maths? 84000 ÷ 100 = 840 x 27 = 22680 48000 ÷ 100 = 480 x 35 = 16800 or in fraction notation 84000 x 27 = 22680 100 48000 x 35 = 16800 100 5880 22680 – 16800 = 5880 © T Madas

The table below shows the Average Hourly Rate of Pay (AHRP) for men and women in 1955 and 2005. 1. 2. 1955 2005 Women £ 0. 14 £ 10. 91 Men £ 0. 31 £ 13. 50 For 1955, calculate the AHRP for women as a percentage of the AHRP for men. Show by calculation that the AHRP for women is a greater proportion of the AHRP for men in 2005 1955 0. 14 0. 452 = 45. 2% ≈ 0. 31 1955 10. 14 0. 751 = 75. 1% ≈ 13. 50 In 1955 women earned on average 45% of what men earned In 2005 women earn on average 75% of what men earn © T Madas

The table below shows the daily sales in a flower stall. Flower Roses Carnations Tulips Orchids Lilies TOTAL Number 155 95 75 40 50 415 Takings £ 46. 50 £ 38. 00 £ 26. 25 £ 34. 00 1. 2. 3. £ 37. 50 £ 182. 25 Work out the least and the most expensive flower. What percentage of the total number of flowers were roses? What percentage of the total takings were from lilies? Roses: 46. 50 ÷ Carnations: 38 ÷ Tulips: 26. 25 ÷ Orchids: 34 ÷ Lilies: 37. 50 ÷ 155 95 75 40 50 = = = £ 0. 30 £ 0. 40 £ 0. 35 £ 0. 85 £ 0. 75 Roses are the least expensive at 30 pence each Orchids are the most expensive at 85 pence each © T Madas

The table below shows the daily sales in a flower stall. Flower Roses Carnations Tulips Orchids Lilies TOTAL Number 155 95 75 40 50 415 Takings £ 46. 50 £ 38. 00 £ 26. 25 £ 34. 00 1. 2. 3. £ 37. 50 £ 182. 25 Work out the least and the most expensive flower. What percentage of the total number of flowers were roses? What percentage of the total takings were from lilies? 155 0. 373 = 37. 3% ≈ 415 37. 5 ≈ 0. 206 = 20. 6% 182. 25 © T Madas

Albert and Bernard are the two pet dogs shown. Albert weighs 32 kg and Bernard weighs 50 kg. 1. Express the weight of Albert as a percentage of the weight of Bernard. 2. How many times bigger is Bernard than Albert? Albert 32 kg Bernard 50 kg Albert’s weight 64 32 = 64% = = Bernard’s weight 100 50 Albert’s weight is 64% of Bernard’s weight 50 = Albert’s weight 32 = 1. 5625 Bernard is 1. 5625 times bigger than Albert © T Madas

What is 12. 5% of 48% as a percentage? Finding something of something always means multiplication © T Madas

What is 12. 5% of 48% as a percentage? method 1 12. 5 100 x 48 600 6 = = = 6% 10000 100 method 2 12. 5% = 0. 125 48% = 0. 48 0. 125 x 0. 48 = 0. 06 = 6% method 3 50% = ½ 25% = ¼ 12. 5% = ⅛ Finding 12. 5% of 48% … … is the same as finding ⅛ of 48% … … i. e. 6% © T Madas

Match with an arrow each statement to a calculation. For each of the calculations that you did not pick, write a statement involving percentages about what it could possibly represent. a 85 x 0. 93 Find 7% of 85 b 85 x 1. 07 Increase 85 by 7% c 85 x 0. 07 Decrease 85 by 7% d 85 x 0. 7 e 85 x 1. 7 d 85 x 0. 7 Find 70% of 85 e 85 x 1. 7 Find 170% of 85 Decrease 85 by 30% Increase 85 by 70% © T Madas

A computer sales assistant earns a commission of 2. 5% on the sales that she makes. One week her commission was £ 185. What was the value of the computer goods that she sold? Method 1 2. 5% = £ 185 1% = £ 185 ÷ 2. 5 = £ 74 100% = £ 37 x 100 = £ 7400 Method 2 x 7400 x 0. 025 185 ÷ 0. 025 © T Madas

A wine merchant buys a case of 12 bottles of wine for £ 30. He sells each bottle of wine for £ 4. What is the percentage profit for this transaction? Method 1 £ 30 ÷ 12 = £ 2. 50 purchase cost: £ 2. 50 Sale price: £ 4 Profit: £ 1. 50 Actual profit 15 3 1. 5 Fractional profit = = = 0. 6 Original amount 2. 5 25 5 Percentage profit = 60% © T Madas

A wine merchant buys a case of 12 bottles of wine for £ 30. He sells each bottle of wine for £ 4. What is the percentage profit for this transaction? Method 2 £ 4 x 12 = £ 48 purchase cost: £ 30 Sale price: £ 48 Profit: £ 18 Actual profit 3 18 Fractional profit = = 0. 6 Original amount 5 30 Percentage profit = 60% © T Madas

An electrical retailer buys a steam iron for £ 16 and sells it on for £ 28. Find the percentage profit on this iron. Actual profit 3 12 Fractional profit = = 0. 75 Original amount 4 16 Percentage profit = 75% © T Madas

Beth paid £ 9600 for her car and sold it for £ 7200 two years later. Calculate her percentage loss. 12 Fractional loss = Actual loss 1 2400 = = = 0. 25 Original amount 9600 4 48 Percentage loss = 25% © T Madas

Calculate the percentage saving on this sofa Calculating: % loss % decrease % reduction % saving Same Calculation Actual saving 450 Fractional Saving = = 0. 36 = Original amount 1250 Percentage saving = 36% © T Madas

You can buy a cooker for £ 400 cash or you can pay a 10% deposit and 24 monthly instalments of £ 19. 75. 1. Work out the cost of buying this cooker on credit. 2. The percentage extra you pay on the cash price if you buy this cooker on credit. Deposit: 10% of £ 400 = £ 40 Instalments: 24 x £ 19. 75 = £ 474 £ 514 Calculating: % profit % increase % extra Same Calculation © T Madas

You can buy a cooker for £ 400 cash or you can pay a 10% deposit and 24 monthly instalments of £ 19. 75. 1. Work out the cost of buying this cooker on credit. 2. The percentage extra you pay on the cash price if you buy this cooker on credit. Deposit: 10% of £ 400 = £ 40 Instalments: 24 x £ 19. 75 = £ 474 £ 514 Extra Amount 114 Fractional Extra = = 0. 285 = 400 Original amount Percentage Extra = 28. 5% © T Madas

A certain brand of corn flakes is sold in boxes that weigh 375 grams. A promotional pack of 450 grams is to be produced in order to boost sales. This is indicated by a sticker on the box that states: … % extra for free. What percentage do you get for free according to the sticker? standard size: 375 promotional size: 450 increase: 75 Actual increase 1 75 Fractional increase = = 0. 2 Original amount 375 5 Percentage increase = 20% © T Madas

A flat was bought for £ 120000. A year later its value increased by 20%. The following year its value decreased by 12. 5% What is its current value? What was its percentage increase/decrease calculated over the last 2 years? 120000 x 1. 2 = 144000 Value after 1 year: Value after 2 years: 144000 x 0. 875 = 126000 [120000 x 1. 2 x 0. 875 = 126000] © T Madas

A flat was bought for £ 120000. A year later its value increased by 20%. The following year its value decreased by 12. 5% What is its current value? What was its percentage increase/decrease calculated over the last 2 years? 120000 x 1. 2 = 144000 Value after 1 year: Value after 2 years: 144000 x 0. 875 = 126000 – 120000 % increase = x 100 120000 Fractional increase © T Madas

A flat was bought for £ 120000. A year later its value increased by 20%. The following year its value decreased by 12. 5% What is its current value? What was its percentage increase/decrease calculated over the last 2 years? 120000 x 1. 2 = 144000 Value after 1 year: Value after 2 years: 144000 x 0. 875 = 126000 – 120000 x 100 % increase = x 100 = 120000 = 60 12 = 5% © T Madas

The exchange rate between Sterling and Euros in 2002 was: £ 1 = € 1. 60 The value of sterling has now decreased from € 1. 60 to € 1. 52 Calculate the percentage decrease. Initial rate: 1. 60 Final rate: 1. 52 % decrease = Actual decrease x 100 Original amount 1. 60 – 1. 52 % decrease = 1. 60 0. 08 x 100 = 1. 60 Fractional increase 8 = 160 1 = 20 = 5% © T Madas

How much more does £ 1000 invested at 10% compound interest for 10 years gain than £ 1000 invested at 10% simple interest? Simple interest: 10% of 1000 is £ 100 10 years earning £ 100 per year gains £ 1000 The investment doubles to £ 2000 Compound interest: 1000 x (1. 1)10 = 2593. 74 an extra £ 593. 74 © T Madas

How many years will it take £ 100 to double in value when invested at: 1. 5% simple interest 2. 5% compound interest Simple interest: 5% of 100 is £ 5 Every year £ 5 is earned For the investment to double another £ 100 must be gained 100 ÷ 5 = 20 years © T Madas

How many years will it take £ 100 to double in value when invested at: 1. 5% simple interest 2. 5% compound interest Compound interest: In order for the £ 100 to double the investment must be worth £ 200 in n number of years n 100 x ( 1. 05 ) = 200 This is an equation which requires logarithms to solve We are going to use trial and improvement © T Madas

How many years will it take £ 100 to double in value when invested at: 1. 5% simple interest 2. 5% compound interest Compound interest: In order for the £ 100 to double the investment must be worth £ 200 in n number of years n 100 x ( 1. 05 ) = 200 n = 15 n = 14 100 x (1. 05 )10 = 162. 89 100 x (1. 05 )15 = 207. 89 100 x (1. 05 )14 = 197. 99 Is the correct answer 14 or 15 years? © T Madas

A factory bought a new piece of machinery for £ 80000. The machinery depreciates at the rate of 10% per annum. 1. Calculate the value of the machinery after 6 years. 2. After how many years will this piece of machinery be worth less than £ 8000? Original value 80000 x (0. 9)6 years depreciation as a % multiplier © T Madas

A factory bought a new piece of machinery for £ 80000. The machinery depreciates at the rate of 10% per annum. 1. Calculate the value of the machinery after 6 years. 2. After how many years will this piece of machinery be worth less than £ 8000? 80000 x (0. 9)6 © T Madas

A factory bought a new piece of machinery for £ 80000. The machinery depreciates at the rate of 10% per annum. 1. Calculate the value of the machinery after 6 years. 2. After how many years will this piece of machinery be worth less than £ 8000? 80000 x (0. 9)6 = £ 42515. 28 n = 10 80000 x (0. 9) 10 ≈ £ 27894. 28 n = 15 80000 x (0. 9) 15 ≈ £ 16471. 29 n = 20 80000 x (0. 9) 20 ≈ £ 9726. 13 n = 21 80000 x (0. 9) 21 ≈ £ 8753. 52 n = 22 80000 x (0. 9) 22 ≈ £ 7878. 17 © T Madas