Grow your brain N4 Numeracy Book 4 The wee Maths Book of Big Brain Growth Guaranteed to make your brain grow, just add some effort and hard work Don t be afraid if you don t know how to do it, yet! It s not how fast you finish, but that you finish. It s always better to try something than to try nothing. Don t be worried about getting it wrong, getting it wrong is just part of the process known better as learning. Foreign Exchange and Ratio
I Foreign Exchange I1 I can convert between currencies, in both directions, in a problem solving context For the following questions use this table of exchange rates, unless instructed otherwise in the question, which gives the amount of each currency you will receive in exchange for 1. Country Currency Rate per USA Dollars ($) $1.55 JAPAN Yen ( ) 184 EUROZONE Euros( ) 1.40 CZECH REPUBLIC Korona (K) 36.25 K ICELAND Kroner (k) 196 k SWITZERLAND Francs (f) 1.45 f INDIA Rupees (r) 98 r CANADA Dollars ($) $1 95 SOUTH AFRICA Rand (R) 18 75 R 1. Maria and Vicki are going on a school trip to Europe. Maria has saved 110 spending money and Vicki has saved 94. How much will they each get when they change their money into Euros? Page 2
2. Martin is travelling to America on a business trip. He changes 550 into dollars before he goes. (a) How many dollars does he receive? (b) If he spends $800 how many dollars will he have left? 3. Carol is going on holiday to Japan with her parents. She takes 75 of her savings to the bank to change into yen. (a) How many yen does she receive? (b) At the end of her holiday she has 1420 yen left. How many yen did she spend? 4. Jean-Pierre is visiting some friends in England. He bought some presents in Geneva before he left home. The presents are shown below. Swiss cheese 13 57 f French wine 20 93 f Chocolate 55 66 f How much did each item cost in pounds? Page 3
5. Ben has been on holiday in India. He comes home with 945 rupees. How much is this in pounds? 6. John and Graeme are off on a camping holiday to Switzerland. John has 750 spending money and Graeme has 680. (a) They changed their spending money into Swiss francs. How many francs did each receive? (b) John returned home with 217.50 francs and Graeme with 79.75 francs. How much did each boy spend in pounds? 7. Soraya changes 245 into Rand for a visit to South Africa. (a) How many Rand does she receive? (b) She spends 3344 Rand. How much does she have left? (c) When she returns home she exchanges her Rand back into pounds. How many pounds will she get back? Page 4
8. Kelbay has 300 spending money for her trip to Rome. She wants to return with at least a quarter of it left. She returns with 84 euros which she changes back to British pounds at an exchange rate of 1 = 1 20 euros. Did she spend more than she had hoped? You must show working and give a reason for your answer. 9. On the first weekend that the film Slumdog Millionaire was released in USA the box office takings amounted to 1 570 260 US dollars. In the UK the same film took 1 827 457 on the first weekend of release. How much more was taken in the UK than in the USA? Give your answer in pounds. [Exchange rate at the time: 1 = $1.25] 10. Christine is driving to France on holiday and arrives at the ferry port with not a lot of petrol left in her car. She decides she needs to buy petrol either here in the UK or immediately on her arrival in France. She knows that the cost of a litre of petrol next to the ferry port is 138.5p and the cost of a litre of petrol in France is 1.54 Euros. She intends to buy 40 litres of petrol. If the exchange rate is her petrol? 1 1.25 Euros, where should Christine buy Page 5
J Ratio J1 I understand how to express a ratio and can simplify ratios 1. Write these ratios in their simplest form. (a) 3 : 6 (b) 15 : 5 (c) 12 : 36 (d) 16 : 56 (e) 20 : 44 (f) 18 : 81 (g) 5 : 10 (h) 12 : 18 (i) 26 : 52 (j) 21 : 28 (k) 15 : 55 (l) 24 : 56 2. Write the number which should replace the. (a) 3 : 6 = 12 : (b) : 5 = 30 : 10 (c) 18 : 4 = : 2 (d) 3 : 5 = 15 : (e) 1 : 6 = : 18 (f) 5 : 13 = : 26 (g) 5 : = 30 : 6 (h) : 9 = 6 : 27 (i) 2 : 17 = 4 : (j) 23 : 7 = : 14 (k) 150 : 50 = 15 : (l) 7 : = 49 : 70 Page 6
J2 I can distribute a total amount in a given ratio 3. Larry works with the council. Last week his duties were split between photocopying and working on reception in the ratio of 3:4. If Larry worked for 35 hours last week how much time did he spend on photocopying? 4. Scotia High has its own school flag. The ratio of the length to the breadth of a flag is 3:2. If the Scotia High flag has a perimeter of 4m, what is the length of the flag? 5. Eva works with her dad. Last week her duties were split between office work and deliveries in the ratio of 3:5. If Eva worked for 40 hours last week, how much time was spent on office work? 6. Aamir splits his pocket money between spending and saving in the ratio of 4:1. If his pocket money last week was 7 50 how much did he save? Page 7
7. Linzi knows that to make a good mortar for bricklaying she should mix the cement and sand in a ratio of 1:3 cement to sand. If Linzi follows this rule how much cement does she need for 2 kilograms of mortar? 8. Joan s recipe mixes flour and sugar in the ratio of 3:2. How many grams of flour are required for 100 grams of this mixture? 9. Ben makes purple paint from mixing blue and red in the ratio of 3:2. To stick to this ratio what volume of blue paint does he require to make 30 ml of purple paint? 10. Scotia High School distributes its charity money between three charities in the ratio of 2:3:4. This year the school raised a total of 450. How much did it give to each charity? Page 8
J3 I can solve problems that involve ratio 11. A coffee shop blends its own coffee and sells it in one-kilogram bags. One blend consists of two kinds of coffee, Brazilian and Columbian, in the ration 2:3. The shop has 20 kilograms of Brazilian and 25 kilograms of Columbian in stock. What is the maximum number of one-kilogram bags of this blend which can be made? 12. To make 14 carat gold, copper and pure gold are mixed in the ratio 5:7. A jeweller has 160 grams of copper and 245 grams of pure gold. What is the maximum weight of 14 carat gold that the jeweller can make? 13. School theatre visits are arranged for parents, teachers and pupils. The ration of parents to teachers to pupils must be 1:3:15. (a) 45 pupils want to go to the theatre. How many teachers must accompany them? (b) The theatre gives the school 100 tickets for a play. What is the maximum number of pupils who can go to the play? Page 9