1 2 Mr Mrs Phillips Carpet Sales

1 2 Mr & Mrs Phillips Carpet Sales A shop increased the price of its carpets by 20%, and sales of the carpets dropped by 20% When Mr and Mrs Phillips married, the sum of their ages was 44. Did the shop’s profits from carpet sales rise or fall? The difference between their ages was onesixth of the sum of their ages 10 years before their marriage. How old were Mr and Mrs Phillips when they married? 3 Eights and nines The integers from 1 to 9 are listed on a whiteboard 1, 2, 3, 4, 5, 6, 7, 8, 9 The mean of all the numbers in the list is 5. Some extra eights and nines are added to the list. The mean of the list is now 7. 3 How many eights and nines are added? 4 At the table There are six people in the Micklefield family: 2 parents, 2 girls and 2 boys. They all sit around the table as shown. The two girls never sit opposite or next to each other. The two boys never sit opposite or next to each other. The parents never sit opposite or next to each other. How do the Micklefield family sit at the table?

5 Mashed potatoes Jay and Joy are peeling potatoes for a dinner party, and they each start with the same number of potatoes to peel. Every minute, each of them peels two potatoes, and Jay sneakily throws one of his unpeeled potatoes on Joy’s pile. After 10 minutes, Joy has three times as many potatoes still to peel as Jay. How many potatoes did each of them have to start with? 7 Boxed in The diagram shows a rectangular box. The areas of the faces are 3, 12 and 25 square centimetres. 25 cm 2 12 cm 2 3 cm 2 What is the volume of the box? If the areas of the faces are p, q and r, what is the volume of the box in terms of p, q and r? 6 Cash point Flash Jack went to the cash point. He drew out the same amount of money as he had in his pocket. He then spent £ 40 on CDs. Jack went back to the cash point. He drew out the same amount of money as he had in his pocket. He then spent a further £ 40 on CDs. Jack did this a third time. He then had no money left. How much money did he have with him to start? 8 Overlap 5/ 6 4/ 5 of the circle is shaded pink of the hexagon is shaded yellow Area of 15 circles = Area of ? hexagons

9 10 A builder can build either luxury houses or standard houses on a plot of land. Planning regulations prevent the builder from building more than 30 houses altogether, and he wants to build at least 5 luxury houses and at least 10 standard houses. Each luxury house requires 300 m 2 of land, and each standard house require 150 m 2 of land. The total area of the plot is 6500 m 2. Given that the profit on a luxury house is £ 14000 and the profit on a standard house is £ 9000, find how many of each house he should build to maximise his profit. The object of this puzzle to create a "fence" that connects dots horizontally or vertically, but not diagonally. The numbers in the grid indicate how many sides of the fence go around that space. Try to find as many different solutions as you can for each problem. In the example shown, there are three different solutions. Example

11 12 Broom handles A shop sells handles for garden brooms which are made up of cylinders of wood, diameter 5 cm. I bought three of these and, to keep them together, put a rubber band round each end of the bundle. How long will each rubber band be? 13 Candlelight One night two candles were lit, one of which was 3 cm longer than the other. The longer one was lit at 5. 30 pm and the shorter one at 7 pm. At 9. 30 pm they were both the same length. The longer one burned out at 11. 30 pm and the shorter one burned out at 11 pm. How long was each candle originally? 14 Exactly how many minutes is it before six o’clock if 50 minutes ago it was four times as many minutes past three o’clock? A 6 x 6 cube is painted red. It is then cut up into a number of identical cubes as shown in the picture. How many of the cubes have (a) 3 red faces (b) 2 red faces (c) 1 red face (d) 0 red faces What would the answers be for an n x n cube?

15 16 Which is a better fit – a square peg in a round hole or a round peg in a square hole? 17 The diagram shows a semi-circle and an isosceles triangle which have equal areas. What is the value of tan x° x° 18 Beverley’s watch gains 30 minutes every hour, whilst Jason’s watch loses 30 minutes every hour. At midnight, they both set their watches to the correct time of 12 o’clock. What is the correct time when their two watches next agree? The ratio a: b is 1: 2, the ratio a: c is 2: 3, the ratio c: e is 1: 4 and the ratio d: e is 2: 5 What is the ratio b: d in its lowest terms?

19 Rectangle problem 20 A large rectangular piece of card is (√ 5 + √ 20) cm long and √ 8 cm wide. A small rectangle √ 2 cm long and √ 5 cm wide is cut of the piece of card. What percentage of the original rectangle remains? In this multiplication each letter represents a different digit between 0 and 9. Solve for F, G, H, J and K. (√ 5 + √ 20) √ 8 Word multiplication F G H J K X 4 K J H G F √ 5 √ 2 21 A large window consists of six square panes of glass as shown. Each pane is x m by x m and all the dividing wood is y m wide. The total area of the glass is 1. 5 m 2 and the total area of the dividing wood is 1 m 2. Find the values of x and y. 22 The diagram shows two circles and four equal semi-circular arcs. The area of the inner shaded circle is 1. What is the area of the outer circle?

Answer sheet for …………………… 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 6 x 6: (a) n x n: (a) 15. 16. 17. 18. 19. 20. 21. 22. (b) (c) (d)

1. Fell by 4% 2. 20 years and 24 years 3. Fifteen 8 s and six 9 s, or six 8 s and fourteen 9 s B P 4. E. g P 11. 12. 13. 14. G G B 5. 40 6. £ 35 7. w = 2. 5 cm, h = 1. 2 cm, l = 10 cm, volume = 30 cm 2, volume = √pqr 8. 18 9. 13 luxury, 17 standard, profit £ 335, 000 10. Answers 15. 16. 17. 18. 19. 20. 21. 22. 15 + 5π ≈ 30. 7 cm 24 cm and 27 cm 26 minutes 6 x 6: (a) 4 (b) 48 (c) 96 (d) 64 n x n: (a) 4 (b) 12(n-2) (c) 6(n-2)2 (d) (n-2)3 The circle covers more of the square than the square does the circle. Therefore a round peg in a square hole is a better fit. π/2 12. 00 midday – both watches will show 6. 00 5: 6 83. 3% F = 2, G = 1, H = 9, J = 7, K = 8 x = ½, y = ¼ 2