P6 Maths SA Grade AA Paper 2 Word Problems - Rosyth. Word Problem Worksheet & Solutions Difficulty: AA P6 Mathematics SA2 2017

Transcription

1 P6 Maths SA Grade AA Paper 2 Word Problems - Rosyth Word Problem Worksheet & Solutions Difficulty: AA P6 Mathematics SA

2 P6 Maths SA Grade AA Paper 2 Word Problems - Rosyth Show your working clearly in the space provided for each question and write your answers in the spaces provided. 6. Whole Numbers The average of 26 numbers is 45. When 14 more numbers are added, the average becomes 52. What is the average of the 14 new numbers? Total of 26 numbers = 26 x 45 = 1170 Total of 40 numbers = 40 x 52 = 2080 Total of 14 numbers = = 910 Average of 14 numbers = = 65 Ans: Area The figure below is a rectangle ABCD. The ratio of AE : ED = 3 : 2. The area of triangle ABE is 60 cm 2. Find the area of rectangle ABCD. Height of ΔABE = height of ΔCDE = CD Therefore area of triangle is proportional to length of base. Area of ΔCDE = 2 3 x 60 = 40 cm ² Total Area of ΔABE and ΔCDE = = 100 cm ² Area of rectangle ABCD = 100 x 2 = 200 cm ² Ans: 200 cm ² 2

3 P6 Maths SA Grade AA Paper 2 Word Problems - Rosyth 8. Measurements Money Molly and Alan had a total of $160 on Monday. After Alan received $5 from his mother and Molly spent $20 on a book, Molly had $38 more than Alan. How much did Molly have at first? After receiving $5 and spending $20, Molly and Alan had = $145 Amount Alan had at last = (145-38) 2 = $53.50 Amount Molly had at last = = $91.50 Amount Molly had at first = = $ Ans: $ Ratios Efron is 30 years younger than Danny. The ratio of Danny s age to Efron s age is 8 : 3. In how many years time will the ration of Danny s age to Efron s age be 5 : 3? 8u - 3u = 5u = 30 u = 30 5 = 6 Danny's age = 8 x 6 = 48 5p - 3p = 2p = 30 p = 30 2 = 15 In future Danny's age = 5 x 15 = 75 Number of years later = = 27 Ans: 27 3

4 P6 Maths SA Grade AA Paper 2 Word Problems - Rosyth 10. Ratios There were 64 more buttons in box A than box B at first. Ken then added some more buttons in box A. For every 1 button he added to box A, he removed 2 buttons from box B. The number of buttons in box B became 28 fewer than before. In the end, the ratio of the total number of buttons in both boxes to the number of buttons left in box B was 4 : 1. How many buttons were in box A at first? Number of buttons added to box A = 28 2 = 14 Difference between box A and box B at last = = 106 At last, ratio of A + B to B 4 : 1 4u : 1u A - B 4u - 1u - 1u = 2u = 106 u = = 53 A = 4u - 1u = 3u = 3 x 53 = 159 At first number of buttons in box A = = 145 Ans: 145 4

5 P6 Maths SA Grade AA Paper 2 Word Problems - Rosyth 11. Measurements Volume Tank X was empty. Tank Y was filled with water to the brim. Then, Tap A was turned on to fill Tank X and Tap B was turned on to drain water from Tank Y. Both taps were turned on at the same time with water flowing at the same rate of 2.8 litres per minute. How long did it take for the height of water to be the same in both tanks? Area of Tank X = 50 x 14 = 700 cm² Rate of height rising in Tank X = = 4 cm per minute Area of Tank Y = 50 x 20 = 1000 cm² Rate of height falling in Tank Y = = 2.8 cm per minute Height of water in Tank X = 4 x t (where t = time in minutes) Height of water in Tank Y = t When both heights are the same level, 4t = t 4t + 2.8t = t = 34 t = = 5 minutes Ans: 5 minutes 5

6 P6 Maths SA Grade AA Paper 2 Word Problems - Rosyth 12. Fractions Mrs Lee had used some dark and white chocolate chips for baking cookies. She used an equal amount of dark and white chocolate chips. She had 2 7 of the dark chocolate chips and 3 5 of the with chocolate chips left. a) What fraction of the chocolate chips were used? b) If there were 304 g of the chocolate chips left, what was the mass of the chocolate chips at first? a) 5 parts of dark chocolate chips = 2 parts of white chocolate chips 5u = 2p 5p = 5u x 2.5 = 12.5u 12.5u + 7u = 19.5u Chocolates used = 5u + 5u = 10u Fraction of chocolates used = 10u 19.5u = 20u 39u = b) chocolates chips left = 2u + 3p = 2u + 3x 2.5u = 9.5u 9.5u = 304g u = 32g Total chocolate chips at first = 19.5 u = 19.5 x 32 = 624g Ans: (a) (b) 624g 6

7 P6 Maths SA Grade AA Paper 2 Word Problems - Rosyth 13. Whole Numbers There was a total of 748 oranges and apples at a fruit stall in the morning. By afternoon, the number of oranges sold was thrice the number of apples sold. The number of apples left was twice the number of oranges left. There were 22 more apples left than the apples sold. a) How many apples were sold? b) How many oranges were there in the morning? a) Total number of oranges and apples = 748 Let number of apples sold = u Number of oranges sold = 3 x apples sold = 3u Number of apples left = 22 + apples sold = 22 + u Number of apples left = 2 x oranges left Oranges left = ½ x apples left = ½ (22 + u) = 11 + ½ u Oranges sold + oranges left + apples sold + apples left = 748 3u + (11 + ½ u) + u + (22 + u) = ½ u = = 715 Apples sold = u = = 130 b) Number of oranges in the morning = 3u ½ u = 3.5u + 11 = 466 Ans: (a) 130 (b) Speed Cheryl and Milton left for the park from their respective homes at the same time. Milton travelled 120 km at an average speed of 90 km/h and reached the park first. Cheryl travelled at an average speed of 80 km/h and reached the park 55 minutes later than Milton. If Cheryl wanted to reach the park the same time as Milton, what would be her new speed? Time Milton travelled = = 80 minutes Time Cheryl travelled = = 135 minutes Distance Cheryl travelled = 135 x = 180 km New speed = 180 x = 135 km/h Ans: 135 km/h 7

8 P6 Maths SA Grade AA Paper 2 Word Problems - Rosyth 15. Measurements Area, Perimeter The figure below is made up of four quarter circles and straight lines. All corner angles are at right angles. Each number represents the length of the straight line in centimeters. The radius of each quarter circle is 6 cm. a) What is the area of the figure? Leave your answer in terms of π. b) What is the perimeter of the figure? Leave your answer in terms of π. a) Area = 6 x x 6 x x 6 x π = ( π) cm 2 b) Perimeter = 2 π x x 4 = ( π) cm Ans: (a) ( π) cm 2 (b) ( π) cm 8

9 P6 Maths SA Grade AA Paper 2 Word Problems - Rosyth 16. Percentages There were some pens in boxes A, B and C. Box A had 25% more pens than Box B. Box C had 45 more pens than Box A. 40% of pens from each box were taken to pack into 73 packets. All the packets had an equal number of pens. A total of 288 pens from Boxes B and C were taken for the packing. How many pens were there in each packet? Number of pens in box A = a Number of pens in box B = b Number of pens in box C = c 0.4 x (b + c) = 288 b + c = = 720 u + (1.25u + 45) = u = = 675 u = = 300 a = 300 x 1.25 = % of a = 0.4 x 375 = 150 Total pens packed = = 438 Number of pens per packed = = 6 Ans: 6 9

10 P6 Maths SA Grade AA Paper 2 Word Problems - Rosyth 17. Fractions A bakery made some buns for charity. 3 5 of them were chicken buns and the rest were tuna buns. 7 8 of the chicken buns and 600 of the tuna buns were eaten buns were left. a) How many buns were made? b) How many tuna buns were left? of al the a) Let u = 1 40 Number of tuna buns = 16u Number of chicken buns = 24u Total number of buns = 40u Number of tuna buns eaten = 600 Number of chicken buns left = 1 x 24u = 3u 8 Total leftover = 7 40 = 7u Leftover = 16u u = 19u 600 = 7u 12u = 600 u = = 50 Total buns made = 40u = 40 x 50 = 2000 b) Number of tuna buns left = 16u 600 = 16 x = = 200 Ans: (a) 2000 (b)

11 P6 Maths SA Grade AA Paper 2 Word Problems - Rosyth 18. Measurement Volume Mrs Gopal prepared some juice for a party. She poured half the amount of juice in big cups and the other half of the amount of juice in small cups as shown in the diagram below. After filling the big cups and small cups to the brim with the juice, she counted that there were 48 more small cups than big cups. How much juice did Mrs Gopal prepare for the party? Give your answer in litres. Volume of 48 small cups = 48 x 150 = 7200 m l Difference in capacity between big and small cups = = 200 m l Number of big cups = = 36 Number of small cups = = 84 Total volume of juice Mrs Gopal prepared = 36 x x 150 = = 25.2 l Ans: 25.2 l 11

12

13

14

15

16

17

18

19

20

21

22

23

24