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The sum of four consecutive natural numbers is 86. Workout the range if the biggest number is P. (5 marks)...

26. The sum of four consecutive natural numbers is 86. Workout the range if the biggest number is P. (5 marks)
27. Amiru borrowed some money from the bank at an interest of 15% per year. If the paid amount of sh 810,000 over 10 months. How much did Amiru borrow? (5 marks)
28. (a) If he fenced the garden using poles of 8m apart. How much did he spend on poles if each pole cost sh. 5,000? (3 marks)
28. A science teacher at Masindi Port Primary School wanted to make a circular garden and used a rope of radius 14m tied on a peg, he wounded the garden once. (a)What is the total distance around the garden he made? (02 marks)
29. Using a ruler, a pencil and a pair of compasses only, construct a triangle PQR where angle PQR = 105° and PRQ = 30° and line PQ = 7cm. (4 marks)
(b) Measure length PR. (1 mark)
30. Martha had playing cards, when he grouped them in threes, 2 cards remained, when he grouped them in fours, 3 cards remained and finally when he grouped them in fives, 3 cards remained, find the least number of playing cards Martha had? (3 marks)

Answer

  1. Let the four consecutive numbers be (P-3), (P-2), (P-1), and P. Their sum is 86: (P-3) + (P-2) + (P-1) + P = 86. Simplifying gives 4P - 6 = 86, so 4P = 92, and P = 23. The range is P - (P-3) = 3.

  2. Let the borrowed amount be X. The interest for 10 months is 15% of X. Therefore, X + 0.15X = 810,000. Simplifying gives 1.15X = 810,000, so X = 810,000 / 1.15 = 704,347.83. Amiru borrowed approximately 704,348 shillings.

  3. The number of poles needed is the total distance divided by 8m. If the total distance is not given, assume a circular garden with circumference 2πr = 2 * 3.14 * 14 = 87.92m. Number of poles = 87.92 / 8 = 11 (rounded up). Cost = 11 * 5,000 = 55,000 shillings.

  4. The total distance around the garden is the circumference of the circle, which is 2πr = 2 * 3.14 * 14 = 87.92 meters.

  5. Construct the triangle using a ruler and compass. Measure length PR after construction.

  6. The least number of cards is the smallest number that leaves a remainder of 2 when divided by 3, a remainder of 3 when divided by 4, and a remainder of 3 when divided by 5. The number is 23.

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