This business/management problem is solved step by step below, with detailed explanations to help you understand the method and arrive at the correct answer.
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Here are the solutions to your questions: Q1. a) Find the total marks Step 1: Let the total marks be T. We are given that 45 marks is 60% of the total marks. 0.60 × T = 45 Step 2: Divide by 0.60 to find T. T = (45)/(0.60) T = 75 The total marks are 75. 75 marks b) How many more marks are needed to reach 80%? Step 1: Calculate 80% of the total marks. 80\% of 75 = 0.80 × 75 0.80 × 75 = 60 Step 2: Find the difference between 80% of the total marks and the student's current marks. Marks needed = 60 - 45 Marks needed = 15 The student needs 15 more marks to reach 80%. 15 marks Q2. a) Kofi’s share b) Ama’s share c) Yaw’s share Step 1: Find the total number of ratio parts. Total ratio parts = 2 + 3 + 4 = 9 Step 2: Find the value of one ratio part. Value per part = GH₵3609 = GH₵40 Step 3: Calculate each person's share. a) Kofi's share: Kofi's share = 2 × GH₵40 = GH₵80 GH₵80 b) Ama's share: Ama's share = 3 × GH₵40 = GH₵120 GH₵120 c) Yaw's share: Yaw's share = 4 × GH₵40 = GH₵160 GH₵160 Q3. a) Find the perimeter Step 1: The formula for the perimeter of a rectangle is P = 2(L+W). P = 2(20 m + 15 m) P = 2(35 m) P = 70 m The perimeter is 70 m. 70 m b) Find the area Step 1: The formula for the area of a rectangle is A = L × W. A = 20 m × 15 m A = 300 m^2 The area is 300 m^2. 300 m^2 c) Find the cost of fencing it at GH₵5 per metre Step 1: Multiply the perimeter by the cost per metre. Cost = 70 m × GH₵5/m Cost = GH₵350 The cost of fencing is GH₵350. GH₵350 Q4. a) Find x Step 1: Angles on a straight line sum to 180°. (x+10)^ + (3x-20)^ = 180^ Step 2: Combine like terms. 4x - 10 = 180 Step 3: Add 10 to both sides. 4x = 190 Step 4: Divide by 4. x = (190)/(4) x = 47.5 The value of x is 47.5. x = 47.5 b) If one of the angles is part of a triangle, find the third angle if the other two are 50° and that angle. Step 1: Calculate the values of the two angles on the straight line. First angle: x+10 = 47.5+10 = 57.5^ Second angle: 3x-20 = 3(47.5)-20 = 142.5-20 = 122.5^ Let's use the first angle, 57.5^, as "that angle" for the triangle. Step 2: The sum of angles in a triangle is 180°. Third angle = 180^ - 50^ - 57.5^ Third angle = 130^ - 57.5^ Third angle = 72.5^ The third angle is 72.5°. 72.5^ Q5. a) What was the original price? Step 1: A 10% discount means the shirt was sold for 100\% - 10\% = 90\% of its original price. Let the original price be P. 0.90 × P = GH₵180 Step 2: Divide by 0.90 to find P. P = GH₵1800.90 P = GH₵200 The original price was GH₵200. GH₵200 b) A shopkeeper bought goods for GH₵450 and sold them for GH₵540. Find the profit percentage. Step 1: Calculate the profit. Profit = Selling Price - Cost Price Profit = GH₵540 - GH₵450 Profit = GH₵90 Step 2: Calculate the profit percentage. Profit Percentage = ProfitCost Price × 100\% Profit Percentage = GH₵90GH₵450 × 100\% Profit Percentage = 0.2 × 100\% Profit Percentage = 20\% The profit percentage is 20%. 20\% Q6. i. Find the mode Step 1: List the marks and count their frequencies: 42 (1), 55 (3), 50 (2), 48 (2), 62 (1), 38 (1), 60 (1), 45 (1) Step 2: The mode is the mark that appears most frequently. The mark 55 appears 3 times, which is more than any other mark. The mode is 55. 55 ii. Find the range Step 1: Identify the highest and lowest marks. Highest mark = 62 Lowest mark = 38 Step 2: Calculate the range. Range = Highest mark - Lowest mark Range = 62 - 38 Range = 24 The range is 24. 24 b) A bag contains 4 red, 3 blue and 3 green balls. One ball is drawn at random. Step 1: Find the total number of balls. Total balls = 4 (red) + 3 (blue) + 3 (green) = 10 i. Find the probability that it is: Blue Step 2: The probability of drawing a blue ball is the number of blue balls divided by the total number of balls. P(Blue) = Number of blue ballsTotal balls P(Blue) = (3)/(10) The probability of drawing a blue ball is (3)/(10). (3)/(10) ii. Not green Step 2: The number of balls that are not green is the sum of red and blue balls. Not green balls = 4 (red) + 3 (blue) = 7 Step 3: The probability of drawing a ball that is not green is the number of non-green balls divided by the total number of balls. P(Not green) = Number of not green ballsTotal balls P(Not green) = (7)/(10) The probability of drawing a ball that is not green is (7)/(10). (7)/(10) Q7. a) A taxi company charges a fixed fee of GH₵10 plus GH₵1.20 per kilometer. How much will a passenger pay for a trip of 15 km? Step 1: Calculate the variable cost for 15 km. Variable cost = 15 km × GH₵1.20/km Variable cost = GH₵18.00 Step 2: Add the fixed fee to the variable cost. Total cost = Fixed fee + Variable cost Total cost = GH₵10.00 + GH₵18.00 Total cost = GH₵28.00 A passenger will pay GH₵28.00 for a 15 km trip. GH₵28.00 b) A rectangular field is 85 m long and 60 m wide. A farmer wants to put a fence around the field and also divide the field into 5 equal smaller plots by lines parallel to the shorter side. i. What is the perimeter of the field? Step 1: The formula for the perimeter of a rectangle is P = 2(L+W). P = 2(85 m + 60 m) P = 2(145 m) P = 290 m The perimeter of the field is 290 m. 290 m ii. How many metres of fencing will be needed altogether? Step 1: The fencing around the field is its perimeter, which is 290 m. Step 2: To divide the field into 5 equal smaller plots by lines parallel to the shorter side (60 m), 4 dividing lines are needed. Each dividing line will be 60 m long. Length of dividing lines = 4 × 60 m = 240 m Step 3: Add the perimeter and the length of the dividing lines to find the total fencing needed. Total fencing