This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
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You're on a roll — Here are the solutions to the tasks: a) Help the Leisure Centre Manager to determine the number of people in the fitness class. Step 1: Calculate the number of people swimming. Total people hosted = 150. Percentage swimming = 30\%. Number of people swimming = 0.30 × 150 = 45 people. Step 2: Calculate the number of people in fitness class or the gym. Remaining people = Total people - People swimming Remaining people = 150 - 45 = 105 people. Step 3: Determine the number of people in the fitness class. Let F be the number of people in the fitness class and G be the number of people in the gym. We know F + G = 105. We are given that the number of people in the fitness class is double the number in the gym, so F = 2G. Substitute F = 2G into the equation: 2G + G = 105 3G = 105 G = (105)/(3) G = 35 people Now find F: F = 2G = 2 × 35 = 70 people The number of people in the fitness class is 70 people. b) Help the coach to determine the maximum number of teams he can make. Step 1: Determine the number of males and females swimming. Total people swimming = 45 (from part a). Number of males swimming = 25. Number of females swimming = Total swimming - Males swimming Number of females swimming = 45 - 25 = 20. Step 2: Find the maximum number of teams. To make teams with the same number of males and females in each team, the coach needs to find the Greatest Common Divisor (GCD) of the number of males and the number of females. Number of males = 25. Number of females = 20. Factors of 25: 1, 5, 25. Factors of 20: 1, 2, 4, 5, 10, 20. The greatest common divisor of 25 and 20 is 5. The maximum number of teams the coach can make is 5 teams. c) Did Aunt Sarah make profits? Support your answer. Step 1: Calculate the total cost of buying the apples. Number of boxes bought = 25. Cost per box = Ugx. 24,000. Total cost = 25 × 24,000 = Ugx. 600,000. Step 2: Calculate the total number of apples bought. Apples per box = 30. Total apples bought = 25 × 30 = 750 apples. Step 3: Calculate the number of unsellable apples. Apples damaged on transportation = 25. Apples later discovered rotten = 35. Total unsellable apples = 25 + 35 = 60 apples. Step 4: Calculate the number of sellable apples. Sellable apples = Total apples bought - Total unsellable apples Sellable apples = 750 - 60 = 690 apples. Step 5: Calculate the total revenue from selling the apples. Selling price per apple = Ugx. 1,000. Total revenue = 690 × 1,000 = Ugx. 690,000. Step 6: Calculate the profit or loss. Profit/Loss = Total Revenue - Total Cost Profit/Loss = Ugx. 690,000 - Ugx. 600,000 = Ugx. 90,000. Aunt Sarah made a profit of Ugx. 90,000. This is because her total revenue (Ugx. 690,000) was greater than her total cost (Ugx. 600,000). Got more? Send 'em!