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A leisure centre hosts 150 people. 30% are swimming, and the rest are in the fitness class or gym. The number in the fitness class is double the number in the gym. How many people are in the fitness c

Mathematics

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Answers

3 parts
a

70 people70 \text{ people}

b

5 teams5 \text{ teams}

c

Ugx. 90,000\text{Ugx. } 90,000

Step-by-step solution

11 steps

Here are the solutions to the tasks:

Part a· 3 steps

Help the Leisure Centre Manager to determine the number of people in the fitness class.

  1. Calculate the number of people swimming.

    Total people hosted = 150.
    Percentage swimming = 30%30\%.
    Number of people swimming = 0.30×150=450.30 \times 150 = 45 people.

  2. Calculate the number of people in fitness class or the gym.

    Remaining people = Total people - People swimming
    Remaining people = 150−45=105150 - 45 = 105 people.

  3. Determine the number of people in the fitness class.

    Let FF be the number of people in the fitness class and GG be the number of people in the gym.
    We know F+G=105F + G = 105.
    We are given that the number of people in the fitness class is double the number in the gym, so F=2GF = 2G.
    Substitute F=2GF = 2G into the equation:

    2G+G=1052G + G = 105 3G=1053G = 105 G=1053G = \frac{105}{3} G=35 peopleG = 35 \text{ people}

    Now find FF:

    F=2G=2×35=70 peopleF = 2G = 2 \times 35 = 70 \text{ people}

    The number of people in the fitness class is 70 people\boxed{70 \text{ people}}.

Part b

5 teams5 \text{ teams}

Help the coach to determine the maximum number of teams he can make.

  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=2045 - 25 = 20.

  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: 1,5,251, 5, 25.
    Factors of 20: 1,2,4,5,10,201, 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\boxed{5 \text{ teams}}.

Part c

Ugx. 90,000\text{Ugx. } 90,000

Did Aunt Sarah make profits? Support your answer.

  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. 600,00025 \times 24,000 = \text{Ugx. } 600,000.

  2. Calculate the total number of apples bought.

    Apples per box = 30.
    Total apples bought = 25×30=75025 \times 30 = 750 apples.

  3. Calculate the number of unsellable apples.

    Apples damaged on transportation = 25.
    Apples later discovered rotten = 35.
    Total unsellable apples = 25+35=6025 + 35 = 60 apples.

  4. Calculate the number of sellable apples.

    Sellable apples = Total apples bought - Total unsellable apples
    Sellable apples = 750−60=690750 - 60 = 690 apples.

  5. Calculate the total revenue from selling the apples.

    Selling price per apple = Ugx. 1,000.
    Total revenue = 690×1,000=Ugx. 690,000690 \times 1,000 = \text{Ugx. } 690,000.

  6. Calculate the profit or loss.

    Profit/Loss = Total Revenue - Total Cost
    Profit/Loss = Ugx. 690,000−Ugx. 600,000=Ugx. 90,000690,000 - \text{Ugx. } 600,000 = \text{Ugx. } 90,000.

    Aunt Sarah made a profit of Ugx. 90,000\boxed{\text{Ugx. } 90,000}. This is because her total revenue (Ugx. 690,000) was greater than her total cost (Ugx. 600,000).

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