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25 January, 00:46

there are 25 animals in the field. Some are horses, some are ducks. There are 84 legs in all. How many of animal are in the field?

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  1. 25 January, 01:03
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    Ducks = 8

    Horses = 17

    Step-by-step explanation:

    From the question;

    Total number of animals = 25 Total number of legs = 84 legs

    We are required to determine the number of ducks and horses;

    We need to know that;

    A duck has two legs while a horse has four legs;

    Assuming there were x ducks and y horses

    Then;

    x + y = 25 ... Eqn 1

    And;

    2x + 4y = 84 ... Eqn 2

    Solving the two equations simultaneously we can get the number of each animal.

    x + y = 25

    2x + 4y = 84

    Multiplying the first equation by 2, we get

    2x + 2y = 50

    2x + 4y = 84

    Subtracting the two equations;

    2x + 2y = 50

    2x + 4y = 84

    ...

    - 2y = - 34

    y = 17

    Solving for x

    x = 25 - 17

    = 8

    Therefore; there were 8 ducks and 17 horses in the field
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