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?

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