Answer:
There are 11 goats and 20 ducks.
Step-by-step explanation:
Given:
While on a walk in the country you pass a field full of goats and ducks.
After quick count you determine there are 31 heads and 84 feet in each animal.
Now, to find the number of each animals.
Let the number of goats be [tex]x.[/tex]
And let the number of ducks be [tex]y.[/tex]
So, total number of heads:
[tex]x+y=31[/tex]
[tex]y=31-x\ \ \ .......(1)[/tex]
As, the goats have 4 feets and ducks have 2.
Now, the total number of feet:
[tex]4x+2y=84[/tex]
Substituting the value of [tex]y[/tex] from equation (1) we get:
[tex]4x+2(31-x)=84\\\\4x+62-2x=84\\\\2x+62=84[/tex]
Subtracting both sides by 62 we get:
[tex]2x=22[/tex]
Dividing both sides by 2 we get:
[tex]x=11.[/tex]
The number of goats = 11.
Substituting the value of [tex]x[/tex] in equation (1) we get:
[tex]y=31-x\\\\y=31-11\\\\y=20.[/tex]
The number of ducks = 20.
Therefore, there are 11 goats and 20 ducks.
