Answer:
He saw 1 duck and 3 dogs.
Step-by-step explanation:
Given:
Evan went to the park and saw four animals.
Each animal was either a duck or a dog.
He saw a total of 14 legs.
Now, to find the number of each animal he had seen.
Let the number of duck be [tex]x.[/tex]
And the number of dog be [tex]y.[/tex]
So, total number of animals:
[tex]x+y=4\\y=4-x[/tex]
Now, the total number of legs he did see:
As we know the legs of a duck are 2 and a dog are 4.
[tex]2x+4y=14\\2x+4(4-x)=14\\2x+16-4x=14\\-2x+16=14[/tex]
Adding both sides by -16 we get:
[tex]-2x=-2[/tex]
Dividing both sides by -2 we get:
[tex]x=1[/tex]
The number of duck = 1.
Now, putting the value of [tex]x[/tex] in above equation we get:
[tex]y=4-x[/tex]
[tex]y=4-1\\y=3.[/tex]
The number of dogs = 3.
Therefore, he saw 1 duck and 3 dogs.
