Answer:
Total pigs in the farm = 15
Total chickens in the farm = 25
Explanation:
Given - Chickens and pigs are raised on a farm. Between the two classes
of animals there are 40 heads and 110 legs.
To find - How many animals are there of each class?
Proof -
Given that , there are two types of animals - Chicken and pigs.
Let Chicken is represented by c
Pigs are represented by p
Given , there are 40 heads and 110 legs.
As we know that both chicken and pigs has 1 head
⇒1c + 1p = 40
⇒c + p = 40 .........(1)
Also, we know
Chicken has 2 legs whereas pigs have 4 legs
⇒2c + 4p = 110
Divide the whole equation by 2, we get
⇒c + 2p = 55 .............(2)
∴ we get
c + p = 40 .........(1)
c + 2p = 55 .............(2)
subtract equation (1) from equation (2) , we get
c + 2p - ( c+ p) = 55 - 40
⇒c + 2p - c - p = 15
⇒p = 15
Now,
Put the value of p in equation (1), we get
c + 15 = 40
⇒c = 40 - 15
⇒c = 25
∴ we get
c = 25
p = 15
So, Total pigs in the farm = 15
Total chickens in the farm = 25