A Zoo keeper counted the heads of the animals in a zoo and found it to be 80. When he counted the legs of the animals he found it to be 260. If the zoo had either pigeons or horses, how many horses were there in the zoo?

Question: A Zoo keeper counted the heads of the animals in a zoo and found it to be 80. When he counted the legs of the animals he found it to be 260. If the zoo had either pigeons or horses, how many horses were there in the zoo?

Solution:
let, there are x horses and y pigeons.

ATQ,
x + y = 80
⇒ x = 80 - y

and
4x + 2y = 260
⇒ 4 (80 - y) + 2y = 260
⇒ 320 - 4y + 2y = 260
⇒ 320 - 2y = 260
⇒ - 2y = 260 - 320
⇒ - 2y = - 60
∴ y = 30

∴ x = 80 - 30
= 50
∴ There are 50 horses.