Question

System of equations

A zoo keeps birds (2-legged) and beasts (four-legged). If the zoo contains 60 heads and 200 feet, how many birds and how many beasts live there? Let X represent the number of birds and Y represent the number of beasts in the zoo.

Answer 1

let X be birds = ?
Y be beasts = ?
heads = 60
feet = 200
feet of birds = 2
feet of beast = 4
From data we come to know that
total animals = X+Y=60____1
total feet = 200 = 2X + 4Y_____2
from equation 1 X= 60-Y
put this value of X in equation 2
2(60-Y) + 4Y = 200
120 - 2Y + 4Y = 200
2Y= 200 - 120
2Y = 80
Y = 40
Now from value of Y we can calculate X
X + Y =60
X + 40 = 60
Or X = 20
The number of beasts is equal to 40 where as number of birds is equal to 20.