The average number of chickens, ducks, rabbits and sheep = 315 per type of animal.
The average number of chickens, ducks and rabbits = 320 per type of animal.
The number of sheep is 60 more than the number of rabbits.
Let us assume number of rabbits = x.
Number of sheep is 60 more than number of rabbits, that is = x+60.
There are half as many ducks as there are rabbits.
Therefore, number of ducks = x/2.
Let us assume number of chickens = y.
Adding number of chickens, number of rabbits, number of sheep and number of ducks and dividing by 4 (because those are four types of animal).
Multiplying both sides by 4, we get
y+x+x+60+x/2 = 1260
Subtracting 60 from both sides
y+x+x+60-60+x/2 = 1260-60
y+x+x+x/2 = 1200.
Combining like terms .
y + 5x/2 = 1200
Multiplying both sides by 2, we get
2y +5x = 2400 ------------equation (1)
Adding number of chickens, number of rabbits and number of ducks and dividing by 3 (because those are three types of animal).
Multiplying both sides by 3, we get
y+x+60+x/2 = 960
Subtracting 60 from both sides
y+ x+x/2 = 900
Combining like terms .
y+ 3x/2 = 900
Multiplying both sides by 2, we get
2y+3x = 1800 --------------------equation (2)
Multiplying first equation by 3 and second equation by -5, we get
(2y +5x = 2400 ) * 3 => 6y +15x = 7200
(2y+3x = 1800) *-5 =>
Adding
6y +15x = 7200
-10x + -15x = -9000.
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-4y = -1800.
Dividing both sides by -4, we get
y=450.
Therefore, number of chickens are 450 there at the farm.