TUTORIAL: NUMBER OF PIGS/COWS AND CHICKENS IN A FARM
To find the number of pigs or cows (or any other animals with 4 feet), the formula is just subtract the number of heads from the half of the number of legs. To find the number of chickens (or any other animal with 2 feet), just subtract the number of pigs/cows from the total number of heads.
EXAMPLE #1:
Hokage has chickens and pigs in his farm. If the total number of heads is 69 and the total number of legs is 200, find the number of chickens and pigs.
SOLUTION:
Pigs = Legs/2 - Heads
Pigs = 200/2 - 69
Pigs = 100 - 69
Pigs = 31
Chickens = Number of heads - Pigs
Chickens = 69 - 31
Chickens = 38
Thus, Hokage has 31 Pigs and 38 Chickens
CHECKING:
Pigs + Chickens = Number of heads
31 + 38 = 69
69 = 69
4*Pigs + 2*Chickens = Number of legs
4*31 + 2*38 = 200
124 + 76 = 200
200 = 200
EXAMPLE #2:
Luyde has lions and ostriches in his backyard. If the total number of heads is 143 and the total number of legs is 522, how many lions and ostriches does he have?
SOLUTION:
Lions = Legs/2 - Heads
Lions = 522/2 - 143
Lions = 261 - 143
Lions = 118
Ostriches = Number of heads - Lions
Ostriches = 143 - 118
Ostriches = 25
Thus, Luyde has 118 Lions and 25 Ostriches
CHECKING:
Lions + Ostriches = Number of heads
118 + 25 = 143
143 = 143
4*Lions + 2*Ostriches = Number of legs
4*118 + 2*25 = 522
472 + 50 = 522
522 = 522
DERIVATION:
Let x be any animal with 2 feet
Let y be any animal with 4 feet
Legs = 2x + 4y
Divide it by 2
Legs/2 = x + 2y -----> Eq. 1
Heads = x + y -----> Eq. 2
Eq.1 - Eq.2
Legs/2 - Heads = x + 2y - (x + y)
Legs/2 - Heads = y
Thus, the number of animal with 4 feet is the difference between half of the legs and heads.
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-shinnichi
