Formula 1: (rabbit foot number × total foot number-total foot number) ÷ (rabbit foot number-chicken foot number) = chicken foot number; Total number-number of chickens = number of rabbits.
Formula 2: (total number of feet-chicken feet × total number of feet) ÷ (rabbit feet-chicken feet) = number of rabbits; Total number-rabbit number = chicken number.
Formula 3: total number of feet ÷2- total number of heads = number of rabbits; Total number-rabbit number = chicken number.
Formula 4: Total number of rabbits = (total number of chicken and rabbit feet -2× total number of chicken and rabbit feet) ÷ 2; Number of chickens = total number of chickens and rabbits-total number of rabbits.
Formula 5: Number of chickens =(4× total number of chickens and rabbits-total number of chickens and rabbits) ÷ 2; Number of rabbits = total number of chickens and rabbits-number of chickens.
Equation 6: 4×+2 (total number x)= total number of feet (x= rabbits, total number -x= number of chickens, used in the equation).
Historical origin:
Chicken and rabbit in the same cage is one of the famous mathematical problems in ancient China. About 1500 years ago, this interesting question was recorded in Sun Tzu's calculation. It is described in the book that there are pheasant rabbits in the same cage, with 35 heads on the top and 94 feet on the bottom. What are the geometric shapes of pheasant rabbits? These four sentences mean that there are many chickens and rabbits in the same cage. From the top, there are 35 heads, and from the bottom, there are 94 feet. How many chickens and rabbits are there in each cage?
Simple calculation method: (total number of feet-total number of heads × number of chicken feet) ÷ (number of rabbit feet-number of chicken feet) = number of rabbits.
(94-35×2)÷2= 12 (number of rabbits) Total number (35)- number of rabbits (12)= number of chickens (23) Explanation: Let rabbits and chickens lift their feet at the same time, so that the total number of feet in the cage is reduced by 2, because there are only two chickens.