1, (total number of feet-chicken feet × total number of chickens) ÷ The difference between the number of feet of each chicken and rabbit = the number of rabbits.

2. Number of rabbits = (total number of legs-total number of heads ×2)÷2

3. Number of chickens = (total number of heads ×4- total number of legs) ÷2

4. (The number of rabbits × the total number of rabbits-the total number of rabbits) ÷ The difference between the number of rabbit feet per chicken = the number of chickens.

Solution method of chicken and rabbit cage equation

If there are x chickens, there will be (-x) rabbits, because each rabbit has 4 feet and each chicken has 2 feet. So there are 2x chicken feet and 4 rabbit feet (-x in all). So we can get the equation: 2x+4 (total -x)= total number of feet.

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. The book describes how many chickens and rabbits are 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?

The simplest algorithm for breeding chickens and rabbits: (total number of feet-total number of heads × number of chickens) ÷ (number of rabbits-number of chickens) = number of rabbits, that is, (94-35×2)÷2= 12 (number of rabbits). Total number of heads (35)- number of rabbits (12)= number of chickens (23).

One-dimensional linear equation solution: ① Suppose there are x rabbits, then there are (35-x) chickens. 4x+2(35-x)=94，x= 12。 Chicken: 35- 12=23 (only). ② If there are x chickens, there are (35-x) rabbits. 2x+4(35-x)=94，x=23。 Rabbit: 35-23= 12 (only).

Solution of binary linear equation: suppose there are x chickens and y rabbits. The equation is: x+y=35 2x+4y=94. X=23，y= 12。 A: Rabbits 12, 23 chickens.

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