Solution 1: (Number of rabbit's feet × total number of feet - total number of feet) ÷ (Number of rabbit's feet - number of chicken's feet) = number of chickens

Total number of feet - number of chickens = number of rabbits

Solution 2: (Total number of feet -Chicken's Feet x Total Heads) ÷ (Rabbit's Feet - Chicken's Feet) = Rabbit's Only

Total Only - Rabbit's Only = Chicken's Only

Solution 3: Total Feet ÷ 2 - Total Heads = Rabbit's Only

Total Only -Number of rabbits = number of chickens

Example 1 (Classical question) How many chickens and rabbits are there in the same cage, with head ***46 and feet ***128?

Analysis If 46 are rabbits, a *** should have 4×46=184 feet, which is 184-128=56 feet more than the known 128 feet. If a chicken is used to replace a rabbit, the number of legs should be reduced by 4-2=2. So, how many chickens should be substituted for the 46 rabbits so that the difference of 56 feet is gone? Obviously, 56 ÷ 2 = 28, as long as 28 chickens are used to replace 28 rabbits. So the number of chickens is 28 and the number of rabbits is 46-28=18.

Solution: 1) How many chickens are there?

(4×6-128)÷(4-2)

=(184-128)÷2

=56÷2

=28

②How many rabbits are there?

46-28=18 (only)

Answer: There are 28 chickens and 18 exemptions.

Let's summarize the solution to this question: first assume that they are all rabbits. So according to the total number of chickens and rabbits can be calculated under the assumption of *** how many feet, so that the number of feet with the number of feet given in the question, see how much difference. Every difference of 2 feet means that there is one chicken; divide the difference by 2 to find out how many chickens there are in ****. We call this method of solving the problem the hypothesis method. To summarize, the basic equation for solving the chicken-rabbit problem is:

Number of chickens = (number of feet per rabbit × total number of rabbits - actual number of feet) ÷ (number of feet per rabbit - number of feet per chicken)

Number of rabbits = total number of chickens - number of rabbits - number of chickens

Of course, you can also assume that there are all chickens first.

Example 2 There are 100 chickens and rabbits***, and the chickens have 80 more feet than the rabbits, so how many chickens and rabbits are there?

Analysis This example is different from the previous example in that instead of giving the sum of their feet, it gives the difference in their feet. How can this be answered?

Assuming that all 100 are chickens, the total number of feet is 2 x 100 = 200 (only) when the number of rabbit's feet is 0, and the number of chicken's feet is 200 more than the rabbit's feet, while in fact the number of chicken's feet is 80 more than the rabbit's feet. Therefore, the difference between the number of chicken feet and the number of rabbit feet is (200 - 80) = 120 (pieces) more than is known, which is due to the fact that the rabbits are replaced by chickens. For every rabbit replaced by a chicken, the number of chicken feet increases by 2 and the number of rabbit feet decreases by 4. The difference between the number of feet of the chicken and the number of feet of the rabbit increases by (2 + 4) = 6, so there are 120 ÷ 6 = 20 rabbits that have been replaced by chickens. There are chickens (100-20) = 80 (only).

Solution: (2×100-80) ÷ (2+4) = 20 (only).

100-20=80 (only).

Answer: 80 and 20 chickens and rabbits respectively.