How to solve the problem of chickens and rabbits in the same cage, and how to solve the problem of c

There are many ways to solve the problem of chickens and rabbits in the same cage, and the following two methods are the most commonly used. Method 1: (Total number of feet, number of chicken's feet, total number) (number of rabbit's feet, number of chicken's feet) = number of rabbits, assuming that all are chickens, 1 rabbit has 4 feet, and it is regarded as a chicken with 2 legs, each rabbit has 2 feet less, a total of a foot is undercounted, and there are several 2s in a, which is a few rabbits.

Total number of rabbits = number of chickens Method 2: (Number of rabbit feet Total number of feet Total number of feet) (Number of rabbit feet Number of chicken's feet) = The number of chickens Assuming that all are rabbits, 1 chicken has 2 legs, think of it as a rabbit with 4 legs, each chicken has 2 more feet, a total of a foot is counted, a has a few 2 in it, that is, a few chickens.

There are many solutions to the problem of chickens and rabbits in the same cage. It seems to be difficult, but in fact, it is very simple to calm down and ponder carefully! Usually the total number of "heads" and the total number of "legs" (legs) of chickens and rabbits are known, so find the number of chickens and rabbits. If you don't want to use your brain, it's more convenient to use binary equations;

Use arithmetic solution: first count the total number of heads according to the chicken (two legs) how many legs there are (here it is assumed to be a leg), what is the difference between the total number of legs and a, and the relationship with the rabbit? (It's not hard to find a few rabbits, use your brain!) ）

Or first calculate the total number of heads according to rabbits, you can first count how many chickens there are.

The original title in Sun Tzu's Sutra is: "Today there are chickens and rabbits in the same cage, with 35 heads on the top and 94 feet on the bottom. Here's how to solve it:

The number of rabbits (total number of feet, total number of heads, number of feet per chicken) (number of feet per rabbit, number of feet per chicken) that is.

12 (Chickens) The number of chickens (total number of heads per rabbit foot Total number of feet) (number of rabbit feet per rabbit number of chicken feet) That is.

23 (only).

Assuming that all of them are chickens, then there are rabbits = (actual number of feet - 2 total number of chickens and rabbits) (4-2); Assuming that all of them are rabbits, then there are the number of chickens = (4 total number of chickens and rabbits - the actual number of feet) (4-2). Assuming that all of them are chickens, then there are rabbits = (2 total number of chickens and rabbits - the difference between chickens and rabbit feet) (4+2); Assuming that all of them are rabbits, then there are chickens = (4 total number of chickens and rabbits + difference between chickens and rabbits' feet) (4+2).

Chicken and rabbit cage formula:

Solution 1: (the number of rabbit's feet, the total number of feet - the total number of feet) (the number of rabbit's feet - the number of chicken's feet) = the number of chickens; Total number of chickens - number of chickens = number of rabbits.

Solution 2: (Total number of feet - number of chicken's feet Total number) (Number of rabbit's feet - number of chicken's feet) = number of rabbits; Total number of birds - number of rabbits = number of chickens.

Solution 3: Total number of feet 2 - total number of heads = number of rabbits; Total number of birds - number of rabbits = number of chickens.

Let's assume that they are all rabbits, so according to the total number of chickens and rabbits, you can calculate how many feet there are under the hypothesis, compare the number of feet obtained in this way with the number of feet given in the question, see how much the difference is, every 2 feet is a chicken; Divide the number of feet by 2 to calculate how many chickens there are. We call this method of solving the problem a hypothetical method.

Equation 1: (Number of rabbit's feet, total number of feet - total number of feet) (number of rabbit feet - number of chicken's feet) = number of chickens; Total number of chickens - number of chickens = number of rabbits.

Equation 2: (Total number of feet - number of chicken's feet Total number of feet) (Number of rabbit's feet - Number of chicken's feet) = Number of rabbits; Total number of birds - number of rabbits = number of chickens.

Formula 3: Total number of feet 2 - total number of heads = number of rabbits; Total number of birds - number of rabbits = number of chickens.

Equation 4: Number of chickens = (4 total number of chickens and rabbits - total number of feet of chickens and rabbits) 2; The number of rabbits = the total number of chickens and rabbits - the number of chickens.

Equation 5: Total number of rabbits = (total number of feet of chickens and rabbits - 2 total number of chickens and rabbits) 2 number of chickens = total number of chickens and rabbits - total number of rabbits.

Equation 6: (number of heads x 4 - actual number of legs) 2 = chicken.

Equation 7: 4 + 2 (total number - x) = total number of feet (x = rabbit, total number - x = number of chickens, used in the equation).

Equation 8: Number of chickens: Number of rabbits = Number of rabbit's feet - (total number of feet) :(Total number of feet) - number of chickens' feet.

Chicken and rabbit in the same cage leg lifting method one:

Let's say each chicken lifts one foot and each rabbit lifts two feet.

By 94 2 = 47, i.e. there are 47 feet under the cage, so a chicken corresponds to 1 leg, a rabbit corresponds to 2 legs, and the cage has 35 heads on it.

From 47-35 = 12, that is, if 35 heads correspond to 35 feet, there will be 12 more feet, which means that there are 12 rabbits in the cage.

By 35 12 = 23, i.e. there are 23 chickens in the cage.

Chicken and rabbit in the same cage to raise the leg method two:

Suppose each chicken and rabbit lift 2 feet.

By 35 2 = 70, 94 70 = 24, i.e. there are 24 feet under the cage, and these feet are rabbits. So 24 2 = 12, i.e. there are 12 rabbits in the cage.

By 35 12 = 23, i.e. there are 23 chickens in the cage.

Chickens and rabbits raise their legs in the same cage method three:

Let the rabbit lift 2 feet first, that is, from 35 2 = 70, 94 70 = 24, and there are 24 feet under the cage, and these feet are all rabbits.

By 24 2 = 12, i.e. there are 12 rabbits in the cage.

By 35 12 = 23, i.e. there are 23 chickens in the cage.