How to use equations to solve chickens and rabbits in the same cage?

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Topic topic, how to help without topic.

There are x chickens and (35-x) rabbits.

2x+4（35-x）=96

2x+140-4x=96

2x=-44

x=2235-x=35-22=13

22 chickens and 13 rabbits.

An efficient solution to the chicken-rabbit cage problem.

Chickens and rabbits in the same cage:

Hypothesis method: hypothesis - calculation - reasoning - solution.

Arithmetic: Total number of feet 2 - total number of heads = number of rabbits.

Total number of birds - number of rabbits = number of chickens.

Mantra method: "Half of the feet are reduced to the head of the rabbit, and the first four are half of the feet are the chicken." This means that half of the number of feet minus the number of heads is the number of rabbits, and four times the number of heads minus half of the number of feet is the number of chickens.

Equation method: A head, B legs.

There are x chickens.

Then rabbits have.

a-x only. then x*2+(a-x)*4=b

If you don't understand it yet, just look at the example question:

Chickens and rabbits in the same cage, head 9, feet 30, ask for chickens and rabbits how many each?

Equipped with x chickens, then there are 9-x rabbits.

2x+（9-x）*4=30

2x multiplies the number of chickens by two legs to get the total number of legs of chickens.

9-x)*4 is to multiply the number of rabbits by 4 feet to get the total number of legs of rabbits.

The quantity relationship is: the total number of feet of chickens + the total number of feet of rabbits = the number of feet common to chickens and rabbits.

Chickens: 35-12 = 23 (pcs). If there are x chickens, then rabbits have (35-x).

2x+4(35-x)=94, the solution is x=23Rabbits: 35 - 23 = 12 (only).

Binary Equation Solution: Let there be x chickens and y rabbits. The system of equations is: x+y=35 2x+4y=94. The solution is x=23 and y=12. A: There are 12 rabbits and 23 chickens.

If there are x chickens, then the rabbit has (total -x) rabbits, because each rabbit has 4 legs and each chicken has 2 legs. Therefore, there are 2x chicken feet and 4 rabbit feet (total - x).

So we can get the equation: 2x + 4 (total - x) = total full number.

For example, there are several chickens and rabbits in the same cage, counting from above, there are 35 heads; Counting from below, there are 94 feet. How many chickens and rabbits are in the cage?

If there are x rabbits, then there are 35-x chickens.

4x+2(35-x)=94

4x+70-2x=94

2x=24x=12

A: There are 12 rabbits and 23 chickens.

Topic: Chickens and rabbits in the same cage, with 17 heads and 42 legs, how many chickens and rabbits are there?

Suppose: two-legged chickens x and four-legged rabbits 17-x 2x+4(17-x)=42

2x+68-4x=42

2x=26x=13

13 chickens and 4 rabbits.

Use the foot lifting method, if the chicken's feet are all raised, first use the total number of feet to subtract the total number of heads, and then use the number to divide by 2

A lot of people come to know it, and then find out that the horn must be a little less than the foot of the main palace, the horn is subtracted, the horn is cut off, and then the more feet, divided by the base of the bird.

35 heads, 94 legs, chickens and rabbits.

Solution: If there are x rabbits, then there are 35 x chickens (when the chickens are x, then the rabbits are 35 x, this kind of problem is generally when the legs are more x, the equation is better to solve).

4x+（35－x）×2＝94

4x+70－2x＝94

2x+70＝94

x 12 chickens: 35 12 23 chickens.

Two unknown quantities, they are the relationship of and, one is x, and the other is and—x.

10 heads, 26 legs, a few chickens and rabbits.

Solution: If there are rabbits with x, then there are 10-chickens 4x+2[10-x] 4x+20-2x=26 2x=6 x=3 10-6=4 A: There are 6 chickens and 4 rabbits.

Directly set the unknowns, and solve the equations.

If there are x chickens, there will be 12-x chickens, and 2x+4(12-x)=38.

2 ways:

Unary Equation:

Suppose there are x rabbits and (35-x) chickens.

2(35-x)+4x=94

Solution: x=12

Binary Linear Equation:

There are x chickens and y rabbits.

x+y=35；2x+4y=94

The solution is x=23 and y=12.

Equation 1Write an equivalence relation.

2.Solution: One of them (small) is x, and the other is the total number - x example problem: chicken leg + rabbit leg = 14.

Solution: There are x chickens and (5-x) rabbits.

2x+(5—x)x4=14

2x+20—4x=14

4x—2x=20—14

2x=6x=3 (chicken).

5-3=2 (rabbits).

Chickens: 35-12 = 23 (pcs). If there are x chickens, then rabbits have (35-x).

2x+4(35-x)=94, the solution is x=23Rabbits: 35 - 23 = 12 (only).

Binary Equation Solution: Let there be x chickens and y rabbits. The system of equations is: x+y=35 2x+4y=94. The solution is x=23 and y=12. A: There are 12 rabbits and 23 chickens.

35 heads, 94 legs, chickens and rabbits.

Solution: If there are x rabbits, then there are 35 x chickens (when the chickens are x, then the rabbits are 35 x, and the equation is better to solve when the problem is generally set to x with more feet).

4x+（35－x）×2＝94

4x+70－2x＝94

2x+70＝94

x 12 chickens: 35 12 23 chickens.

Two unknown quantities, they are the relationship of and, one is x, and the other is and—x.

There are x chickens and rabbits each.

4x-2x=28

x = 14 chickens and 14 rabbits each.

For example, there are several chickens and rabbits in the same cage, counting from above, there are 35 heads, and counting from the bottom, there are 94 legs. Q: How many chickens and rabbits are in each cage?

Solution: If there are x rabbits, then there are (35-x) chickens.

4x +2(35-x)=9

Solution: x=12

Chickens: 35-12 = 23 (pcs).

Solution: If there are x chickens, then there are (35-x) rabbits.

There are 100 chickens and rabbits with a total of 280 legs, how many chickens are there? There is no situation mentioned above in this question, how to write it with equations?

Let's say there are x chickens, well, rabbits have 100-x.

2x+4*(100-x)=280

There are 100 chickens and rabbits with a total of 280 legs, how many chickens are there? There is no situation mentioned above in this question, how to write it with equations?

Let's say there are x chickens, well, rabbits have 100-x.

2x+4*(100-x)=280

Solution: Let the chicken be x x (chicken legs) y (rabbit legs) z (the number of legs) x + y = 280

280 minus (2x times 100z) 80z

80z divided by (4y-2x) 40

40 rabbits and 60 chickens.

Solution 1: Arithmetic.

Suppose it is all rabbits, then there are 4 100 400 (legs) but in fact there are only 280 legs, which is 400 280 120 (legs) because 1 rabbit has 4 2 (legs) more than a chicken, then there is a total of 120 divided by 2 60 chickens, because there are 100 chickens and rabbits, 100 60 40 rabbits.

A: There are 40 rabbits and 60 chickens.

Solution 2: Equation.

Solution: If there are x chickens, then there are 100 x rabbits.

2x＋4（100－x）＝280

2x＋400－4x＝280

4x－2x＝400－280

2x＝120

x 60100 60 40 (only).

A: There are 40 rabbits and 60 chickens.

Or with x rabbits, then there are 100 x chickens.

4x＋2（100－x）＝280

4x＋200－2x＝280

2x＝80x＝40

A: There are 40 rabbits and 60 chickens.

There are chickens and rabbits each have x, y, then.

x+y=100

2x+4y=280

So x=60 y=40

Chickens and rabbits in the same cage is one of the famous mathematical problems in ancient China. About 1,500 years ago, this interesting question was recorded in the "Sun Tzu's Sutra". Here's how it is narrated in the book:

Today there are pheasants and rabbits in the same cage, there are thirty-five heads on the top, and there are ninety-four feet under it.

The meaning of these four sentences is:

There are several chickens and rabbits in the same cage, counting from above, with 35 heads, and counting from below, with 94 legs. Q: How many chickens and rabbits are in each cage?

There's a simplest algorithm for this.

Total number of feet - total number of heads Number of chicken's feet) (Number of rabbit's feet - Number of chicken's feet) = Number of rabbits.

94 35 2) 2 = 12 (number of rabbits) Total number of heads (35) Number of rabbits (12) = number of chickens (23).

Explanation: Let the rabbit and chicken lift both feet at the same time, so that the total number of feet in the cage is reduced by 2, since the chicken only has 2 feet, so there are only two feet left in the cage of the rabbit, and then 2 is the number of rabbits.

Chickens: 35-12 = 23 (pcs). If there are x chickens, then rabbits have (35-x).

2x+4(35-x)=94, the solution is x=23Rabbits: 35 - 23 = 12 (only).

Binary Equation Solution: Let there be x chickens and y rabbits. The system of equations is: x+y=35 2x+4y=94. The solution is x=23 and y=12. A: There are 12 rabbits and 23 chickens.