There are 35 heads and 96 legs in the same cage. How many chickens and rabbits are there?

Suppose there are x chickens and y rabbits,

According to the meaning of the question, chickens and rabbits have 35 heads, and both chickens and rabbits have only 1 head.

Then X+Y=35,

According to the meaning of the question, chicken legs and rabbits have 94 legs, chickens have two legs and rabbits have four legs.

Then prescription set 2X+4Y=94,

By solving this binary linear equation system, we can get X=23, Y= 12.

So there are 23 chickens, 12 rabbits.

Extended data:

Formula for solving the problem of chicken and rabbit in the same cage

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 of rabbits = number of chickens

Formula 3: total number of feet ÷ 2-total number of heads = number of rabbits.

Total number of rabbits = number of chickens.

Formula 4: 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.

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 = chickens, used in the equation).

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