Today, there are pheasant rabbits in the same cage, with 35 heads above and 94 feet below. Pheasant rabbit geometry?
Example: A chicken and a rabbit live in the same cage. They have 22 heads and 70 legs. Excuse me, how many chickens and rabbits are there respectively?
The solution is as follows:
Hypothesis method solves this kind of problem.
Assuming that these 22 animals are all chickens, their number of legs is 22× 2 = 44 (strips), which is 70-22× 2 = 26 (strips) less than the actual number of legs (70). Because each rabbit has four legs, assuming that all animals are chickens and each rabbit lacks 4-2 = 2 (legs), it can be calculated that the number of rabbits is 26 ÷ 2 = 13 (only).
Number of rabbits: (70-22× 2) ÷ (4-2) = 13 (only)
Number of chickens: 22- 13 = 9 (only)
List method to solve this kind of problem
① Assuming that there are 1 chicken and 2 1 rabbit, calculate the total number of legs and fill in the table.
2× 1+4× 2 1 = 86 (strips)
② Adjust according to the change of the total number of legs of chickens and rabbits after hypothesis.
Suppose there are 2 rabbits and 20 chickens, and calculate the total number of legs.
2× 2+4× 20 = 84 (strips)
Suppose there are 3 rabbits and 19 chickens, and calculate the total number of legs.
2× 3+4× 19 = 82 (pieces)
etc ...
(3) Adjust according to the meaning of the question until you get the correct answer.
The following table starts with the assumption that there are 1 chicken and 2 1 rabbit.
Equation method to solve this kind of problem.
According to the meaning of the question, if there are x rabbits, there will be (22-x) chickens. Rabbits have 4x legs and chickens have 2x (22-x) legs.
See the figure below for the solution process.
The above three solutions are summarized as follows:
List method. According to different situations, the method of listing one by one can be adopted. When enumerating, it is necessary to estimate the possible range of the quantity before calculating, which can reduce the number of enumerations, or adopt the method of enumerating in the middle, which is simpler and clearer.
Hypothesis method. Suppose the cage is full of chickens or rabbits, calculate the number of legs, and then compare the calculated number with the actual number. If it is assumed that there are more legs than the actual number, then reduce the number of rabbits. If it is assumed that the legs are less than the actual ones, increase the number of rabbits.
Equation method. According to the meaning of the question, let a chicken or a rabbit be an unknown X, and solve the equation according to the equivalence relation: "The number of legs of a chicken+the number of legs of a rabbit = the total number of legs".