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About 1500 years ago, Sun Tzu, a great mathematician, recorded such a question in Sun Tzu's Mathematical Classics: "Today, there are young rabbits in the same cage, with 35 heads above and 94 feet below. Ask the rabbits about their geometry? " These four sentences mean: there are several chickens and rabbits in the same cage, counting from the top, there are 35 heads; It's ninety-four feet from the bottom. How many chickens and rabbits are there in each cage? Students, can you answer this question? Do you know how Sun Tzu solved the problem of "chickens and rabbits in the same cage"?

It turned out that Sun Tzu put forward a bold idea. He assumed that if you cut off half the feet of every chicken and rabbit, then every chicken would become a "chicken with one leg" and every rabbit would become a "rabbit with two legs". In this way, the feet of "chicken with one leg" and "rabbit with two legs" changed from 94 to 47; The ratio of the number of heads and feet of each "chicken" becomes 1: 1, and the ratio of the number of heads and feet of each "rabbit" becomes 1: 2. Therefore, if there is a "two-legged rabbit", the number of feet will be more than the number of heads 1. Therefore, the difference between the number of feet and the number of heads of a chicken with one leg and a rabbit with two legs is the number of rabbits, that is, 47-35 = 12 (only); The number of chickens is 35- 12 = 23 (only).

Of course, this problem can also be solved by equations. We can first assume that the number of rabbits (that is, the number of rabbits) is X, because "the head of a chicken+the head of a rabbit =35", so "the head of a chicken =35-x". Therefore, if there are x rabbits, there should be 4x rabbit feet, and the number of chickens is (35-x), so there should be 2x (35-x) chicken feet. Now it is known that the total number of feet of chickens and rabbits is 94, and the following relationship can be listed:

4x+2×(35-x)=94

x= 12

So it can be calculated that the number of chickens is 35- 12=23.

Another problem is this: "100 monks eat 100 steamed buns." One big monk eats three, and three little monks eat one. How many monks are there? "Its answer is that there are 25 big monks and 75 little monks. Do you know how to calculate?

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