Chickens and rabbits are in the same cage, which is one of the famous interesting topics in ancient China. About 1500 years ago, this interesting question was recorded in Sun Tzu's calculation. In the book, it is described as follows: "Today, there are pheasant rabbits in the same cage, with 35 heads on the top and 94 feet on the bottom. What is the geometric figure of pheasant rabbit? " These four sentences mean: there are several chickens and rabbits in a cage, counting from the top, there are 35 heads; It's 94 feet from the bottom. How many chickens and rabbits are there in each cage? Hypothesis: Solution: Suppose that all chickens: 2× 35 = 70 (only) are less than the total number of feet: 94-70 = 24 (only) and their leg difference: 4-2 = 2 (strips) 24 ÷ 2 = 12 (only)-. 4x+2 (35-x) = 944x+70-2x = 942x = 24x =1235-x = 35-12 = 23 A: There are 65,438 rabbits and 23 chickens. In ancient China, Sunzi Suanjing has three volumes, written in the 5th century. This book is easy to understand, and there are many interesting arithmetic problems, such as "chickens and rabbits in the same cage": today, there are pheasants and rabbits in the same cage, with 35 heads above and 94 feet below. What are the geometric shapes of pheasants and rabbits? There are 35 chickens and rabbits in the title. If the rabbit's two front legs are tied with rope as one foot and the two rear legs are tied with rope as one foot, then the rabbit becomes two feet, that is, the rabbit is regarded as a two-legged chicken first. The total number of feet of chickens and rabbits is 35×2=70 (only one), which is only 94-70=24 (only one) less than the 94 mentioned in the question. Now, if you loosen the rope on a rabbit's foot, the total number of feet will increase by 2, that is, 70+2=72 (one). If you loosen the rope on the rabbit's feet, the total number of feet will increase by 2, 2, 2 ... and continue until it increases by 24, so the number of rabbits is 24÷2= 12 (one). Let's sum up the idea of solving this problem: first, suppose that they are all chickens, then according to the total number of chickens and rabbits, we can calculate how many feet there are in the hypothesis. Compare the number of feet obtained by this method with the number given in the question to see how much difference there is. Every two feet difference means 1 rabbit. Divide the difference by two to calculate how many rabbits are in * *. To sum up, the basic formula to solve the problem of chickens and rabbits in the same cage is: number of rabbits = (actual number of feet-number of feet per chicken × total number of chickens and rabbits) ÷ (number of feet per rabbit-number of feet per chicken). Similarly, it can be assumed that all rabbits. We can also use the method of column equation: let the number of rabbits be x and the number of chickens be y, then: X+Y=35, then 4X+2Y=94. After solving this equation, we can get that there are 12 rabbits and 23 chickens.

[Edit this paragraph] Example

1. Teacher Zhang, the head teacher, took 50 students from Class 7, Grade 5 to plant trees. Teacher Zhang planted five trees, three for each boy and two for each girl, making a total of 120 trees. How many boys and girls did he ask? Solution: Suppose there are X boys and (50-X) girls. 3x = 120-5-2(50-x)3x = 1 15-2 * 50+2x3x = 1 15- 100+2x3x = 15。 2. The big oil bottle is 4kg in one bottle, and the small oil bottle is 2 bottles 1kg. The existing 100kg oil contains 60 bottles of * * *. How many oil bottles are there? 1/2 = 0.5 (kg) 4× 60 = 240 (kg) 240-100 =140 (kg)140/(4-0.5) = 40 (units 3. The kitten participated in the math contest, and got 67 points for doing 20 questions, 5 points for doing it right, 0 points for not doing it, and 1 point for doing it wrong. You should know that he did as many wrong questions as he didn't. Please ask the kitten to do a few questions correctly. In this problem, you can set the kitten to do the correct X direction. If (20-X)÷2 is wrong and (20-X)÷2 is not, then multiply the right one by 5 and subtract 1 from the wrong one, which is equal to 67. Equation: 5x-(20-x) ÷ 2x1= 67x =14. There are spiders, dragonflies and cicadas * * 18, and * * has legs of 65438+. Dragonflies have six legs and two pairs of wings; Cicada has six legs, 1 wings). How many are there in each of the three animals? Solution: The equation assumes that the spider is X, the dragonfly is Y, and the cicada is Z, so X+Y+Z =188X+6Y+6Z =182Y+Z = 20, so x=5 y=7 z=6, so the spider is 5.

[Edit this paragraph] Detailed solution

First, the basic problem "Chickens and rabbits in the same cage" is a famous arithmetic problem in ancient China. It first appeared in Sun Tzu's mathematical classics. Many elementary school arithmetic application problems can be transformed into such problems, or solved by its typical solution-"hypothesis method". So we should learn its solutions and ideas. Example 1 How many chickens and rabbits are there? There are 80 in all. Solution: We imagine that every chicken is "golden rooster independent" and stands on one foot; Every rabbit stands on two hind legs like a human. Now, half of the total number of feet appears on the ground, that is, 244÷2= 122 (only). In the number 122, the number of chickens is counted once, and the number of rabbits is equivalent to twice. So, start with 65438+. The above calculation can be summed up as the following formula: total number of feet ÷2- total number of heads = number of rabbits. The above solution is recorded in Sun Tzu's Art of War. How simple it is to find out the number of rabbits immediately by division and subtraction! The number of feet of rabbits and chickens is 4 and 2, respectively, and 4 is twice that of 2. But when other problems are transformed into such problems, the "number of feet" is not necessarily 4 and 2, and the above calculation method will not work. Therefore, we give a general method to solve this kind of problem. Let's also give an example of 1 Suppose 88 rabbits, there are 4 ×. 88×4-244= 108 (only) exceeds 244 feet. Each chicken has (4-2) fewer feet than a rabbit, so * * has chickens (88×4-244)÷(4-2)= 54 (only), which shows what we expected. There are 54 chickens instead of rabbits. Therefore, the formula chicken number = (rabbit foot number × total head number-total foot number) ÷ (rabbit foot number-chicken foot number) can be listed. Of course, we can also imagine that 88 chickens are all "chickens", so * * * has 2×88= 176 (only) feet. 68÷2=34 (only). Explain that 34 of the supposed "chickens" are rabbits, and you can also list the formula rabbit number = (total number of feet-chicken feet × total number of heads) ÷ (rabbit feet-chicken feet). You don't have to use the above two formulas at the same time. Use one of them to calculate the number of rabbits or chickens, and then use the total number.