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Anonymous users2024-02-071) The origin of chickens and rabbits in the same cage.
Problem solving skills: geometric schematic diagram plus basic formula of stroke.
Example 1: Chickens and rabbits are kept in a cage at the same time, and they are counted, and they have a total of 35 heads and 94 legs. Q: How many chickens and rabbits do you have?
Zhonggong Analysis]:
Method 1: Suppose 35 are rabbits, then there are 35 4 = 140 feet, which is 140-94 = 46 feet more than 94 feetEach chicken has 4-2 = 2 feet less than a rabbit, so there are 46 chickens in total 2 = 23 (chickens).
Method 2: It can also be assumed that 35 are all chickens, then there are a total of 2 35 = 70 (feet), 94-70 = 24 feet less than 94 feet, and each chicken has 4-2 = 2 feet less than rabbits, then there are 24 2 = 12 rabbits.
Conclusion: The basic relationship to solve the chicken-rabbit cage problem is:
If we assume that it is all rabbits, then there is:
Number of chickens = (number of feet per rabbit Total number of chickens and rabbits - actual number of feet) (Number of feet per rabbit - Number of feet per chicken).
Number of rabbits = total number of chickens and rabbits - number of chickens.
If you assume it's all chickens, then there's:
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).
Number of chickens = total number of chickens and rabbits - number of rabbits.
2) The Metamorphosis of Chickens and Rabbits.
Problem solving skills: Identify the chickens and rabbits in the question stem and use the hypothetical method to solve them.
Question type characteristics: The number of indicators and the index headquarters of the two subjects are known, and the number of subjects is found.
Example 2: In a mathematics competition, there are 10 test questions, 6 points are awarded for each correct question, and 2 points are deducted for each wrong question. In the end, Xiaohong scored 44 points, and she did more questions right than wrong.
Zhonggong Analysis]:
Assuming that all 10 questions are correct, then the score is 10 6 = 60 points, which is 60-44 = 16 points more than 44 points, and a correct answer is 6 + 2 = 8 points more than the wrong answer, for a total of 16 8 = 2 questions. 10-2 = 8 correct answers, 8-2 = 6 more answers than incorrect answers.
Example 3: There are 18 spiders, dragonflies, and cicadas, with a total of 118 legs and 20 pairs of wings (spiders have 8 legs; Dragonfly 6 legs, two pairs of wings; Cicadas have 6 legs and a pair of wings), how many dragonflies are there?
Zhonggong Analysis]:
Observing the characteristics of the numbers, dragonflies and cicadas have 6 legs, and only spiders have 8 legs. Therefore, you can start with the number of legs to find the number of spiders. If we assume that all three animals have 6 legs, then the total number of legs is 6 18 = 108 (pieces), and the difference of 118-108 = 10 (pieces) must be due to the undercounting of the number of legs of the spider.
So, there should be (118-108) (8-6) = 5 spiders. In this way, the remaining 18-5=13 (only) is the number of dragonflies and cicadas. Starting from the number of wings, assuming that all 13 are cicadas, the total number of wings is 1 13 = 13 (pairs), which is less than the actual number.
20-13=7 (pairs), this is due to the fact that dragonflies have two pairs of wings, and we only calculate the difference based on one pair of wings, so that the number of dragonflies can be found to be 7 (2-1)=7 (only).
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Anonymous users2024-02-06Hello, is the turtle you gave me today still saved, and I ate well in the morning.
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