To solve practical problems by using the idea of hypothesis method, we must first assume that the two quantities in the position are the same quantity according to the meaning of the problem, or that the two unknown quantities needed are equal; Secondly, according to the assumptions made, pay attention to what changes have taken place in the quantitative relationship and make appropriate adjustments. If there are multiple quantities in the problem, we should consider grouping some of them and then assuming.
Example 1
When solving the problem of chickens and rabbits in the same cage, it is generally assumed that they are all chickens or rabbits, and then the total number of hypothetical hind legs is calculated, and then compared with the actual number of feet, so as to calculate the number of rabbits or products. It should be noted that when we assume that all chickens are chickens, the number of rabbits is obtained by comparing the number of legs, because the difference between the assumed number of legs and the actual number is caused by the difference in the number of legs of rabbits.
Practice: Mother rabbit can pick 32 mushrooms every day in sunny days and only 22 mushrooms every day in rainy days. She picks 390 mushrooms every day, with an average of 26 mushrooms every day. How many days has it rained these days? (Reference answer: It rained for 9 days)
Example 3
To solve this kind of problem, assume that everything is right, and calculate the difference between all the scores and the actual scores. Divide this difference by the difference between the scores of a correct question and a wrong question, which is equal to the number of wrong questions.
Example 4
Practice: A logistics company delivers 800 vases, and each vase costs 100 yuan. According to the contract, each vase is worth 5 yuan. Every time a vase is damaged, in addition to not giving freight, it also pays half of the vase price, and the actual freight is 3780 yuan. Q: How many vases were damaged? (Reference answer: 4 vases are damaged)
Example 5
The key to solve the problem of chickens and rabbits in the same cage by grouping hypothesis method is to divide the three quantities into two groups Generally, the related quantities are divided into one group, and then assumptions are made between the two groups, and then the total difference is divided by the difference of each group.
Practice: Tickets for 5 yuan, 8 yuan and 10 yuan are sold in the park *** 100 yuan, and the income is 748 yuan, of which the number of tickets for 5 yuan and 8 yuan is the same. How many tickets do you sell for each kind? (Reference answers: 5 yuan 36, 8 yuan 36, 10 yuan 28)