Example of the problem of chartering a boat 1 In the park, a big boat can take six people and a small boat can take four people. 104 teachers and students rented two boats, which were just full. How many boats and big boats did you rent? Analysis: If everyone rents a boat, they can only take 4× 20 = 80 (people), and some people can't get on the boat. If everyone rents a big boat, they can take 6× 20 = 120 (person),120-104 = 16 (person), leaving16 seats, which is not in line with "just full". Generally speaking, we think of it this way: suppose we rent 20 boats at the beginning, and only 80 people can get on board, and 104-80 = 24 (people) can't get on board. Then change the boat into a big boat, so that you can take 6-4 = 2 (people) every time you change it. If there are several 2 people in 24 people, you need to change the same number of boats into big boats. Formula: (1) Suppose you rent 20 boats, you can take one: 4× 20 = 80 (people) (2) How many people can't get on the boat? 104-80 = 24 (man) (3) How many ships need to be converted into large ships? 24 ÷ (6-4) = 12 (articles) Number of rented large boats 20- 12 = 8 (articles) Number of rented small boats A: Rent large boats 12, and rent small boats 8. This topic can also assume that 20 large ships are rented first and then adjusted. Or suppose that the ship and the boat rent 10 and then adjust. The same characteristics of the above methods are: first, assume a situation, and then divide the difference between the number of people who can take a boat under the assumed situation and the actual total number of people by the number of people who take each boat to get the number of ships that need to be adjusted. We call this kind of topic "hypothetical problem". Practice: 1. Forty-two young pioneers went boating, and one rented seven boats. Each big boat takes 10 people, and each small boat takes 3 people. How many big boats and small boats are rented? (Second solution) 2. There are chickens and rabbits *** 100. If the number of feet of chickens and rabbits is 1 * * * 240, how many chickens and rabbits are there? One RMB * * 37 3.2 yuan and one RMB * * 149 5 yuan. How much is each RMB? Example 2 quiz *** 10. If you answer one question correctly, you will get 10. If the answer is wrong, no points will be given, and 4 points will be deducted. Li Ming answered all the questions and got only 16. How many questions did he answer correctly and wrongly? Analysis: What rules can you find after filling in the following form? Correct answer 109853, missed the total score. We can find that wrong questions can not only get 10 points, but also be deducted 4 points. In fact, the wrong question will lose 10+4 = 14 points. Wrong two questions actually cost 20× 2+4× 2 = 28 (points), and so on. The law of losing points is: (10+4) × number of wrong questions = losing points. Formula: (1) Assuming that all the questions are done correctly, The score should be: 10× 10 = 100 (points) (2) Loss score: 100- 16 = 84 (points) (3 Comprehensive formula: (/kloc-0) When you answer, you often assume one of the numbers first, or assume that one number is equal to another, so that the meaning of the question becomes specific and clear, and it is easy to find the corresponding relationship and solve the problem. Practice: 1. Quiz *** 10, if you answer one question correctly, you will get 10. If you answer one question incorrectly, you will not get a point, but you will be deducted 4 points. Li Ming answered all the questions and got 44 points. He answered several questions correctly. 2. Deliver 2000 cases of glass to the consignor. According to the contract, the glass will be sent to 5 yuan in good condition, and the damaged box will be accompanied by the owner 40 yuan without paying the freight. After the glass is delivered, the payment is 9 190 yuan. How many cases of glass have been damaged? Exercise: 1 There are 40 chickens and rabbits in the cage, with a total of *** 100 legs. How many chickens and rabbits are there? In ancient China, the "hypothetical problem" was also called the "chicken and rabbit in the same cage" problem. There are larks and squirrels on a big pine tree, with a total of *** 15 legs. How many larks and squirrels are there? 3. 74 extra-curricular books were distributed to 18 students who won the first and second prizes in the skipping competition. Each student who won the first prize got 7 books and each student who won the second prize got 3 books. How many students won the first prize and the second prize? 4. There are 30 tractors, large and small, which can cultivate 1620 hectares a day. It is known that each large tractor can farm 60 hectares a day and each small tractor can farm 40 hectares a day. How many tractors are there? 5. Use 50 plastic buckets, just enough for104kg orange juice. If each vat can hold 4 kg of orange juice, then each keg can hold 1 kg of orange juice. How many plastic buckets are there? 6. Three students from Shengli Primary School took part in a math contest with 20 questions. It is stipulated that you get 5 points for a correct answer and 2 points for a wrong answer. Xiao Ming, Xiao Qiang and Liang Xiao all answered 20 questions. Xiao Ming got 86 points, Xiao Qiang got 65 points and Liang Xiao got 44 points. How many questions did the three of them answer correctly? 7. The precision instrument factory entrusted the handling station to transport 200 instruments. Both parties agree that the freight for each set is 18 yuan. If one set is damaged, it will not only be free of freight, but also pay 190 yuan. Results The freight of the handling station was 3 184 yuan. How many instruments were damaged? Seek adoption ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~