Who can give me some questions and answers about binary linear inequalities (groups), factorization factors and fractional equations below grade 8?

Junior high school mathematics application problem one-dimensional linear inequality 1. The first floor of the hotel has five fewer rooms than the second floor, and there are 48 people in a tour group. If all rooms are arranged on the 1 floor, there are four people in each room, and each room is not enough for five people. If all rooms are arranged on the second floor, with three people in each room, and the room is not enough, then the room will be unoccupied. If there are X rooms on the first floor of a hotel, then the room on the second floor is X+5, and there are 48 people in the tour group. If all rooms are arranged on the 1 floor, with 4 people in each room and not enough for 5 people in each room, then 48/5

So there are six students and 26 books. 4. Solving common problems in equation application: ① Travel problem: travel = speed× time ② Engineering problem: workload = working efficiency× working time ③ Concentration problem: solute solubility = solution quality× concentration solution quality ④ Deposit problem: sum of principal and interest = principal+interest = principal× interest rate× number of periods ⑤ Allocation problem ⑤ Scheme design and optimal scheme selection problem. ⑤ Profit: Profit. Example 1. There is a two-digit number, and its ten digits are 2 larger than the single digits. This two-digit number is between 30 and 50. Find this two-digit number. Analysis: to ask for two digits, first find its ten digits and single digits. Therefore, one digit can be indirectly set to x, and the ten digit is (x+2). These two digits = 10 (x+2)+X, and two inequalities can be listed between 30 and 50. Solution: Let the unit digit of this two-digit number be x, according to the problem, ∵x is a positive integer or 0, the qualified one is X = 1, 2, and the corresponding ten digits are 3,4. So this two-digit number can be 3 1 42. A: This two-digit number is 3 1 or 42. Example 2. (Practical problem) The starting price of city taxis is 7 yuan. When it reaches 5km, the fare will increase by 1km/.20 yuan. (The part less than 1km is calculated as 1km). Now someone takes a taxi from A to B and pays 17.8 yuan. What is the approximate distance from a to b? Analysis: It is known that the distance from A to B must be greater than 5km, because 17.8 yuan >; 7 yuan, if the distance from a to b is xkm, there is a solution: if the distance from a to b is xkm, the answer depends on the question: the distance from a to b is about greater than 13km and not greater than 14km. Example 3. After each issue of junior high school students was released, Xiaogang read it carefully. If he reads five pages a day, he can't finish it in nine days, and there are less than five pages left on day 10. If he reads 23 pages a day, he can't finish it in two days, and there are less than 23 pages left on the third day. How many pages are there in each issue for junior high school students? (Even pages) Analysis: "Can't finish reading" means that some of them are not finished, and "insufficient" means "less than". Solution: Assume that junior high school students have X pages per period. According to the meaning of the question, junior high school students have 48 pages each. Example 4. According to the following conditions, set appropriate unknowns and list binary linear equations or binary linear equations. The sum of (1) 8% of A and 10% of B is 9% of the sum of A and B. (2) The speed of the train is three times that of the car, and the sum of their speeds is 380 km/h. (3) The purchase price of toys A and B is ***55 yuan, and the loss of toy A is/. Analysis: Find out what the unknown of each small question means. If there are several equal relationships, several equations can be listed. If there are two unknowns and only one equation relationship, only one binary linear equation can be listed. If there are two equal relationships, you can make an equation. Solution: (1) If the number of A is X and the number of B is Y, we can get the following results according to the topic: (2) If the speed of the car is x km/h and the speed of the train is y km/h, we can get the following results according to the topic: (3) If the purchase price of toy A is X yuan, the purchase price of toy B is Y yuan, according to the topic. A factory borrows two kinds of loans from the bank. Analysis: Two equivalent relationships were found: loan A+ loan B = 400,000 yuan, loan A interest+loan B interest = 29,500 yuan. Solution: Assume that loan A and loan B are X million yuan and Y million yuan respectively. According to the meaning of the question, the answer is: loan A and loan B are 250,000 yuan and 6.5438+0.5 million yuan respectively. Example 6. (Asking questions) The ticket price to a tourist spot is as follows: the number of ticket buyers is 1 ~ 50, and 5 1 ~ 100, and the per capita ticket price is more than 100. There are two classes A and B in a school in 4 yuan, 4.5 yuan and 5 yuan * * 103 students (in which Class A has more students than Class B). (1) If the two classes are merged, how much can the group purchase tickets save? (2) How many students are there in each class? Analysis: How many people are needed in each class, that is, two unknowns. We need to find two equal relationships: number of people in class A+number of people in class B = 103, number of people in class A+number of people in class B = 486. However, there are three rules for paying tickets. Because the number of Class A is more than that of Class B, the number of Class A is X, and the number of Class B is Y. Y, and x+y= 103, the first case may occur, 5 1≤x≤ 100,1≤ y≤ 50,5/kloc. 100, 1≤y≤50 cannot appear, X >；; 100, y > 100 or 1≤x≤50 and 1≤y≤50 are divided into three cases. Solution: (1) 486-4× 103 = 74 yuan, which can save 74 yuan. (2) There are X students in Class A and Y students in Class B, because X >；; y，x+y= 103a。 If 5 1≤x≤ 100, 1≤y≤50, then B. If 51≤ x ≤100,565438+. 100, 1≤y≤50, then x> 100 and 1≤y≤50 are contradictory. Therefore, there are 58 students in Class A and 45 students in Class B. Example 7. A pool is equipped with a normally open drain pipe at the bottom and several water inlet pipes with the same thickness at the top. Four water inlet pipes are opened, and it takes 5 hours to fill the pool. Two water inlet pipes are opened, and it takes 15 hours to fill the pool. It takes four hours to fill the swimming pool now. How many water inlet pipes should be opened at least? Analysis: We don't know the amount of water injected into the water inlet pipe per hour and the amount of water discharged from the water outlet pipe per hour. If you want to fill the pool in 4 hours, I don't know how many water pipes you need to open. This problem involves three unknowns, so we can eliminate the other two unknowns when solving the equations of one unknown. Solution: Let the water injection amount of each inlet pipe 1 hour be A, and the water displacement of the drainage pipe 1 hour be B. If you want to fill the pool within 4 hours, you need to open x water inlets. According to the meaning of the question, it means ①, 4a-b=6a-3b, then a = b3 instead of ②. Because the number of water pipes can't be a fraction, you need to open at least 5 water inlets within 4 hours to fill the pool. Mock exam (answer time: 30 minutes) 1. A store bought a batch of computers at a purchase price of 7,000 yuan each, hoping to get a gross profit not lower than that of 600 yuan (gross profit = sales price-purchase price), but the higher authorities stipulated that it should not exceed 20% of the sales price. In what range should the sales price of these computers be set? There are many toys for children to play in the kindergarten. Give each child 3 yuan, and there are 77 yuan left. If you give each child 5 yuan, then the last person will get less than 5 yuan. How many toys are there in this kindergarten? How many children? 3. Taxi starting price in a city 10 yuan. After reaching or exceeding 5 km (within 5 km), the fare will be increased by 1km. 2 yuan (the part less than 1km will be calculated as 1km). Now someone takes this taxi to pay the fare from A to B. Shop A and Shop B have 200 exercise books. One day, Store A sold 19 and Store B sold 97. The number of exercise books left in shop A and shop B is equal, so how many exercise books are there in shop A and shop B? Two cyclists drive along the circular lane at a constant speed. When they ride in the opposite direction, they encounter 1 times every 20 seconds. If they ride in the same direction, one person will catch up with the other every 100 second. Suppose the circular track is 400 meters long. What is the speed of each person? 6. A clothing factory wants to produce a batch of sportswear of the same model. It is known that a certain fabric can be made into 2 tops or 3 pairs of pants every 3 meters. At present, this fabric is 600 meters long. Please help me design how to distribute the cloth, so that the sportswear can be complete and not wasted. How many sets of sportswear can you produce?

The answer is 1. Not less than 7600 yuan, not more than 8750 yuan. 2. There are 39 people, 194 toys, or 40 people, 197 toys, or 4 1 person, and 200 toys. 3. More than or equal to 10km and less than 1 1km 4. A store 6 1 copy, B store 139, 5 copies. 12m/s, 8m/s, 6. Coat 360 m, pants 240 m, *. There are two kinds of application problems in linear inequalities: (1) problem contains an unknown number, and the result is to find an unknown number; (2) If the problem contains multiple unknowns, find out one or more unknowns; The (1) problem contains an unknown number, and the result is an unknown number. Example 1: 2 times 5 of a number is not more than 3 times less than 4, so what is the range of this number? Analysis: there is only one unknown number in this question, that is, a certain number, which can be set as an inequality according to the meaning of the question. Solution: Let this number be X2x+5.