Knowledge point 1: market economy and discount sales
(1) commodity profit = commodity selling price-commodity cost price (2) commodity profit rate = × 100%.
(3) Commodity sales = commodity sales price × commodity sales volume (4) Commodity sales profit = (sales price-cost price) × sales volume.
(5) If the commodity is sold at dozens of percent of the original price, if the commodity is sold at 20%, it will be sold at 80% of the original price (0.8 times of the original price).
1. A shop increased the purchase price of a bicycle by 45%, then marked the price and sold it at a 20% discount. As a result, every bicycle still earned 50 yuan. What is the purchase price of each bicycle? If the purchase price of each bicycle is X yuan, then the equation listed is ()
a . 45%×( 1+80%)x-x = 50 b . 80%×( 1+45%)x-x = 50
C.x-80%×( 1+45%)x = 50d . 80%×( 1-45%)x-x = 50
When a shop opens, in order to attract customers, all goods are sold at a 20% discount. It is known that when 60 yuan buys a pair of leather shoes, the profit rate of the merchants after 20% discount is 40%. What's the price of this kind of leather shoes? What's the preferential price?
3. A store increased the purchase price of a certain clothing by 40%, then marked it and sold it at a 20% discount. As a result, each piece of clothing still earned 15 yuan. What is the purchase price of each piece of clothing?
4. The purchase price of a commodity is 800 yuan, and the price at the time of sale is 1200 yuan. Later, due to the backlog of this product, the store was prepared to sell it at a discount, but if the profit rate was not less than 5%, it would be discounted at most.
Knowledge point 2: Scheme selection
1. If the vegetables of a vegetable company are directly sold in the market, the profit per ton is 1000 yuan. After rough machining,
Sales, the profit per ton can reach 4500 yuan, after finishing, the profit per ton rises to 7500 yuan. A local company bought 65,438+040 tons of this vegetable. The processing capacity of this company is: vegetables can be processed 16 tons per day if they are refined, and 6 tons per day if they are refined, but the two processing methods cannot be carried out at the same time, depending on the season and so on.
Scheme 1: Roughly process all vegetables.
Scheme 2: Vegetables should be coarsened as much as possible and sold directly in the market before processing.
Scheme 3: Sort out some vegetables and roughly process the remaining vegetables in exactly 15 days.
Which scheme do you think is the most profitable? Why?
2. A mobile communication company in a city has started two kinds of communication services: users of "GSM" pay the basic fee of 50 yuan first, and then
Pay the phone bill every 1 minute, 0.2 yuan; "Shenzhouxing" doesn't pay the monthly basic fee, and 1 minute needs to pay 0.4 per call.
Yuan (here refers to the local telephone). If you talk for x minutes a month, the cost of the two ways of talking is y 1 yuan and y2 respectively.
Yuan.
(1) Write the functional relationship between y 1, y2 and x (i.e. equation).
(2) How many minutes do you talk a month, and the cost of the two ways of talking is the same?
(3) If someone expects to use the phone bill of 120 yuan within one month, which call mode should he choose?
3. A home appliance store plans to buy 50 TV sets from manufacturers, with a cost of 90,000 yuan. It is known that this manufacturer produces three different models of TV sets, with ex-factory price of A 1, 500 yuan, B10,000 yuan and C/2,500 yuan.
(1) If the appliance store buys 50 sets of two different models of TV sets at the same time, which costs 90,000 yuan, please study the purchase scheme of the store. New lesson-the first net.
(2) If a shopping mall sells a model A TV set with a profit of 150 yuan, a model B TV set with a profit of 200 yuan and a model C TV set with a profit of 250 yuan, and buys two different TV sets at the same time, which scheme is the most profitable?
Xiaogang bought a lamp for the study. There are two kinds of lamps to choose from, one is 9-watt energy-saving lamp, the other is 40-watt incandescent lamp, 18 yuan/lamp. Assuming that the lighting effect of the two lamps is the same, the service life can reach 2800 hours. It is understood that the electricity price of Xiaogang's home is 0.5 yuan per kWh.
(1). If the lighting time is x hours, please use the algebraic formula containing x to indicate the cost of using energy-saving lamps and incandescent lamps respectively. (Cost = price of lamps+electricity fee)
Xiao Gang wants to buy two such lamps. Suppose the lighting time is 3000 hours and the service life is 2800 hours. Please design a lighting scheme with the lowest cost and explain the reasons.
5. The basic price of electricity for residents in a certain area is 0.40 yuan per kWh. If the monthly electricity consumption exceeds one kilowatt hour, it will exceed.
The excess is charged at 70% of the basic electricity price. (1) In August, a household used 84 degrees of electricity, and * * * paid 30.7 2 yuan for electricity, so find A.
(2) If the average electricity bill of users in September is 0.36 yuan, how many kWh will be used in September? How much should I pay for the electricity?
Knowledge point 3: engineering problems
Workload = working efficiency × working time = workload ÷ working time
Working hours = workload ÷ work efficiency = sum of workload to complete a task = total workload = 1
1. A job is completed by Party A alone 10 days and Party B alone for 8 days. How many days does it take for two people to cooperate?
2. For a project, it takes 15 days for Party A to do it alone and 12 days for Party B to do it alone. Now that Party A and Party B have cooperated for three days, Party A has other tasks, and the remaining projects will be completed by Party B alone. How many days does it take Party B to complete all the projects?
3. A reservoir has two water inlet pipes A and B and a drain pipe C, which can be filled only by opening pipe A for 6 hours; The cell can be filled by opening tube B for 8 hours and tube C for 9 hours. If tube A and tube B are opened for 2 hours at the same time, how many hours can the pool be filled after opening tube C?
4. A batch of latest industrial dynamic information is input into the management storage network. Party A does it for 6 hours, Party B does it for 4 hours, and Party A does it first.
30 minutes, and then Party A and Party B do it together. How many hours does it take for Party A and Party B to finish this work together?
5. There are 16 workers in a workshop, and each person can process 5 A parts or 4 B parts every day. Of these 65,438+06 workers,
Some people process type A parts, while others process type B parts. It is known that each type A part can make a profit 16 yuan.
24 yuan can make a profit for each type B part. If this workshop is profitable 1440 yuan, how many workers will process it this day?
Part one.
Knowledge point 4: Travel problems
Relationship between basic quantities: distance = speed × time = distance/speed/speed = distance/time.
(1) Encounter problem (2) Tracking problem
Fast spacing+slow spacing = original spacing Fast spacing-slow spacing = original spacing
(3) Navigation problem: downstream (wind) speed = still water (wind) speed+current (wind) speed.
Current (wind) speed = still water (wind) speed-current (wind) speed
Grasp the characteristics of constant distance between the two terminals, constant current speed and constant ship speed (static speed).
The distance between 1.a station and bilibili is 480 kilometers. The local train departs from Station A at a speed of 90km per hour, and the express train departs from bilibili at a speed of140km per hour. The key to this problem is to understand the meanings of opposite direction, opposite direction and same direction. , and understand the driving process. So it can be combined with graphic analysis. )
(1) The local train starts first 1 hour, and the express train starts again. The two cars are driving in opposite directions. How many hours after the express train leaves, will the two cars meet?
(2) After two cars started at the same time and walked in opposite directions for several hours, the two cars were 600 kilometers apart?
(3) Two cars start at the same time, and the local train runs in the same direction behind the express train. How many hours later, the distance between the express train and the local train is 600 kilometers?
(4) Two cars leave in the same direction at the same time, and the express train is behind the local train. How many hours will the express catch up with the local train?
(5) After the local train 1 hour, the two cars are driving in the same direction, and the express train is behind the local train. How many hours after the express train leaves, will it catch up with the local train?
2. A ship went downstream from A to B, and then returned to C between A and B, sailing for 7 hours. It is known that the speed of this ship in still water is 8 km/h, the current speed is 2 km/h, and the distance between A and C is 10 km. Find the distance between a and b. ..
A train must cross the first and second iron bridges at a speed of 600 meters per minute. It takes 5 seconds longer to cross the second iron bridge than the first one, and knowing that the length of the second iron bridge is 50 meters shorter than that of the first one, try to find the length of each iron bridge.
4. It is known that the distance between Party A and Party B is 120km, and the speed of Party B is faster than that of Party A 1km. Two hours later, Party A will depart from Party A, and Party B will meet Party A in 10 hour. What is the speed of Party A and Party B?
Knowledge point 5: Numbers.
(1) Need to know the representation method of numbers: the hundredth digit of a three-digit number is A, the tenth digit is B, and the first digit is C (where A, B and C are integers, 1≤a≤9, 0≤b≤9, and 0≤c≤9), then this three-digit number is represented as: 65438. Then grasp the relationship between numbers or between new numbers and original numbers, and find the equation of equal relationship series.
(2) Some representations in the number problem: the relationship between two consecutive integers, the larger one is larger than the smaller one1; Even numbers are represented by 2n, and continuous even numbers are represented by 2n+2 or 2n-2; Odd numbers are represented by 2n+ 1 or 2n- 1.
1. A three-digit number, the sum of the numbers on the three digits is 17, the number on the hundredth digit is 7 larger than the number on the tenth digit, and the number on the digit is 3 times that of the tenth digit. Find this three-digit number
2. A two-digit number, the number of one digit is twice that of ten digits. If the number of ten digits is reversed with the number of one digit, the obtained two digits are 36 larger than the original two digits, so find the original two digits.
Knowledge point 6 savings and savings interest.
(1) The money deposited by the customer in the bank is called the principal, and the reward paid by the bank to the customer is called interest. Principal and interest are collectively referred to as the sum of principal and interest, the time of deposit in the bank is called the number of periods, and the ratio of interest to principal is called the interest rate. Interest tax is paid at 20% of interest.
(2) Interest = principal × interest rate × sum of principal and interest in each period = principal+interest tax = interest × tax rate (20%)
(3)
1. A classmate deposited 250 yuan in the bank at one time for half a year. After half a year, * * * got the principal and interest and 252.7 yuan. What is the annual interest rate of the bank for half a year? (excluding interest tax)
Xiaogang's father bought a two-year bond of a company for 4500 yuan the year before last, and it will expire this year. After deducting interest tax, * * * will get capital.
The interest is about 4700 yuan. What is the annual interest rate of this bond (accurate to 0.0 1%)?
He bought a one-year bond with a few yuan, with the annual interest rate of 10%. After the maturity, he took out half of the principal for shopping, and the remaining half and the interest earned all bought this one-year bond (the interest rate remained unchanged). After the maturity, I got the principal and interest and 1320 yuan. Ask uncle Zhang how much it cost to buy this bond.
Knowledge point 7: the law of equivalence relation in some application problems
(1) Sum, Difference, Multiplication and Division. These problems can represent both operational relations and equal relations. Pay special attention to the meaning of keywords in the topic, such as equality, sum difference, multiple, score, more, less, fast, slow and so on. , can guide us to list algebraic expressions or equations correctly. Growth amount = original amount × growth rate cash amount = original amount+growth amount
(2) Equal product deformation problem
The formulas for calculating the area, volume and perimeter of common geometric figures vary with shapes, but the volume remains unchanged.
① Formula of cylinder volume V= bottom area × height = s? h= r2h
② cuboid volume v = length× width× height = =abc
1. The grain in one grain depot is three times that in the second warehouse. If 20 tons are taken from the first warehouse and put into the second warehouse, the grain in the second warehouse is the first. How much food is there in each warehouse?
2. Pour the water in a cuboid iron box filled with water with the length, width and height of 300mm, 300mm and 80mm respectively into a cylindrical bucket with the inner diameter of 200mm, and just fill it to find the height of the cylindrical bucket (accurate to 0. 1mm, ≈ 3. 14).