2. 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?
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
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.
A store first increases the original selling price of a color TV by 40%, and then writes "big reward, 20% discount" in the advertisement. After the customer dismantled it, the demolition department will impose a fine of 2700 yuan per set according to 10 times of the illegal income, so as to seek the original price of each color TV.
6. If the vegetables of a vegetable company are directly sold in the market, the profit per ton is 1 1,000 yuan; If it is sold after rough machining, the profit per ton can reach 4500 yuan; If it is sold after fine processing, the profit per ton will rise to 7500 yuan. A local company buys this vegetable 1400 tons, and its processing capacity is as follows: if the vegetable is finely processed, it can process 6 tons a day, but the two processing methods cannot be carried out at the same time. Due to seasonality and other conditions, the company must sell or process all these vegetables within 15 days. Therefore, the company has formulated three feasible schemes:
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?
9. An appliance store plans to buy 50 TV sets from manufacturers for 90,000 yuan. It is known that this manufacturer produces three different models of TV sets, with ex-factory prices of A 1.500 yuan, B 2 1.000 Yuan and C 2500 Yuan respectively.
(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.
(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?
10. 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 expression 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.
2.25 a year
2.70 pounds for three years
Six years 2.88
12. In order to prepare for Xiaoming's college tuition of 20,000 yuan six years later, his father has now participated in education savings. There are three ways to save for education:
(1) directly deposited in 6 years;
(2) Deposit for three years first, and after three years, the principal and interest will be automatically transferred to three years;
(3) Deposit for one year, and then automatically transfer the principal and interest to the next year; What kind of education savings do you think will start with less principal?
13. Xiaogang's father spent 4500 yuan the year before last to buy a two-year bond of a company, which will expire this year. After deducting the interest tax, * * * will get the principal and interest of about 4700 yuan. What is the annual interest rate of this bond (accurate to 0.0 1%)?
14. (Haidian District, Beijing) The purchase price of a commodity in Baiyun Shopping Mall is 8 yuan/piece, and the sales price is 10 yuan/piece (the difference between the sales price and the purchase price is the profit obtained by selling a commodity in 2 yuan). Now, in order to expand sales, the sales price of each commodity is reduced by x%, but the profit obtained by selling a commodity is required to be 90% of the profit obtained before the price reduction, then X.
a . 1 b . 1.8 c . 2d . 10
15. He bought a one-year bond with a few yuan, with an 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.
16. A job is completed by Party A alone 10 days, and Party B alone completes 8 days. How many days does it take for two people to cooperate?
17. It takes 15 days for a project to be completed by Party A alone and 12 days for Party B 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?
18. the reservoir has two water inlet pipes a and b and a drain pipe C. You can fill the pool just by turning on the A tube for six 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?
19. A batch of latest industrial dynamic information is input into the management storage network. Party A does it alone for 6 hours, Party B does it alone for 4 hours, Party A does it for 30 minutes first, 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?
20. There are 16 workers in a workshop, and each person can process 5 parts A or 4 parts B every day. Of these 16 workers, some process parts A and the rest process parts B. It is known that each part A can make a profit 16 yuan, and each part B can make a profit in 24 yuan. If this workshop is a * * *.
2 1. It takes Party A 10 days, Party B 12 days and Party C 15 days to do a project alone. After Party A and Party C do it for 3 days, Party A has something to leave and Party B takes part in the work. How many days will it take to complete?
22. Input a batch of latest industrial dynamic information into the management storage network. Party A does it alone for 6 hours, Party B does it alone for 4 hours, Party A does it for 30 minutes first, 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?
22. The grain in one grain depot is three times that in the second. 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?
23. Pour the water in the cuboid iron box with the length, width and height of 300mm, 300mm and 80mm filled with water into the cylindrical bucket with the inner diameter of 200mm, and find the height of the cylindrical bucket (accurate to 0. 1mm, ≈ 3. 14).
24. The length, width and height of cuboid A are 260mm, 150mm and 325mm respectively, and the bottom area of cuboid B is 130× 130mm2. I also know that the volume of A is 2.5 times that of B. What is the height of B?
26. Party A and Party B start from Party A and Party B, which are 5 kilometers apart, and walk in the same direction on the same road. Party A's speed is 5 kilometers per hour, and Party B's speed is 3 kilometers per hour. Party A brings a dog. When A catches up with B, the dog catches up with B first, then returns to meet A, then returns to catch up with B, and repeats in turn until A catches up with B. It is known that the speed of the dog is 15.
27. A ship went downstream from A to B, and then returned to C by countercurrent between A and B, sailing for 7 hours. It is known that the speed of the 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. ..
28. A train must cross the first and second iron bridges at a speed of 600 meters per minute. It takes 5 seconds 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.
29. 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?
30. A group of students went to military training. On the way, the captain has something to inform from the head to the end of the team. The correspondent returns to the end of the queue at the speed of 18 m/min. The known fleet speed is 14 m/min. Q:? If the captain is known to be 320 meters long, how many minutes will the correspondent return? ? If it is known that the correspondent took 25 minutes, how many meters is the captain?
3 1. An airplane flies between two cities with a wind speed of 24 km/h, and it takes 2 hours and 50 minutes to fly with the wind and 3 hours to fly against the wind. What is the flying distance between the two cities?
32. When a ship sails between Pier A and Pier B, it takes 4 hours to sail downstream and 5 hours to sail upstream. The speed of the current is 2 kilometers per hour. Find the distance between terminals a and b ..
33. For a three-digit number, the sum of the numbers on the three-digit number is 17, the number on the hundredth digit is 7 larger than that on the decimal digit, and the number on the single digit is 3 times that on the decimal digit. Find this three-digit number
34. For two-digit numbers, one-digit number is twice as large as ten-digit number. If the number of ten digits is reversed with the number of one digit, then the two digits obtained are 36 larger than the original two digits, so the original two digits are found.
Answer:
1. [Analysis] Through the list analysis of known conditions, the equivalence relation is found.
Purchase price discount rate, preferential price, profit rate
60 yuan is 20% off x 20% off x 40% off.
Equivalence relationship: commodity profit rate = commodity profit/commodity purchase price
Solution: Set the price as X yuan,
Solution: x= 105 preferential price is
2. [Analysis] It is the key to explore the implied conditions in the topic, and the cost can be directly set to X yuan.
Purchase discount rate, bid price, preferential price and profit
Twenty percent off (1+40%) X twenty percent off (1+40%) X 15.
Equivalence relationship: (profit = discount price-purchase price) discount price-purchase price = 15.
Solution: Let the purchase price be X yuan, 80% x (1+40%)-x = 15, X= 125.
A: The purchase price 125 yuan.
3.B
4. Solution: Make X discount at most. According to the meaning of the question, x = 100% = 5% and x=0.7=70%.
A: A maximum of 30% discount.
5. Solution: Let the original price of each color TV set be X yuan. According to the meaning of the question, there are10 [x (1+40%) × 80%-x] = 2700 and x=2250.
A: The original price of each color TV set is 2250 yuan.
6. Solution: Scheme 1: profit 140×4500=630000 yuan.
Scheme 2: the profit is15× 6× 7500+(140-15× 6) ×1000 = 725000 yuan.
Scheme 3: finish machining x tons and rough machining (140-x) tons.
According to the meaning = 15, x=60.
The profit is 60× 7500+(140-60 )× 4500 = 810000 yuan.
Because the third one is the most profitable, we should choose the third one.
7. Solution: (1)y 1=0.2x+50, y2=0.4x 。
(2) y2 with y 1 = 0.2x+50=0.4x is solved as x = 250.
That is, 250 minutes a month, and the cost of the two call methods is the same.
(3) From 0.2x+50= 120, x = 350; from 0.4x+50= 120, x=300.
Because it's 350 & gt300, it's more cost-effective to call for the first time.
8. Solution: (1) From the meaning of the question, we get 0.4a+(84-a)×0.40×70%=30.72, and a=60.
(2) If the electricity consumption in September is X kWh, then 0.40×60+(x-60)×0.40×70%=0.36x is x=90.
So 0.36×90=32.40 (yuan)
A: In September, * * * used 90 degrees of electricity, and the electricity bill payable was 32.40 yuan.
9. Solution: According to the three schemes of buying A and B TVs and B and C TVs, calculate A and C TVs respectively.
If you buy X A-type TVs and Y B-type TVs.
(1)① When buying two kinds of TV sets, A and B, and B buys (50-x) sets, the equation can be obtained.
1500x+2100 (50-x) = 90000, which means 5x+7 (50-x) = 300x = 50x = 25 50-x = 25.
(2) When buying two kinds of TV sets, A and C, C will buy (50-x) sets.
The equation1500x+2500 (50-x) = 90003x+5 (50-x) =1800x = 3550-x =15 can be obtained.
③ When buying B and C TV sets, the C TV set is (50-y).
Equation 2100y+2500 (50-y) = 900021y+25 (50-y) = 900, and 4y=350 is irrelevant.
From this, we can choose two schemes: one is to buy 25 TV sets of A and B respectively; The second is to buy 35 A TV and 15 C TV.
(2) If scheme ① in (1) is selected, the profit can be150× 25+250×15 = 8750 yuan.
If scheme ② in (1) is selected, the profit can be150× 35+250×15 = 9000 yuan.
9000 & gt Therefore, in order to get the maximum profit, choose the second scheme.
10. Answer: 0.005x+49 2000.
1 1. [Resolution] Equivalence relation: sum of principal and interest = principal ×( 1+ interest rate)
Solution: Let the real interest rate for half a year be X, and according to the meaning of the question, the equation 250( 1+X)=252.7, and the solution is X=0.0 108.
So the annual interest rate is 0.0 108×2=0.02 16.
A: The annual interest rate of the bank is 265,438+0.6%.
12. [Analysis] We can calculate the principal of each education savings separately and compare them.
Solution: (1) Suppose the principal of a 6-year deposit is X yuan. According to the meaning of the question, the equation X( 1+6×2.88%)=20000, and the solution X= 17053.
(2) Let the principal deposited at the beginning of two three-year periods be Y yuan, y (1+2.7 %× 3) (1+2.7 %× 3) = 20000, and x =171.
(3) Let the one-year principal deposit be Z yuan, Z( 1+2.25%)6=20000, Z= 17894.
Therefore, saving the principal for six years is the least.
13. solution: according to the meaning of the question, suppose the annual interest rate of this bond is X.
4500+4500× 2××× (1-20%) = 4700, and the solution is x=0.03.
The annual interest rate of this bond is 0.03.
14. C[ Direction: According to the problem sequence equation, it is (10-8) × 90% =10 (1-x%)-8, and the solution is x=2, so c is selected].
15.22 million yuan
16. [Analysis] A works alone 10 days, which shows that his work efficiency is B.
The equivalent relationship is: cooperation efficiency of Party A and Party B × cooperation time = 1.
Solution: let the cooperation be completed in x days, and get the equation according to the meaning of the question.
A: The cooperation between two people was completed in days.
17. [Analysis] Let the total project amount be 1, and the equivalent relationship is: a completed workload +B completed workload = total workload.
Solution: Assume that it takes X days for B to complete all projects, and the total workload is 1.
A:B It will take another day to finish all the projects.
18. 【 Analysis 】 The equivalent relationship is: A water injection quantity +B water injection quantity -C water drive = 1.
Solution: Assume that the pool can be filled in x hours after the C tube is opened.
Judging from the meaning of the question,
A: The pool can be filled in a few hours after opening the C tube.
19. solution: it takes x hours for both parties to complete the work together.
According to the meaning of the question, x+(+) x = 1 Solve this equation, x= =2 hours 12 minutes.
A: It will take two hours for Party A and Party B to complete this work together.
20. Solution: Suppose that there are X workers processing A-type parts on this day, then there are 5x A-type parts and 4 B-type parts on this day. According to the meaning of the question, it is16× 5x+24× 4 (16-x) =18.
A: There are six workers processing Class A parts on this day.
2 1. This will take x days to set up.
22. Establish a second warehouse to store food.
23. solution: let the height of the cylindrical bucket be x mm according to the meaning of the question, what is it? ()2x=300×300×80 x≈229.3
Answer: The height of the cylindrical bucket is about 229.3 mm. 。
24. Set the height of B to
26. [Analysis] The pursuit problem can't directly solve the total distance of the dog, but turns the indirect problem into the pursuit problem of both parties. The total distance a dog runs = its speed × time, and the total time it takes is the time for A to catch up with B.
Solution: Let A catch up with B in X hours and make an equation according to the meaning of the question.
5X=3X+5 gives X=2.5, and the total distance of dogs is 15×2.5=37.5.
A: The total distance of dogs is 37.5 kilometers.
27. [Analysis] This is a navigation problem. In this kind of problem, it is necessary to clarify:
(1) Downstream speed = speed of ship in still water+current speed;
(2) Velocity = the velocity of the ship in still water-velocity. The equivalent relationship is: downstream sailing time+upstream sailing time =7 hours.
Solution: If the voyage between terminals A and B is X kilometers, then the voyage between terminals B and C is (x- 10) kilometers.
Judging from the meaning of the question,
A: The distance between A and B is 32.5 kilometers.
28. Solution: If the length of the first railway bridge is x meters, then the length of the second railway bridge is (2x-50) meters, and the time required to cross the first railway bridge is minutes. It takes several minutes to cross the second railway bridge. According to the meaning of the question, you can list the equations.
+= Solve the equation x+50=2x-50 to get x= 100.
∴2x-50=2× 100-50= 150
Answer: The length of the first railway bridge is 100 meters, and the length of the second railway bridge is 150 meters.
29. Set the speed of armor as X km/h ... rule.
30.( 1) Tell the correspondent to return in x minutes. Then the x-90
(2) Set the captain to x meters. rule
3 1. Let the flight distance between two cities be x kilometers. rule
32. The distance between pier A and pier B is x kilometers. Then. x=80
33. [Analysis] According to the known conditions, the relationship between the number in percentile and the number in unit is given. If the number in the tenth place is X, the number in the hundredth place is x+7, and the number in the unit is 3x, the equivalence relation is that the sum of the numbers in the three digits is 17.
Solution: Let the number in the tenth place of this three-digit number be X, then the number in the hundredth place is x+7, and the number in the unit place is 3x.
X+x+7+3x= 17, and the solution is x=2.
X+7=9, 3x=6 A: This three-digit number is 926.
34. Equivalence relationship: original two digits +36= new two digits after switching.
Solution: Let the number x on the ten digits, then the number on the one digit is 2X.
10× 2x+x = (10x+2x)+36 gives X=4 and 2X=8. A: The original two-digit number was 48.
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