(3+V) ×10 ÷ (V-3) ÷10 (3+V )×10 ÷ (V-3) ÷12 Solution: V. P54 page solution: Assume that the merchant sets the selling price at least X yuan. 1.5 ≤ (100%-5%) x1.5 ≤ 0.95xx ≥1.5789 A: If the seller's price is at least1.5789 58 yuan, the loss can be avoided. 9. There were 280 people in a factory the year before last, but 40 people were reduced after the structural reform last year. The annual profit of the whole plant will increase by at least 6,543,800 yuan, and the per capita profit will increase by at least 6,000 yuan. What was the profit of the whole factory the year before last? Solution: Let's assume that the profit of the whole factory in the previous year was X million yuan. P55 Page X ÷ 280+0.6 ÷ (x+100) ÷ (280-40) 6x+1008 ÷ 7 (x+100)-X. In 2002, the proportion of days with excellent air quality (above Grade II) in Beijing reached 55%. If the proportion exceeds 70% by 2008, how many days with good air quality will increase in 2008 at least compared with 2002? (Calculated as 365 days per year) P55 page solution: Suppose that the number of days with good air quality in 2008 is at least X days more than that in 2002. X ≥ 365× (70%-55%) x ≥ 365×15% x ≥ 54.75a: The number of days with good air quality in 2008 was at least 55 days more than that in 2002. 1 1. has a two-digit number. If its single digit A and ten digit B are reversed, under what circumstances will the two digits be larger than the original two digits? When do you get two digits smaller than the original two digits? When did you get two digits equal to the original two digits? P55 page solution:10a+b-10b+a (1)10b+a-10a+b (2)10a+b = 65438. ∴ (1), when a b, the obtained two digits are larger than the original two digits (2), when b a, the obtained two digits are smaller than the original two digits (3), when b=a, the obtained two digits are equal to the original two digits (12), a. Xiaoming got more than 90 points in the exam. He should at least answer a few questions correctly. P55 page solution: Suppose he got at least X questions correctly. 10x-(20-x)×5 ~ 90 10x- 100+5x ~ 90 15x ~ 190 x ~ 10。 The merchant claims that the gold content is not less than 90%, and the densities of gold and silver are 19.3g/cm3 and 10.5g/cm3 respectively. List inequalities and point out what conditions the volume of this kind of jewelry should meet. P56 (hint: mass = density× volume) Solution: V ￠ 0.9a19.3+0.1a10.5 ◆14, two stores, A and B, sell the same goods at the same price. After the accumulative purchase of 50 yuan goods in Store B, the re-purchased goods will be charged at 95% of the original price. How can customers choose a store to get a bigger discount? P56 page solution: let the customer's consumption amount be X yuan A100+(X-100) X 0.9b50+(X-50) X 0.95 ∴ A100+(X-660x) P60 Page Solution: Let Li Yong read (X+3) pages every day. Tension: read X pages 7x ~ 98 (1) 7 (x+3) ~ 98 (2) x ~14 (1) x ~1every day. 16, three teams plan to produce 500 products on 10 (the daily output is unchanged), and the task cannot be completed at the original production speed; If each team produces more 1 product every day than before, it can finish the task ahead of schedule. How many products did each group initially produce every day? P60 Page Solution: Assume that each group originally produced X products per day. 3x× 10￠500( 1)3(x+ 1)× 10￠500(2)x￠50/3( 1)x￠。
17. The price of a commodity is 150 yuan, and the profit that a merchant can get from selling a commodity is 10% ~ 20% of the purchase price. What is the range of purchase price (accurate to 1 yuan)? P62 Page Solution: Set the purchase price of X yuan. x+ 10% x = 150( 1)x+20% x = 150(2)x≈ 136( 1)x = 125(。 ◆ 18, pumping with a type A pump that can pump 1. 1 ton of water per minute can be finished in half an hour; If B-type pump is used, it is estimated that it will take 20 to 22 minutes to finish pumping. How many tons of water does type B pump pump per minute more than type A pump? Solution on page P63: Set a B-type water pump to pump X tons of water every minute. 20≤ 1. 1×30/X≤22 20X≤ 1×30 22X≥ 1. 1×30 20X≤33 22X≥33 X≤ 1.65 X≥ 1.5
∴1.5 ≤ x ≤1.651.5-1= 0.65-1.1= 0.55: ∴0.4≤Y≤0.55 A: Compared with the A pump, how much 0.4 ~ 0.55 tons of water is pumped per minute by the B pump? ◆ 19. Distribute some books to several students. If each student is divided into three books, then the remaining eight books; If each student in front gets 5 copies, then the last student gets less than 3 copies. How many books are there? How many students are there? Solution on page P64: Suppose there are X books and Y students. 3y+8 = x (1) 5 (y-1)+3 = x (2) Solution: 3Y+8=X (1)5Y-X =2 (2). (2)-( 1) 2Y= 10 Y=5 substitute y = 50% (1)15+8 = xx = 23 ∴ x = 23y = 5a: There are 23 books? There are five students? Solve the equation and apply the problem 1. To transport 29.5 tons of coal, transport it three times by a truck with a load of 4 tons, and transport the rest by a truck with a load of 2.5 tons. How many times will it take to complete? Solution: suppose it takes x times to complete. 29.5-3× 4 = 2.5x17.5 = 2.5xx = 7 A: It takes seven times to complete. 2. The trapezoidal site covers an area of 90 square meters, with an upper bottom of 7 meters and a lower bottom of 1 1 meter. How high is it? Solution: Its height is x m x (7+11) = 90 * 218x =180x =10 and its height is 10 m 3. A workshop plans to produce 5480 parts in April. It has been in production for 9 days, and 908 more are about to complete the production plan. How many pieces will be produced on average every day in these 9 days? In these nine days, the average daily output is X 9x+908=5408 9x=4500 x=500. During these nine days, an average of 500 were produced every day. 4. The two cars of Party A and Party B walked in opposite directions at the same time from two places 272km apart. After three hours, the distance between the two cars was still17km. A travels 45 kilometers per hour, and B travels how many kilometers per hour? B travel x kilometers per hour (45+x)+17 = 272 3 (45+x) = 255 45+x = 85 x = 40 b travel 40 kilometers per hour. 5. There are two classes in grade six in a school, and the average score of mathematics last semester is 85. There are 40 students in six classes (1) with an average score of 87. 1. There are 42 students in Class Six (2). What is the average score? The average score is 40 * 87.1+42x = 85 * 82 3484+42x = 6970 42x = 3486x = 83. 6. The school bought 10 boxes of chalk, used 250 boxes, and left 550 boxes. How many boxes are there in each box? On average, there are10x = 250+55010x = 800x = 80 cases per case. There are 200 students in Grade 7 and Grade 4. During extracurricular activities, 80 girls jumped rope. The boys are divided into five groups to play football. How many people are in each group? The average number of people in each group is 5x+80 = 200x = 160x = 32. The average number of people in each group is 32. 8. The canteen brought 150 kg of rice, which was 30 kg less than the flour. How many kilograms of flour does the canteen send? Flour in the canteen x kg 3x-30 =150 3x =180 x = 60 flour in the canteen 60 kg 9. There are 52 peach trees and 6 rows of pear trees in the orchard. There are 20 more pear trees than peach trees. How many pear trees are there in each row on average? There are x pear trees in each row, 6x-52=20 6x=72 x= 12. There are 12 pear trees in each row on average. The area of a triangular plot is 840 square meters, the bottom is 140 meters, and the height is how many meters? The height is x m140x = 840 * 2140x =1680x =12, and the height is 12m 1. Li Shifu bought 72m cloth and just made 20 adult clothes, 65438+. Adult dresses are 2.4 meters each, and how many meters are children's dresses? The fabric for children's wear is16x+20 * 2.4 = 7216x = 72-4816x = 24x =1.5. Mother was six times older than her daughter three years ago. My daughter is 30 = 6 (x-3) 6x-18 = 30 6x = 48 x = 8. Daughter is 8 years old. 13. How long will it take for a car traveling at 50 kilometers per hour to catch up with a car traveling at 40 kilometers per hour that left two hours ago? Need x time 50x=40x+80 10x=80 x=8 need 8 time 14. Xiaodong went to the fruit shop and bought 3 kilograms of apples and 2 kilograms of pears. * * He paid 15 yuan, 1 kg of apples is more expensive than 1 kg of pears in 0.5 yuan. How much are apples and pears per kilogram? Apple 3x+2 (x-0.5) =155x =16x = 3.2 Apple: 3.2 pear: 2.7 15. Two cars, A and B, start from A and B at the same time and face each other. A travels at a speed of 50 kilometers per hour, while B travels at a speed of 40 kilometers per hour. How many hours does it take for A to reach the midpoint? A reaches the midpoint in x hours 50x = 40 (x+1)10x = 40x = 4a reaches the midpoint in 4 hours 16. A and B leave from A and B at the same time, face to face, and meet in 2 hours. If A starts from place A and B goes in the same direction at the same time, then A will catch up with B after 4 hours. It is known that the speed of A is 15km/, and the speed of B is x2 (x+15)+4x = 602x+30+4x = 606x = 30x = 5b and 5 17. Two ropes with the same length, the first one was cut 15m, and the second one was 3m more than the remaining three times of the first one. How long are these two ropes? It turns out that the length of each of the two ropes is xm3 (x-15)+3 = x3x-45+3 = x2x = 42x = 21. Originally, the lengths of the two ropes were 2 1m and 18 respectively. A school bought seven basketballs and 10 football * * and paid 20 yuan. As we all know, the price of each basketball is equivalent to the price of three footballs. How much is basketball and football each? Each basketball is 7x+10x/3 = 248 21x+10x = 744 31x = 744x = 24 each basketball: 24 each football: 8 1, transporting 29.5 tons of coal. How many times will it take to complete? It takes x times to complete 29.5-3 * 4 = 2.5x17.5 = 2.5xx = 7. 2. The trapezoidal site covers an area of 90 square meters, with an upper bottom of 7 meters and a lower bottom of 1 1 meter. How high is it? Its height is x m x (7+11) = 90 * 218x =180x =10. Its height is 10 m3. A workshop plans to produce 5480 parts in April. It has been in production for 9 days, and 908 more are about to complete the production plan. How many pieces will be produced on average every day in these 9 days? In these nine days, the average daily output is X 9x+908=5408 9x=4500 x=500. During these nine days, an average of 500 were produced every day. 4. The two cars of Party A and Party B walked in opposite directions at the same time from two places 272km apart. After three hours, the distance between the two cars was still17km. A travels 45 kilometers per hour, and B travels how many kilometers per hour? B travel x kilometers per hour (45+x)+17 = 272 3 (45+x) = 255 45+x = 85 x = 40 b travel 40 kilometers per hour. 5. There are two classes in grade six in a school, and the average score of mathematics last semester is 85. There are 40 students in six classes (1) with an average score of 87. 1. There are 42 students in Class Six (2). What is the average score? The average score is 40 * 87.1+42x = 85 * 82 3484+42x = 6970 42x = 3486x = 83. 6. The school bought 10 boxes of chalk, used 250 boxes, and left 550 boxes. How many boxes are there in each box? On average, there are10x = 250+55010x = 800x = 80 cases per case. There are 200 students in Grade 7 and Grade 4. During extracurricular activities, 80 girls jumped rope. The boys are divided into five groups to play football. How many people are in each group? The average number of people in each group is 5x+80 = 200x = 160x = 32. The average number of people in each group is 32. 8. The canteen brought 150 kg of rice, which was 30 kg less than the flour. How many kilograms of flour does the canteen send? Flour in canteen x kg 3x-30 =150 3x =180 x = 60 flour in canteen 60 kg 9. There are 52 peach trees and 6 rows of pear trees in the orchard. There are 20 more pear trees than peach trees. How many pear trees are there in each row on average? There are x pear trees in each row, 6x-52=20 6x=72 x= 12. There are 12 pear trees in each row on average. The area of a triangular plot is 840 square meters, the bottom is 140 meters, and the height is how many meters? The height is x m140x = 840 * 2140x =1680x =12, and the height is 12m 1. Li Shifu bought 72m cloth and just made 20 adult clothes, 65438+. Adult dresses are 2.4 meters each, and how many meters are children's dresses? The fabric for children's wear is16x+20 * 2.4 = 7216x = 72-4816x = 24x =1.5. Mother was six times older than her daughter three years ago. My daughter is 30 = 6 (x-3) 6x-18 = 30 6x = 48 x = 8. Daughter is 8 years old. 13. How long will it take for a car traveling at 50 kilometers per hour to catch up with a car traveling at 40 kilometers per hour that left two hours ago? Need x time 50x=40x+80 10x=80 x=8 need 8 time 14. Xiaodong went to the fruit shop and bought 3 kilograms of apples and 2 kilograms of pears. * * He paid 15 yuan, 1 kg of apples is more expensive than 1 kg of pears in 0.5 yuan. How much are apples and pears per kilogram? Apple 3x+2 (x-0.5) =155x =16x = 3.2 Apple: 3.2 pear: 2.7 15. Two cars, A and B, start from A and B at the same time and face each other. A travels at a speed of 50 kilometers per hour, while B travels at a speed of 40 kilometers per hour. How many hours does it take for A to reach the midpoint? A reaches the midpoint in x hours 50x = 40 (x+1)10x = 40x = 4a reaches the midpoint in 4 hours 16. A and B leave from A and B at the same time, face to face, and meet in 2 hours. If A starts from place A and B goes in the same direction at the same time, then A will catch up with B after 4 hours. It is known that the speed of A is 15km/, and the speed of B is x2 (x+15)+4x = 602x+30+4x = 606x = 30x = 5b and 5 17. Two ropes with the same length, the first one was cut 15m, and the second one was 3m more than the remaining three times of the first one. How long are these two ropes? It turns out that the length of each of the two ropes is xm3 (x-15)+3 = x3x-45+3 = x2x = 42x = 21. Originally, the lengths of the two ropes were 2 1m and 18 respectively. A school bought seven basketballs and 10 football * * and paid 20 yuan. As we all know, the price of each basketball is equivalent to the price of three footballs. How much is basketball and football each? 7x+1 0x/3 = 248 21x+10x = 744 31x = 744x = 24 each basketball: 24 each football: 81,carrying a batch of goods. Now we rent three A-class cars and five B-class cars from this company. If the freight is paid per ton, 30 yuan asks the owner how much: A can load X tons, and B can load Y tons. Then 2x+3y= 15.5 5x+6y=35, x=4 y=2.5, (3x+5y)*30=735 2. Now the price of a commodity is reduced by 10%. In order to keep the total sales amount unchanged, how much is the sales volume increased over the original price? Solution: increase the original price by x% (1-10%) * (1+x%). =1x% =111%In order to keep the total sales amount unchanged, the sales volume increased by11./kloc-0. Solution: Let the original price be X yuan (1-10%) X-40 = 0.5xx = 100 A: The original price is100 yuan. 4. There is 40 grams of salt water with 8% salt. How many grams of salt should be added to make the salt water contain 20% salt? Solution: Assuming that the pure salt is 40*8% when X grams of salt is added, and its concentration is 20% when X grams of salt is added, then (40*8%+x)/(40+X) = 20% (3.2+X)/(40+X). =0.2 3.2+x=8+0.2x 0.8x=4.8 x=6。 So I added 6 grams of salt. In the market, the sales of eggs are priced according to the quantity. A vendor bought a batch of eggs at a price of 0.24 yuan each, but accidentally broke 12 eggs in the process of selling, and the remaining eggs were sold at a price of 0.28 yuan each, making a profit 165438+. How many eggs did the vendor buy? Solution: Suppose the vendor bought X eggs at first. According to the meaning of the question, the equation is listed: (x-12) * 0.28-0.24x =11.28x-3.36-0.24x =1/kloc-0 =/. On average, each person can process 15 Class A parts or 10 Class B parts per day, and two Class A parts and three Class B parts are matched with one set. How many people are arranged to process the A-shaped parts and the B-shaped parts respectively to make the A-shaped parts and the B-shaped parts processed every day just match? Solution: Assuming that it takes X people to arrange production A, there will be (85-x) people to produce B. Because two A parts and three B parts are matched, the number of B parts multiplied by 3 can be equal to the number of B parts multiplied by 2:16 * x * 3 =10 * (85-x) * 2 Solution: x = 7. Hong Guang Electric Company can still make a profit of 20% by selling a certain color TV at 20% of the marked price. It is understood that the purchase price of this color TV is 1996 yuan. So what should the price of this color TV be? Solution: Set the list price to X yuan. 80% x = 1996×( 1+20%)80% x = 2395.2 x = 2994 8。 A store can make a profit of 20% by selling a commodity at 20% of the marked price. If the purchase price of this commodity is per piece in 22 yuan, what is the list price of each commodity? Solution: Set the price to X yuan. 80% x = 22×( 180m+20%)80% x = 26.4 x = 33 9。 On a section of double-track railway, two trains pass head-on. The speed of train A is 20m/s and that of train B is 24m/s. If the total length of train A is 65438+, the solution is: (180+160)/(20+24) = 7.28s/kloc-. Two students, A and B, walk in the same direction from two places five kilometers apart on the same road. A's speed is 5km/h, B's speed is 3 km/h, and a classmate is with a dog. It is known that the speed of the dog is 15km/h, and the total distance that the dog runs in this process is calculated. Solution: first of all, be clear. The meeting time between Party A and Party B is equal to the time for the dog to run back and forth, so the dog's time = the meeting time between Party A and Party B = the total distance/the speed sum of Party A and Party B =5km/(5km/h+3km/h)=5/8h, so the dog's distance = the dog's time * the dog's speed = 5/8h *15km/h = 75/h. The temperature of Xiaohong at the top of the mountain is-1 degree. The temperature at the foot of Liangxiao Mountain is 5 degrees. It is known that the height in this area increases by1100m, and the temperature drops by about 0.6 degrees. How high is this mountain? When the temperature rises by 65438 0 degrees, a metal wire will be extended by 0.002MM; conversely, when the temperature drops by 65438 0 degrees, the metal wire will be shortened by 0.002 mm. 15 degrees. When the wire is heated to 60 degrees and cooled to 5 degrees, what happens to the length of the wire? How much longer is the final length than the original length? Taxi charging methods are as follows: within 4km 10 yuan, the part from 4km to15km per kilometer 1.2 yuan, and the part above15km per kilometer 1.6 yuan. A passenger had to take a taxi to a place 50 kilometers away. (1) How much do passengers have to pay if they don't change trains? (2) If passengers change to a taxi midway, where is it more economical to change? Compare the calculated total cost with (1). It is known that the opening price is 25.35 and the closing price is 27.38. Find the percentage of the increase at the opening and closing. (27.38-25.35) × 100% ÷ 25.35 ≈ 8% The number of ticket buyers is less than 50, 50- 100 or more, and the fare per person is 12 yuan,/kloc. How many people are there in each of the two tours? Because 864 > 8× 100, we know that the total number of the two groups exceeds 100, so the total number of the two groups is 864÷8= 108 (people). Because108×10 =1088. 108×12 =1296 >1kloc-0/42. So the number of people in each group will not exceed 50, nor will it be less than 50, that is, there will be more than 50 people in one group and less than 50 people in the other group. Assuming that both groups are above 50, the development salary will be divided. Actual overpayment1142-1080 = 62 yuan. This is an overpayment for a tour group of less than 50 people. So the number of tour groups is 62 ÷ (12-10) = 365438. When the crew found that some water had entered the ship, and the water was still entering the ship at a constant speed. If 8 people wash water, it will take 5 hours to finish washing; If there are 10 people scouring for water, it will take 3 hours to finish scouring. It will take 2.5 hours to finish washing now. How many people does it take to scour this water area? Answer: 1 1 personal solution: let the total volume of the ship be a, the speed of the ship entering the water be b, and the speed of people scouring the water be c, assuming that it takes 2.5 hours for X people to clean up. 8 * c * 5 =1/2 * a+5 * b (1)10 * c * 3 =1/2 * a+3 * b (2) x * C. Replace b=5c. Year-on-year, we know that when the express train is 2/3, the local train should have gone 6/7*2/3 (that is, 4/7), leaving 3/7, which is the known condition of 180, and the whole journey 180/(3/7) = 420! 3. A bank established a student loan for college students, with an annual interest rate of 6% for a six-year loan, and 50% of the loan interest was subsidized by the state. A college student is expected to repay 20,000 yuan in one lump sum after 6 years. How much can he borrow now? (accurate 1 yuan) answer: suppose the amount he can borrow now is x yuan. 0.5 (0.06x * 6)+x = 20000 0.18x+x = 200001.18x = 20000x ≈16949 4. Extend the edge of △ABC to a/. Similarly, extending the edge △ABC to get the point B 1, extending the edge to get the point C 1, and getting △ a1b1,which is called the first extension, and then △A 1 B65438+. Answer: connect a b1:AC = AC1∴ s △ b1AC = s △ b1AC1:CB. 8+0 = s △ ba1b1= 2s △ ABC ∴ s △ a1b1= 7s △ abc △ a2b2c2 = 7s △ a/kloc. Extend the edge of △ABC to A 1 so that b is the midpoint of the line segment A 1. In the same way, extending the edge BC to get the point B 1 and extending the edge to get the point C 1 is called the first extension. Then expand △A 1 B 1 outward according to the above method to get △A2 B2 C2, and so on to get △ anbcnn, and study the area relationship between △ anbcnn and △ABC. Answer: Let the three angles of triangle ABC be α, β and γ respectively, and draw triangle DEF according to the meaning of the question. Then the three angles of DEF are180-(180-α)/2-(180-β)/2 = (α+β)/2180-(180). /2=(α+γ)/2 There must be α+β <180γ+β <180α+γ <180 in the triangular DEF, so all three angles are less than 90, so the DEF is an acute triangular red, and a copy can be finished in a few minutes. Assuming that the materials can be copied in X minutes, there will be 30x = 30 * (2/5x)+30 * (1+50%) * (3/5x-20), and the materials will have 3,000 words.