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A problem of fraction calculation 4x-8xy + 4Y / 2x-2y
4x-8xy + 4Y / 2x-2y
=(4x^2-8xy+4y^2)/(2x^2-2y^2)
=[4(x^2-2xy+y^2)]/[2(x^2-y^2)]
=4(x-y)^2/2(x+y)(x-y)
=2(x-y)/(x+y)
Two methods are used to calculate: (3xx − 2 − XX + 2) · x2 − 4x
The original formula is 3xx − 2 · (x + 2) (x − 2) x-xx + 2 · (x + 2) (x − 2) x = 3 (x + 2) - (X-2) = 3x + 6-x + 2 = 2x + 8
Zhang Ming finished counting half of a batch of books in four hours, and Li Qiang joined the work of counting the other half of the books. They worked together to count the other half of the books in one hour?
Suppose that it takes Li Qiang x hours to count this batch of books separately. According to the meaning of the title, we get 18 + 1 x = 12, and the solution is: x = 83. After testing, x = 83 is the root of the original equation. Answer: it takes Li Qiang 83 hours to count this batch of books separately
Solving the problem of fractional application
How many grams of water need to be added when 35 grams of salt is used to make a salt solution with 28% salt content?
There are two groups in a workshop, group A and group B. the work efficiency of group A is 25% higher than that of group B. therefore, the time for group A to process 2000 parts is half an hour less than that for group B to process 1800 parts. How many parts are processed by group A and group B each hour?
Team a and team B jointly complete a project. Team B completes the whole project after one day alone, and then the two teams cooperate for two days. It is known that the number of days required for team a to complete the project alone is the number of days required for team B to complete the project alone. How many days are required for team a and team B to complete the project alone?
Dahua shopping mall bought a batch of sportswear for 10 000 yuan, and sold each sportswear for 100 yuan. The profit after all sales is just the money used to buy 200 pieces. How many pieces of these sportswear?
A batch of goods is ready to be transported to a certain place, and three trucks (a, B, c) can be employed. It is known that the volume of goods transported by three trucks (a, B, c) each time remains unchanged, and the goods transported by two trucks (a, b) alone can be completed in two times and a time respectively; if the goods are transported by two trucks (a, c) together for the same number of times, a total of 180 tons are transported by car a; if the goods are transported by two trucks (B, c) together for the same number of times, the goods are transported by car a, Car B transported 270 tons in total
(1) How many times more goods does vehicle B transport each time than vehicle a?
(2) At present, when Party A, Party B and Party C ship the goods together for the same number of times, how much is the freight payable to the owner? (calculated by the freight of 20 yuan per ton)
How many grams of water need to be added when 35 grams of salt is used to make a 28% salt solution?
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Let x g of water be added
(35+X)*28%=35
The weight of salt is 28% of the weight of salt and water
There are two groups in a workshop, group A and group B. the working efficiency of group A is 25% higher than that of group B. therefore, the time for group A to process 2000 parts is half an hour less than that for group B to process 1800 parts. How many parts are processed by group A and group B each hour?
————————————————————————————————————————————
Let B do x per hour, then the efficiency of a is (1 + 25%) x per hour
2000/（1+25%）X+0.5=1800/X
Use the time difference between the two sides of half an hour column equation
Team a and team B complete a project together. Team B completes the whole project after one day alone, and then the two teams cooperate for two days. It is known that the number of days required for team a to complete the project alone is 2 / 3 of the number required for team B to complete the project alone. How many days do team a and team B need to complete the project alone?
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If it takes X days for Party B to complete the project alone, then it takes days for Party A to complete the project alone
(this is actually another equation.)
According to the meaning of the title, we can draw a conclusion
(a complete project is completed in three parts)
∴ ,∴x=6
After testing, x = 6 is the root of the equation, and in line with the meaning
(the application of fractional equation also needs to be tested)
When x = 6, (days)
A: team a and team B need 4 and 6 days respectively to complete the project
Dahua shopping mall bought a batch of sportswear for 10 000 yuan, and sold each sportswear for 100 yuan. The profit from all the sales is just the money used to buy 200 pieces. How many pieces are there in this batch of sportswear?
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There are x pieces of clothes
10000/X*200=100*X-10000
On the left is the money for selling 200 pieces of clothes, and on the right is the profit from selling all the clothes
When a batch of goods is ready to be transported to a certain place, three trucks (a, B and C) can be employed. It is known that the volume of goods transported by three trucks (a, B and C) each time remains unchanged, and the goods transported by two trucks (A and b) alone can be transported in two times and a time respectively; if the goods are transported by two trucks (A and C) together for the same number of times, the goods transported by car a total of 180 tons; if the goods are transported by two trucks (B and C) together for the same number of times, the goods can be transported by car a, Car B transported 270 tons in total
(1) How many times more goods does vehicle B transport each time than vehicle a?
(2) At present, when Party A, Party B and Party C ship the goods together for the same number of times, how much is the freight payable to the owner? (calculated by the freight of 20 yuan per ton)
————————————————————————————————————————————
A transports x tons, B transports y tons, C transports Z tons
Because a and B need 2 A and a times respectively, the total quantity of the goods is 2 ax tons, or 5 tons
Cooperation of Party A and Party C:
(x+z)*180/x=2ax;
Joint transportation of B and C
（y+z)*270/y=ay;
Because 2aX = ay;
So we get the equations:
（x+z）*180/x=2ax;… … … … … … … … （1）
（y+z）*270/y=ay;
2ax=ay；
The equation is as follows
2X = y; and 2x = Z; substituting into (1), we get 2aX = 540
When a, B and C are transported together, the number of times is 2 ax / (x + y + Z),
The weight of the goods transported by the three of them is a: 2aX * x / (x + y + Z);
B: 2aX * y / (x + y + Z);
C: 2aX * Z / (x + y + Z);
A: 2aX * x * 20 / (x + y + Z) yuan;
The shipper shall pay Party B: 2aX * y * 20 / (x + y + Z) yuan;
C: 2aX * Z * 20 / (x + y + Z) yuan;
By substituting 2x = y, 2x = Z, 2aX = 540 into the above formula, we get that
A: 2160 yuan;
B: 4320 yuan;
C: 4320 yuan
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