1. A bucket of water can be filled with 10 bowl or 12 cup, and 5 cups of water and 3 bowls of water can be poured into an empty bucket. What is the height of the water?
Bowl110, cup112,112 * 5+110 * 3 = the answer.
2. It takes 20 days for Party A to complete a project alone, and 30 days for Party B.. After Party A works alone for 5 days, how many days does Party B need to complete the task?
(1-1/20 * 5)/(1/20+1/30) = answer.
3. The number of people in one class who participate in the foreign language group accounts for 3/7 of the whole class, the number of people who participate in the math group accounts for 1/6 of the whole class, and the number of people who participate in at least one group of foreign languages and mathematics accounts for 1/2 1 of the whole class, and the number of people who participate in both groups accounts for a fraction of the whole class.
3/7+ 1/6- 1 1/2 1= 18/42+7/42-22/42=3/42= 1/ 14
The number of participants in both groups accounts for114 of the class.
4. 480 movie tickets. If you give it to the fifth-grade students first, the rest can only be given to half of the sixth-grade students. If it is given to the sixth grade, the rest to the fifth grade and the rest to the fifth grade, then the students in the fifth grade 1/3 will not get tickets. How many students are there in Grade Five and Grade Six?
Solution: There are X students in Grade Five and 2 (480-X) students in Grade Six.
Grade 6, grade 2(480-X) students, grade 5 [480-2(480-X)] divided by two thirds.
X+2 (480-x) = 2 (480-x)+[480-2 (480-x)] divided by two thirds.
X=360 ............. Grade 5
2 (480-x) = 2 * (480-360) = 2 *120 = 240 Grade 6 in ...............
5. It takes 3 minutes for Party A, 3.5 minutes for Party B and 4 minutes for Party C to process similar parts. Now add parts like 1825. The three of them process parts at the same time. How many parts will each of them deal with when completing the task?
A's work efficiency 1/3, B's work efficiency 1/3.5=2/7, C's work efficiency 1/4.
The working efficiency is1825 *1/3 =1825/3.
B work efficiency 1825*2/7=3650/7.
C work efficiency1825 *1/4 =1825/4.
This batch of parts1(1/3+2/7+1/4) = 84/73 hours.
Answer 84/73* 1825/3= answer.
B 84/73*3650/7= Answer
C 84/73* 1825/4= answer
6. A project can be completed by Party A for 63 days and then by Party B for 28 days. If both parties cooperate, it will take 48 days to complete. Now A will do it for 42 days, and B will finish it. How many more days will it take?
63 A +28 B =48 (A+B) 3 A =4 A The daily workload is 1\84, and B needs 56 days.
7. A village planted m hectares of corn with a total output of n kilograms; The planting area of rice is p hectares more than that of corn; The total output of rice is twice that of corn. Write the formula representing the yield per unit area of corn and rice. If the denominators of the two formulas are different, divide them!
Corn: the total output is n kilograms, m hectares,
Then: n/m kg per hectare.
Rice: The total output is twice that of corn, which is 2n+q kg.
The planting area is p hectares more than that of corn, which is m+p kg.
Then: 2n+q/m+p kg per hectare.
Corn is n/m kg per hectare, and rice is 2n+q/m+p kg per hectare and then divided equally.
N(m+p)/m(m+p) kg of corn per hectare,
Rice is m(2n+q)/m(m+p) kg per hectare.
9. The school awarded the scholarship of 170 yuan to Zhang San and Li Si, two students who won the prize in the math contest. Zhang San got 2/9, which is equal to Li Si's 1/4. How much money do they each get?
Number of prizes in Zhang Sanzhong *2/9= Number of prizes in Li Si * 1/4.
You can set:
Number of Zhang Sanzhong prizes = 1/4
Number of prizes won by Li Si =2/9
Then:
Number of prizes in Zhang Sanzhong *2/9= Number of prizes in Li Si * 1/4.
1/4*2/9=2/9* 1/4
The ratio of the winning numbers of Zhang San and Li Si is 1/4:2/9=9:8.
And then distribute it in proportion,
170*9/9+8=90 won the third prize.
170 * 8/9+8 = 80 yuan Lisi winning number.
10. It is known that the greatest common factor of two numbers is 4 and the smallest common multiple is 120. How to find these two numbers?
We have an x and a y.
Maximum common divisor 4,
Least common multiple:
4 |X Y
| -
A b
Least common multiple =4*A*B= 120
A*B=30, AB is coprime, so A = 2, B = 15.
X=2*4=8,Y= 15*4=60
So, these two numbers are 8 and 60.
1 1. In the model airplane competition, the proportion of people divided into group A and group B is 7: 8. If eight people are transferred from Group B to Group A, and the number of people in Group B is four fifths (4/5) of that in Group A, how many people are there in the competition?
(specific process)
There are x people in group B and 7/8X people in group A..
X-8=(7/8X+8)*4/5
12. A barrel of salt water weighs 200 kg, and the salt content is 10%. How many kilograms of water should be evaporated to make the salt content reach 16%?
The weight of salt is constant, and the salt is: 200 * 10% = 20kg.
When the salt content is 16%, the total amount is 20/ 16%= 125 kg.
Then the water is evaporated: 200- 125=75 kg.
13. After drinking 25% of a bottle, the bottle weighs 950g. When drinking 50%, the bottle weighs 700g g. How many kilograms are there in drinks and bottles?
Drinking water: 50%-25%=25% weight ratio: 950-700 = 250g.
The total weight of water is: 250/25% =1000g =1kg.
Bottle weight: 950- 1000 * 75% = 200g =0. 2 kg
14. There are two scoring methods for a math contest: the first one gets 5 points for a correct answer, 2 points for a wrong answer, and no points will be deducted for a wrong answer; The second method, give 40 points first, give 3 points for one correct answer, give no points for one wrong answer, and deduct 1 point. A student got 8 1 point for both methods. How many questions are there in this competition?
Answer the X question correctly, don't answer the Y question, and answer the Z question incorrectly.
5x+2y=8 1
40+3x-z = 8 1 gives 3x-z = 4 1.
From 5x+2y = 8 1, we can know that x must be singular.
From 3x-z = 4 1, we know that 4 1+z must be divisible by 3.
When z = 1, x = 14 is irrelevant.
When z = 4, x = 15 and y = 3.
When z = 7, x = 16 is irrelevant.
When Z = 10, X = 17 and Y =-2 are irrelevant.
So this competition has x+y+z= 15+3+4=22 questions.
15. The construction team will build a canal: if 8 meters are built every day, it can be completed 4 days in advance; If it is repaired 8 meters less every day, the completion will be delayed by 4 days. Can you tell me how long this canal is?
Let the specified time be x days.
According to the meaning of the question, the workload of four days is 8[X-4], so one day can be repaired: 2[X-4].
[2(X-4)-8][X+8]=X*2[X-4]
[2X- 16][X+8]=2X^2-8X
2x^2+ 16x- 16x- 128=2x^2-8x
8X= 128
X= 16
That is, the specified time is 16 days, and one day can be repaired: 2*[ 16-4]=24.
Therefore, the total length is: 16 * 24 = 384m.
16. A number is divided by 3, 1, divided by 4, divided by 5, and then divided by 4. What's the smallest number?
The numbers 3, 4 and 5 in the question are pairwise coprime.
Then [4,5] = 20; 〔3,5〕= 15; 〔3,4〕= 12; 〔3,4,5〕=60。
To divide 20 by 3 to get 1, use 20× 2 = 40;
Divide 15 by 4 to get 1, and use15× 3 = 45;
Divide 12 by 5 to get 1, and use 12×3=36.
Then, 40× 1+45× 2+36× 4 = 274,
Because, 274 >; 60, so, 274-60× 4 = 34, which is the number to be found.
17. When a number is divisible by 3, 4, 7 and 5, what is the smallest number?
3, 7 and 8 in the problem are pairwise coprime.
Then [7,8] = 56; 〔3,8〕=24; 〔3,7〕=2 1; 〔3,7,8〕= 168。
In order to divide 56 by 3 to get 1, use 56× 2 =112;
Divide 24 by 7 to get 1, and use 24×5= 120.
Divide 2 1 by 8 to get 1, and use 21× 5 =105;
Then112× 2+120× 4+105× 5 =1229,
Because,1229 >; 168 Therefore, 1229- 168× 7 = 53, which is the number to be found.
18. Divide a number by 5+4, 8+3, 1 1+2 to find the smallest natural number that meets the conditions.
The numbers 5,8, 1 1 in the problem are pairwise coprime.
Then [8,11] = 88; 〔5, 1 1〕=55; 〔5,8〕=40; 〔5,8, 1 1〕=440。
In order to divide 88 by 5 to get 1, use 88× 2 =176;
Divide 55 by 8 to get 1, 55× 7 = 385;
Divide 40 by 1 1 and use 40×8=320.
Then, 176× 4+385× 3+320× 2 = 2499,
Because, 2499 >; 440, so, 2499-440× 5 = 299, which is the number of seeking.
19. There is a classmate in one grade, with 6 people in a row for every 9 people, 2 people in a row for every 7 people and 3 people in a row for every 5 people. How many people are there at least in this grade? (Teacher Lin Ze's topic)
The numbers 9, 7 and 5 in the question are pairwise coprime.
Then [7,5] = 35; 〔9,5〕=45; 〔9,7〕=63; 〔9,7,5〕=3 15。
In order to divide 35 by 9 to get 1, use 35× 8 = 280;
Divide 45 by 7 to get 1, 45× 5 = 225;
Divide 63 by 5 to get 1, and use 63×2= 126.
Then, 280× 6+225× 2+ 126× 3 = 2508,
Because, 2508 >; 3 15, so 2508-3 15× 7 = 303, is the number to be found.
20. There are students in one grade, with five people in a row for every nine people, 1 person for every seven people, and two people for every five people. How many people are there at least in this grade? (Happiness 123 teacher's question)
The numbers 9, 7 and 5 in the question are pairwise coprime.
Then [7,5] = 35; 〔9,5〕=45; 〔9,7〕=63; 〔9,7,5〕=3 15。
In order to divide 35 by 9 to get 1, use 35× 8 = 280;
Divide 45 by 7 to get 1, 45× 5 = 225;
Divide 63 by 5 to get 1, and use 63×2= 126.
Then, 280× 5+225×1+126× 2 =1877,
Because,1877 >; 3 15 Therefore, 1877-3 15× 5 = 302, which is the number to be found.
The story of scientists
Boyle's skeptical chemist
Boyle was born in an aristocratic family in Ireland on1October 25th. My father is an earl and his family is very rich. He is the youngest of the fourteen brothers. Boyle was not particularly smart when he was a child, and he stuttered a little. He doesn't like lively games very much, but he is studious and likes reading and thinking quietly. Received a good education since childhood, and studied in Europe from 1639 to 1644. During this period, he read many natural science books, including the famous book Dialogue between Two World Systems by astronomer and physicist Galileo. This book left a deep impression on him. His later masterpiece The Doubtful Chemist was based on this book.
Due to the war, his father died and his family came down. He returned to China to live in London with his sister in 1644. I started studying medicine and agriculture there. I was exposed to a lot of chemical knowledge and experiments, and soon became a well-trained chemical experimenter and creative theorist. During this period, he organized a scientific society with many scholars and held a weekly seminar, mainly discussing the latest development of natural science and the problems encountered in the laboratory. Boyle called this organization an "invisible university". This society is the predecessor of the famous "Royal Society", and its purpose is to promote the development of natural science. Boyle is an important member of the association. Boyle moved to Oxford on 1654 because the branch of the society was located in Oxford. In Oxford, he set up a well-equipped laboratory and hired some talented scholars as assistants to lead them in various scientific research. Many of his scientific research achievements were obtained here. The epoch-making masterpiece "Skeptical Chemist" is written here. In the genre of dialogue, this book writes four philosophers arguing together. They are skeptical chemists, bardic chemists, medical chemists and philosophers. Bard chemists represent Aristotle's view of "four elements", medical chemists represent the view of "three elements", and philosophers remain neutral in the debate. Here, skeptical chemists have no fear to challenge all kinds of authoritative traditional theories in history, refuting many old ideas with vivid and powerful arguments and putting forward new ones. This book is widely circulated in continental Europe.
Boyle attaches great importance to experimental research. He believes that only experiment and observation are the basis of scientific thinking. He always clarifies his views through rigorous and scientific experiments. In physics, he studied the color of light, the elasticity of vacuum and air, and summarized Boyle's gas law. In chemistry, his research on acid, alkali and indicator, and his discussion on the qualitative test method of salt are quite effective. He was the first chemist to use the juices of various natural plants as indicators. He invented litmus test solution and litmus test paper. He was also the first chemist to give a clear definition of acid and alkali, and divided substances into three categories: acid, alkali and salt. He created many qualitative methods to test salt, such as using copper salt solution to be blue, adding ammonia solution to become dark blue (copper ions and enough ammonia water form copper-ammonia complex ions) to test copper salt; The white precipitate produced by mixing hydrochloric acid and silver nitrate solution is used to test silver salt and hydrochloric acid. Boyle's invention is full of long-term vitality, so that we still often use these oldest methods today. Boyle has also done many experiments in determining the composition and purity of substances, and studying the similarities and differences of substances. A brief review of the history of mineral water experimental research published by 1685 describes a set of methods to identify substances and becomes a pioneer in qualitative analysis.
1668, due to the death of his brother-in-law, he moved to London to live with his sister, and set up a laboratory in his backyard to continue his experimental work. Boyle's work in his later years mainly focused on the study of phosphorus. 1670, Boyle suffered a stroke due to fatigue, and his physical condition was good and bad. When he can't do research in the laboratory, he devotes himself to sorting out the knowledge gained from practice and reasoning for many years. As long as he feels a little light, he goes to the laboratory to do his experiments or write papers for fun. 1680, he was elected president of the royal society, but he refused to accept this honor. Although he was born into a noble family, he devoted his life to scientific research and life. He never married and devoted his life to exploring natural science. 169 165438 On February 30th, the scientist who laid the foundation of chemical science in17th century died in London. Engels once gave him the highest evaluation: "Boyle identified chemistry as science."
Story 2:
Priestley —— Father of Gas Chemistry
Priestley 1733 was born in Leeds, England on March 13, and was raised by poor relatives. He entered the seminary on 175. After graduation, he spent most of his time as a priest, and chemistry was his hobby. He has many works in chemistry, electricity, natural philosophy and theology. He wrote many smug theological works, but it was his scientific works that made him immortal. 1764, when he was 3 1 years old, he wrote the history of electricity. At that time, it was a famous book. Because of its publication, he was elected as a member of the Royal Society at 1766.
1722, when he was 39 years old, he wrote a history of optics. It is also a masterpiece of 18 century. At that time, on the one hand, he served as a priest in Leeds, on the other hand, he began to engage in chemical research. His research on gases is quite effective. He used the generated hydrogen to study the effect of this gas on various metal oxides. In the same year, priestley also burned charcoal in a closed container and found that it could turn one-fifth of the air into carbonic acid gas. After being absorbed by lime water, the remaining gas does not help to burn or breathe. Because he believed in phlogiston, he called this residual gas "air saturated with phlogiston". Obviously, he used charcoal combustion and alkali absorption to remove oxygen and carbonic acid gas from the air and make nitrogen. In addition, he discovered nitric oxide and used it to analyze air. Hydrogen chloride, ammonia, sulfurous acid gas (carbon dioxide), nitrous oxide, oxygen and other gases have also been found or studied. 1766, his experiment and observation of several gases was published in three volumes. This book describes in detail the preparation or properties of various gases. Because of his outstanding achievements in gas research, he is called "the father of gas chemistry".
The most important thing in gas research is the discovery of oxygen. 1774, priestley put mercury soot (mercury oxide) into a glass dish and heated it with a condenser, and found that it quickly decomposed into gas. He thinks that the air has been released, so he collects the generated gas by gas collection and studies it. He found that the gas made the candle burn more brightly, and he felt relaxed and comfortable breathing. He made oxygen, and proved through experiments that oxygen has the properties of combustion-supporting and breathing. However, because he is a stubborn believer in phlogiston, he still thinks that air is a single gas, so he also calls this gas "dephosphorized air". The difference between its nature and the "air saturated with phlogiston" (nitrogen) discovered earlier is only the difference in phlogiston content, so its combustion-supporting ability is also different. In the same year, he visited Europe, exchanged many chemical views with lavoisier in Paris, and told lavoisier about the experiment of decomposing mercury and silver ash with condenser, which benefited lavoisier a lot. Lavoisier just repeated priestley's experiment about oxygen, and linked it with a large number of accurate experimental materials, made scientific analysis and judgment, and revealed the real connection between combustion and air. However, until 1783, when lavoisier's combustion oxidation theory was generally considered to be correct, priestley still refused to accept lavoisier's explanation, insisted on the wrong phlogiston theory, and wrote many articles against lavoisier's opinion. This is an interesting fact in the history of chemistry. A person who discovered oxygen became a person who opposed the theory of oxidation. However, priestley found that oxygen is an important factor in the vigorous development of chemistry. So chemists all over the world still respect Priestley.
179 1 year, he sympathized with the French revolution and made propaganda speeches for the revolution many times, but he was persecuted by some people, his home was copied, and books and experimental equipment were set on fire. He escaped alone and took refuge in London, but it was difficult for him to live in London for a long time. At the age of 6 1, he had to immigrate to the United States. Continue to engage in scientific research in the United States. 1804 is dead. People in Britain and America respect him very much, and England has a full-length statue of him. In the United States, the house where he lived has been built into a memorial hall, and the priestley Medal named after him has become the highest honor in American chemistry.
Story 3:
Madame Curie
Marie Curie (Madame Curie) was a French-born Polish physicist and chemist.
1898, French physicist AntoineHenriBecquerel discovered that uranium-containing substances can emit a mysterious ray, but failed to reveal the mystery of this ray. Mary and her husband Pierrecurie)*** * * both undertook the work of studying this kind of radiation. They separated and analyzed pitchblende under extremely difficult conditions, and finally found two new elements in July 1898 and February 12.
To commemorate her native Poland, she named one element polonium and the other element radium, which means "radioactive substance". In order to prepare pure radium compounds, it took Madame Curie another four years (MarieCuI7e, 1867- 1934) to extract1o0mg of radium chloride from several tons of pitchblende residue, and the relative atomic mass of radium was preliminarily determined to be 225. This simple figure embodies the hard work and sweat of the Curie couple.
1In June, 903, Madame Curie took "Research on Radioactive Substances" as her doctoral thesis and obtained a doctorate in physics from the University of Paris. In June165438+1October of the same year, the Curies were awarded the David Gold Medal by the Royal Society. In February 65438, together with Bekkerel, they won the 1903 Nobel Prize in Physics.
1906, pierre curie died in a car accident. This heavy blow did not make her give up her persistent pursuit. She fought back her grief and redoubled her efforts to complete their beloved scientific career. She continued her husband's lecture at the University of Paris and became the first female professor at the university. 19 10, her famous book on radioactivity was published. She cooperated with Mou and others to analyze pure metal radium and measure its properties. She also measured the half-lives of oxygen and other elements and published a series of important works on radioactivity. In view of the above great achievements, she won the Nobel Prize in chemistry at 19 1 1, becoming the first great scientist to win the Nobel Prize twice in history.
The founder of radiation science, who suffered from scientific hardships, died unfortunately on July 4, 1934 on/kloc-0 because of years of efforts. She devoted her glorious life to the scientific cause of mankind.
I'm sorry that this is all I can find!