12/2* 10=60 (kg)
7+3= 10
60/ 10*7=42 (kg)
60/ 10*3= 18 (kg)
A: There are 42 kilograms of oil in the barrel.
There is18kg oil in the keg.
2, a barrel of gasoline, the weight of the barrel is 8% of the oil, after pouring out 48 kilograms, the weight of the oil is equivalent to half of the original, how many kilograms of the original oil?
48/( 1-8%*0.5)
=48/96%
=50 kg
Answer: 50 kilograms of crude oil.
* = Multiplication symbol
/= division symbol
Responder: Rebel Elf House-Magic Apprentice 1 Level 2-4 17:50
View user comments (3)>& gt
The evaluation has been closed, and there are currently 2 evaluations.
okay
50% (1) is not good
50% ( 1)
Related content
6? 1 sixth grade Olympic math problem
6? 1 fifth grade Olympic math problem
6? 1 help me calculate this sixth-grade Olympic math problem.
6? 1 sixth grade Olympic math problem
6? 1 Who has a third-grade Olympic math problem?
More related issues >>
Check the same question: the sixth grade Olympic math problem
Other answers *** 1
China's Remainder Theorem "and Its Application: (You can learn and test others)
Why are you doing this? Because 70 is a common multiple of 5 and 7, dividing by 3 is 1. 2 1 is the common multiple of 3 and 7. Divided by 5, the remainder is 1. 15 is a common multiple of 3 and 5. Divided by 7, the remainder is 1. (Any congruence group is not difficult to solve as long as the key figures are obtained according to this law. ) Multiply the three numbers 70,21and 15 by their remainders respectively, and then add up the three products to get 233, which is in line with the meaning of the question, but not the smallest. 105 is the least common multiple of 3,5,7. Remove the multiple of 105, and the remaining difference is the smallest answer.
Solving problems with rhyme is easy to remember, but it has its limitations. It can only be divided by 3, 5 and 7, and it is impossible to be divided by other numbers. Later, mathematicians in China studied this problem again and answered it with the above analysis method.
Example 1: A number divided by 3 is 1, divided by 4 is 2, and divided by 5 is 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.
Example 2: What is the smallest number when a number is divided by 3, 4 by 7 and 5 by 8?
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.
Example 3: Divide a number by 5+4, 8+3, 1 1+2 to find the minimum 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.
Example 4: There is a classmate in a certain grade, with five students for every nine people, one for every seven people 1 student, and two for every five people. How many students 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.
Example 5: There is a classmate in a certain 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.
(Example 5 and Example 4 have the same divisor, so the "number" to be multiplied by each remainder is also the same, but the difference is the last two steps. )
Brief introduction of "China remainder theorem";
There is a question in Sun Tzu's Art of War, China's Classical Mathematics: "The present matter is unknown, and the number of three and three leaves two, the number of five and five leaves three, and the number of seven and seven leaves two. Ask the geometry of things. " In the current words, it is: "There is a batch of goods, three more than two, five more than three, and seven more than two. Ask how many pieces are there in this batch. " The ideas to solve this problem are called "Sun Tzu Problem", "Ghost Valley Calculation", "Partition Calculation" and "Han Xin Point Troops".
So, how to solve this problem? Cheng Dawei, a mathematician in the Ming Dynasty, compiled this solution into four songs:
All three are seventy (70) thin,
Twenty-one (2 1) plum blossoms on five trees,
The first month of seven sons' reunion (15),
Divided by 105 (105).
Every rhyme is a one-step solution: the first sentence refers to dividing the remainder by 3 times 70; The second sentence means that the remainder is divided by 5 times 21; The third sentence means that the remainder is divided by 7 times15; The fourth sentence means that if the sum of the above three products exceeds 105, subtract the multiple of 105 to get the answer. Namely:
70×2+2 1×3+ 15×2- 105×2=23
Although the topic of "I don't know the number of things" in Sunzi Suanjing pioneered the study of congruence, it has not yet risen to the height of a whole set of calculation procedures and theories because the topic is relatively simple and can be obtained even if you try to guess. Qin, a mathematician in the Southern Song Dynasty, really solved this problem from a complete set of calculation programs and theories. Qin put forward a mathematical method, "Finding the Skill by the Great Circle Method", in the book "Nine Chapters of Several Books" written in A.D. 1247, and systematically discussed the basic principle and general procedure of the solution of a congruence group.
The research results of a congruence problem, from the mathematical classic of Sun Tzu's Art of War to Qin's mathematical work Nine Chapters, began to attract the attention of western mathematics circles in the middle of19th century. 1852, British missionaries introduced the topic of "I don't know how to count things" in Sun Tzu's The Art of War and Qin's Seeking Skills. 1876, German Mattison pointed out that China's solution was completely consistent with the solution of the first congruence group in Gauss's arithmetic query in19th century. Since then, China's creation of ancient mathematics has gradually attracted the attention of scholars all over the world, and it has been officially called "China's remainder theorem" in western works on the history of mathematics.
There are still some test questions.
Sixth grade Olympic math test questions
(Write a detailed solution for each problem)
1. The sum of three numbers is 555. These three numbers can be divisible by 3, 5 and 7 respectively, and the same is true for manufacturers. Find these three numbers.
2. It is known that A is a natural number, which is a multiple of 15, and there are only two numbers in it: 0 and 8. What is the minimum quantity of a?
3. Arrange natural numbers into the following array:
1,2,4,7,…
3,5,8,…
6,9,…
10,…
…
Now it is stipulated that the horizontal line is a row and the vertical line is a column. ask
What is the number in the fifth column of (1) 10?
(2) What is the number in column 10 in line 5?
(3) In which row and column was it ranked in 2004?
4. The product of three prime numbers is exactly equal to 1 1 times of their sum. Find these three prime numbers.
5. There are two integers, the sum of which happens to be two numbers with the same number, and the product of which happens to be three numbers with the same number. Find these two integers.
On the 6.800-meter roundabout, a colorful flag was inserted every 50 meters, and later some colorful flags were added to shorten the interval of colorful flags, and the colorful flags at the starting point did not move. After re-plugging, I found that the colorful flags on all sides did not move. How many meters are the intervals of colored flags now?
7. 135 1 1, 13903, 14589 divided by the natural number m, the remainder is the same. What is the maximum value of m?
8. 1 to 200 How many natural numbers are not divisible by any of 2, 3 and 5?
9. There is a list of numbers: 1, 999,998, 1, 997,996, 1, … Starting from the third number, each number is the difference of the first two numbers. Find the sum of 999 numbers from number 1 to number 999.
10.200 to 1800 How many natural numbers have odd divisors?
1 1. In the figure below, there are two isosceles right triangles with the same area, both of which are 100. Cut two small squares along the dotted line in the picture. Please find the area of each square and compare the sizes.
12. Party A said, "I have 100 yuan with Party B and Party C." Party B said, "If Party A's money is six times as much as it is now, my money is13, and Party C's money remains unchanged, the three of us still have 100 yuan." C said, "My money is not even 30 yuan." Ask them how much money each of them has.
13. Two people are going to explore the desert. They go deep into the desert for 20 kilometers every day. It is known that each person can carry one person's food and water for up to 24 days. If some food is not allowed to be stored on the way, how many kilometers can one of them go deep into the desert (the last two have to return to the starting point)? What if some food can be stored on the way back?
14. Bonuses are divided into first prize, second prize and third prize. The bonus of each first prize is twice that of each second prize, and the bonus of each second prize is twice that of each third prize. There are two people in the first, second and third prizes, and each first prize is 308 yuan; If there are/kloc-0 first prize, 2 second prizes and 3 third prizes, what is the bonus of the first prize?
15. Divide 1296 into four numbers: A, B, C and D. If A adds 2, B subtracts 2, C multiplies 2, and D divides 2, the four numbers are equal. What are these four numbers? 1 In a right triangle, the ratio of two angles is 1: 3, so the degree of the smallest angle in this triangle may be () or ().
Isosceles trapezoid, 9 cm high and 38 cm in circumference. If the height is increased by 3 cm, the area of the trapezoid will increase by 27 cm 2, and the waist length of the trapezoid is () cm.
3 Four numbers are arranged in a row. The average of the first two numbers is 9, the average of the middle two numbers is 5.5, and the average of the last two numbers is 7.8, so the average of the first and second numbers is ().
Teacher Zhang gave some sweets to the children in Class One and Class Two, and each of them got 6 pieces. If only one class is given, each person will get 15. If only two classes are given, each class will get () pieces.
5 The following numbers are 1 to 1997, excluding all odd numbers of 5: 1, 3,7,9,1,13, 17,/kloc.
Two options
6. Enclose a piece of land with a fence with a length of 31.4m. The maximum area of the enclosed land is () square meters. a 109.2 B 123.245 C 157D 246.49
Three-column comprehensive formulas or equations are not calculated.
7. An assignment is completed within 65,438+08 days. Now Party A will do it for 3 days first, and then for 4 days * * * How many days will it take for Party B to complete the project alone 1?
8. The age ratio of father and daughter is 3: 1 this year. Five years later, their age ratio is 5: 2. How old is father this year?
Fourth, solve practical problems.
Xiaoming bought eight ballpoint pens and six pencils with 20 yuan money. If he bought two ballpoint pens, he still needs 0.4 yuan. If he bought two pencils, he was more than 0.8 yuan. How much is each pen?
10 A production workshop processes a batch of parts, and the tasks are evenly distributed according to the number of people in the workshop. Therefore, everyone should deal with them.
The number of parts is exactly equal to the number of people in the workshop, and then 10 workers are added, so that each person needs to process 8 parts less. How many parts are there in this batch?
Answer:
1.(30)(22.5)
2.( 10)
3.( 1 1.3)
4.( 10)
5.(7)
6 b
7 120
8 45
Your solution to this problem: 1. This problem is the catch-up problem of "two trains". "Catch up" here means that the front of the first train catches up with the rear of the second train, and "Leave" means that the rear of the first train leaves the front of the second train. Draw a line segment as follows:
Suppose it takes x seconds from the first train catching up with the second train to the departure of the two trains, and the equation is:
102+ 120+ 17x = 20x
x =74。
According to the regulations of the photo studio, one photo is 5.40 yuan, and three photos are given. If you want to add photos, each photo will be 0. 40 yuan. Five years 1 class 20 people took a group photo as a souvenir. Each person wants 1 photo. How much does it cost per person on average? 2. The children divide the candy. If everyone divides by 8, there is still 18 left. If the children of 10 get 7 pills each, and the rest of the children get 10 pills, it's over. How many children are there? How many sweets? The workers in the garment factory produce four coats or seven pairs of trousers every day, and one coat and one pair of trousers is a suit. At present, 66 workers are producing. How many sets can be produced at most every day? 4. Party A and Party B 19 stamp, Party B and Party C 13 stamp, and Party A and Party C 16 stamp. How many stamps does A give C, and the number of stamps for three people is the same? 5. Someone bought two commodities, but he misread the decimal point of one commodity and paid the salesman 14.07 yuan, and the salesman asked him to pay 43.32 yuan. What's the list price of these two pieces? 6. The pony and the tiger do multiplication. The pony misread the single digits of a factor, and the tiger misread the ten digits of the same factor. The pony got 255 and the tiger got 365. What is the correct product of the original problem? Pony and tiger do multiplication. The pony misread the single digits of a factor, and the tiger misread the ten digits of the same factor. The pony got 255 and the tiger got 365. What is the correct product of the original problem? 7. Party A, Party B and Party C have different amounts of money, and Party A has the most money. He gave some money to Party B and Party C, which doubled the money of Party A and Party C. As a result, Party B had the most money. B gave A and C some money, which tripled the money of A and C respectively. As a result, three people have the same amount of money. If the three of them have 8 1 yuan. How much was the original money for three people? The first question: the average person has to pay 0.6 1 yuan 5.4+0.4×(20-3)= 12.2 yuan 12.2/20=0.6 1 yuan. Second question: There are 24 children? 2 10 candy? Solution: There are X children. 8x+18 =10× 7+10× (x-10) Sugar: 24×8+ 18=2 10 Supplementary answer to the third question: 11x = 462x = 42 42× 4 =168 The fourth set of questions: After Party A gives three stamps to Party C, three people have the same number of stamps. a、B、C、I * * *: 1/2×( 19+ 13+ 16)。 =24 Party C has: 24- 19=5 Party A has: 24-13 =1Party B has: 24- 16=8 Party A gives it to Party C:1/kloc. 5 X=32.5 Another piece: 43.32-32.5= 10.82 Yuan Sixth question: The correct product of the original question is 265.255 = 5× 51365 = 5× 7353× 5 = 265 Seventh question: A57B2/kloc-.