In daily life and solving mathematical problems, we often have to calculate. In math class, we learned some simple calculation methods, but if we are good at observation and diligent in thinking, we can find more ingenious calculation methods in calculation, which will not only make you calculate well and quickly, but also make you smart and alert.
Example 1: Calculation: 9.996+29.98+169.9+3999.5.
Solution: It seems that the addition in the formula cannot be calculated by the simple calculation method learned in math class. However, as long as these numbers increase a little, they will become ten, a hundred or a thousand. After rounding these figures off, it is easy to calculate. Of course, remember that you have to subtract as much as you add when rounding.
9.996+29.98+ 169.9+3999.5
= 10+30+ 170+4000-(0.004+0.02+0. 1+0.5)
=42 10-0.624
=4209.376
Example 2: Calculation:1+0.99-0.98-0.97+0.96+0.95-0.94-0.93+…+0.04+0.03-0.02-0.01.
Solution: The number in the formula starts with 1 and decreases by 0.0 1 in turn until the last number is 0.0 1. Therefore, there are 100 numbers in the formula * *, and the operations in the formula are to add two numbers, then subtract two numbers, add two numbers, and then subtract two numbers ... in this order.
Because the arrangement and operation of numbers are very regular, according to the law, we can consider adding a bracket to every four numbers. Is there a certain regularity in the operation results of each group of numbers? It can be seen that if the third number subtracts the number 1 in each group, and the fourth number subtracts the number 2, each gets 0.02, which adds up to 0.04. Then the result of each group number (that is, each bracket) operation is 0.04, and the whole formula 100 is divided into 25 groups, and its result is the sum of 25 and 0.04.
1+0.99-0.98-0.97+0.96+0.95-0.94-0.93+…+0.04+0.03-0.02-0.0 1
=( 1+0.99-0.98-0.97)+(0.96+0.95-0.94-0.93)+…+(0.04+0.03-0.02-0.0 1)
=0.04×25
= 1
If you can flexibly use the law of commutation, you can also add parentheses in the calculation according to the following methods:
1+0.99-0.98-0.97+0.96+0.95-0.94-0.93+…+0.04+0.03-0.02-0.0 1
= 1+(0.99-0.98-0.97+0.96)+(0.95-0.94-0.93+0.92)+…+(0.03-0.02-0.0 1)
= 1
Example 3: Calculation: 0.1+0.2+0.3+…+0.8+0.9+0.10+0.1+0./kloc-0+2+…+0.
Solution: The numbers in this formula are arranged like a arithmetic progression, but if you look closely, it is actually composed of two arithmetic progression. 0. 1+0.2+0.3+…+0.8+0.9 is the first arithmetic progression, and each number behind it is 0. 1 more than the previous one. And 0.10+0.1+0.12+…+0.19+0.20 is the second arithmetic progression, and each number behind it is 0.0/kloc-0 more than the previous one.
0. 1+0.2+0.3+…+0.8+0.9+0. 10+0. 1 1+0. 12+…+0. 19+0.20
=(0. 1+0.9)×9÷2+(0. 10+0.20)× 1 1÷2
=4.5+ 1.65
=6. 15
Example 4: Calculation: 9.9× 9.9+ 1.99
Solution: Of the two factors of 9.9×9.9 in the formula, one factor is enlarged by 10, and the other factor is reduced by 10, and the product remains unchanged, that is, the product can become 99× 0.99; 1.99 can be divided into the sum of 0.99+ 1 After this change, the calculation is simpler.
9.9×9.9+ 1.99
=99×0.99+0.99+ 1
=(99+ 1)×0.99+ 1
= 100
Example 5: Calculation: 2.437× 36.54+243.7× 0.6346
Solution: Although the factors of the two multiplications in the formula are different, the numbers of 2.437 in the previous multiplication and 243.7 in the next multiplication are the same, but the positions of decimal points are different. If the decimal points of two factors in one multiplication are moved in opposite directions by the same number, so that the two numbers become the same, simple calculation can be made by multiplication and division.
2.437×36.54+243.7×0.6346
=2.437×36.54+2.437×63.46
=2.437×(36.54+63.46)
=243.7
* Example 6: Calculation:1.1×1.2×1.3×1.4×1.5
Solution: Although several numbers in the formula are arithmetic progression, the formula is not summation, and the result of this formula cannot be calculated by arithmetic progression summation.
Students who usually pay attention to accumulating calculation experience may notice that the product of multiplying 7, 1 1 and 13 is 100 1, and a three-digit multiplied by 100 1 is their product.
1. 1× 1.2× 1.3× 1.4× 1.5
= 1. 1× 1.3×0.7×2× 1.2× 1.5
= 1.00 1×3.6
=3.6036
Calculate the following questions and write a simple calculation process:
1.5.467+3.8 14+7.533+4. 186
2.6.25× 1.25×6.4
3.3.997+ 19.96+ 1.9998+ 199.7
4.0. 1+0.3+…+0.9+0. 1 1+0. 13+0. 15+…+0.97+0.99
5. 199.9× 19.98- 199.8× 19.97
6.23.75×3.987+6.0 13×92.07+6.832×39.87
*7.20042005×20052004-20042004×20052005
*8.( 1+0. 12+0.23)×(0. 12+0.23+0.34)-( 1+0. 12+0.23+0.34)×(0. 12+0.23)
Calculate the following questions and write a simple calculation process:
1.6.734- 1.536+3.266-4.464
2.0.8÷0. 125
3.89. 1+90.3+88.6+92. 1+88.9+90.8
4.4.83×0.59+0.4 1× 1.59-0.324×5.9
5.37.5×2 1.5×0. 1 12+35.5× 12.5×0. 1 12
Fifth grade, the second volume of mathematical Olympic examination questions
Name class score
Calculate the following questions in a simple way.
20.36-7.98-5.02-4.36 1 17.8÷2.3-4.88÷023
9.56×4. 18-7.34×4. 18-0.26×4. 18
1. There are 123 children. Divide them into a group of 12 or a group of 7, just finished eating, there is nothing left. It is also known that the total population is about 15. So, how many groups of 12 people are there? How many groups are there in a group of seven?
2. The average score of Zhang Ni's five exams is 88.5, and the full score of each exam is 100. How many times does Zhang Ni have to get full marks in order to get the average score above 92 as soon as possible?
The sum of the ages of the father and his three sons is 108 years old. If six years later, the father's age is exactly equal to the sum of the three sons' ages. How old is my father?
4. Processing a batch of parts, originally planned to process 80 parts a day, just to finish the task on schedule. Due to the improvement of production technology, 100 pieces are actually processed every day, which not only completes the processing task four days ahead of schedule, but also processes more 100 pieces. How many parts did they actually process?
5. A pool can hold 8 tons of water, and the pool is equipped with a water inlet pipe and a water outlet pipe, which are two-pronged, and put a pool of water in 20 minutes. It is known that the water inlet pipe injects 0.8 tons of water into the pool every minute. How many tons of water does the water pipe discharge per minute?
6. Cut the wire into 15 segments. One part is 8 meters long and the other part is 5 meters long. The total length of 8 meters is 3 meters more than that of 5 meters. How long is this wire?
7. Divide a big fish into three parts: head, body and tail. The fish tail weighs 4 kilograms. The weight of fish head is equal to the weight of fish tail plus half the weight of fish body, and the weight of fish body is equal to the weight of fish head plus the weight of fish tail. How much does this big fish weigh?
8. The gym needs to pay 287 yuan to buy 5 soccer balls and 4 basketballs. 154 yuan buys 2 soccer balls and 3 basketballs. So how much do you spend on a football and a basketball?
9.5 yuan has RMB *** 14 and RMB *** 100. How many 5-yuan coins and 10 yuan?
10, someone climbed from village a to the top of village b, and it took him 7 hours to walk 30.5 kilometers. He went up the mountain at a speed of 4 kilometers per hour and down the mountain at a speed of 5 kilometers per hour. If the speed of going up and down the mountain remains the same, how long will it take to return from village B to village A along the original road?
1 1, Party A and Party B walk in opposite directions at the same time, with Party A riding at a speed of16km and Party B riding a motorcycle at a speed of 65km. A meets B at a distance of 62.4 kilometers from the starting point. How many kilometers is AB?
12, tortoise and rabbit race, the rabbit runs 35km per minute, and the tortoise climbs10m per minute. On the way, the rabbit slept and woke up to find the tortoise 50 meters in front of him. How long will it take the rabbit to catch up with the tortoise?
13. On the 600-meter-long circular runway, brother and sister run clockwise at the same starting point at the same time and meet every 12 minutes. If the speed of two people is the same, or starting from the original starting point at the same time, my brother runs counterclockwise, then they will meet every 4 minutes. How many minutes does it take for two people to run a lap?
14. In still water, the speed of ships A and B is 20km and 16km/h respectively. Two ships set off from a port one after another, and B set off two hours earlier than A. If the water speed is 4km per hour, how many hours after A sets off, will it catch up with B?
15. It takes 40 seconds for a train to cross a 440m bridge and 30 seconds to cross a 3 10/0m tunnel at the same speed. What is the speed and length of this train?
16, a bookshelf is divided into upper and lower floors, and the number of books on the upper floor is four times that of the lower floor. After taking five books from the lower level and putting them on the upper level, the number of books in the upper level is exactly five times that of the lower level. How many books are there on the ground floor?
17, there is 1800 kg cargo, which is divided into three cars: A, B and C. It is known that the number of kilograms loaded by A car is exactly twice that of B car, and B car carries 200 kg more than C car. Party A, Party B and Party C each have one copy.
Inclusion and exclusion
1. There are 40 students in a class, of which 15 is in the math group, 18 is in the model airplane group, and 10 is in both groups. So how many people don't participate in both groups?
Solution: There are (15+18)-10 = 23 (people) in the two groups.
40-23= 17 (person) did not attend.
A: There are 17 people, and neither group will participate.
-
There are forty-five students in a class who took the final exam. After the results were announced, 10 students got full marks in mathematics, 3 students got full marks in mathematics and Chinese, and 29 students got no full marks in both subjects. So how many people got full marks in Chinese?
Solution: 45-29- 10+3=9 (person)
A: Nine people got full marks in Chinese.
3.50 students stand in a row facing the teacher. The teacher asked everyone to press 1, 2,3, ..., 49,50 from left to right. Let the students who are calculated as multiples of 4 back off, and then let the students who are calculated as multiples of 6 back off. Q: How many students are facing the teacher now?
Solution: multiples of 4 have 50/4 quotients 12, multiples of 6 have 8 50/6 quotients, and multiples of 4 and 6 have 4 50/ 12 quotients.
Number of people turning back in multiples of 4 = 12, number of people turning back in multiples of 6 ***8, including 4 people turning back and 4 people turning back from behind.
Number of teachers =50- 12=38 (person)
A: There are still 38 students facing the teacher.
4. At the entertainment party, 100 students won lottery tickets with labels of 1 to 100 respectively. The rules for awarding prizes according to the tag number of lottery tickets are as follows: (1) If the tag number is a multiple of 2, issue 2 pencils; (2) If the tag number is a multiple of 3, 3 pencils will be awarded; (3) The tag number is not only a multiple of 2, but also a multiple of 3 to receive the prize repeatedly; (4) All other labels are awarded to 1 pencil. So how many prize pencils will the Recreation Club prepare for this activity?
Solution: 2+000/2 has 50 quotients, 3+ 100/3 has 33 quotients, and 2 and 3 people have 100/6 quotients.
* * * Preparation for receiving two branches (50- 16) * 2 = 68, * * Preparation for receiving three branches (33- 16) * 3 = 5 1, * * Preparation for repeating branches (2+).
* * * Need 68+5 1+80+33=232 (branch)
A: The club has prepared 232 prize pencils for this activity.
5. There is a rope with a length of 180 cm. Make a mark every 3 cm and 4 cm from one end, and then cut it at the marked place. How many ropes were cut?
Solution: 3 cm marker: 180/3=60, the last marker does not cross, 60- 1=59.
4cm marker: 180/4=45, 45- 1=44, repeated marker: 180/ 12= 15,15-/kloc-.
Cut it 89 times and it becomes 89+ 1=90 segments.
A: The rope was cut into 90 pieces.
6. There are many paintings on display in Donghe Primary School Art Exhibition, among which 16' s paintings are not in the sixth grade, and 15' s paintings are not in the fifth grade. Now we know that there are 25 paintings in Grade 5 and Grade 6, so how many paintings are there in other grades?
Solution: 1, 2,3,4,5 * * has 16, 1, 2,3,4,6 * * has15,5,6 * * has 25.
So * * has (16+ 15+25)/2=28 (frame), 1, 2,3,4 * * has 28-25=3 (frame).
A: There are three paintings in other grades.
-
7. There are several cards, each with a number written on it, which is a multiple of 3 or 4. Among them, cards marked with multiples of 3 account for 2/3, cards marked with multiples of 4 account for 3/4 and cards marked with multiples of 12 account for 15. So, how many cards are there?
Solution: The multiple of 12 is 2/3+3/4- 1=5/ 12, 15/(5/ 12)=36 (sheets).
There are 36 cards of this kind.
-
-
8. How many natural numbers from 1 to 1000 are divisible by neither 5 nor 7?
Solution: multiples of 5 have 200 quotients 1000/5, multiples of 7 have quotients 1000/7 142, and multiples of 5 and 7 have 28 quotients 1000/35. The multiple of 5 and 7 * * * has 200+ 142-28=3 14.
1000-3 14=686
A: There are 686 numbers that are neither divisible by 5 nor divisible by 7.
-
9. Students in Class 3, Grade 5 participate in extracurricular interest groups, and each student participates in at least one item. Among them, 25 people participated in the nature interest group, 35 people participated in the art interest group, 27 people participated in the language interest group, 12 people participated in the language interest group, 8 people participated in the nature interest group, 9 people participated in the nature interest group, and 4 people participated in the language, art and nature interest groups. Ask how many students there are in this class.
Solution: 25+35+27-(8+ 12+9)+4=62 (person)
The number of students in this class is 62.
- -
10, as shown in Figure 8- 1, it is known that the areas of three circles A, B and C are all 30, the areas of overlapping parts of A and B, B and C, and A and C are 6, 8 and 5 respectively, and the total area covered by the three circles is 73. Find the area of the shaded part.
Solution: The overlapping area of A, B and C =73+(6+8+5)-3*30=2.
Shadow area =73-(6+8+5)+2*2=58.
A: The shaded part is 58.
________________________________________
-Author: abc
-Date of issue: 2004-12-1215: 45: 02
-
Grade four 1 class 1 1 There are 46 students taking part in three extracurricular activities. Among them, 24 students from the math group and 20 students from the Chinese group participated. The number of people who participated in the art group was 3.5 times that of those who participated in both the math group and the art group, and 7 times that of those who participated in all three activities. The number of people who participated in both the literature and art group and the Chinese group was twice that of those who participated in all three activities, and the number of people who participated in both the math group and the Chinese group was 10. The number of people seeking to join the art troupe.
Solution: Let the number of people participating in the art group be x, 24+20+x-(x/305+2/7 * x+10)+x/7 = 46, and the solution is X=2 1.
A: The number of participants in the art group is 2 1.
________________________________________
-Author: abc
-Date of issue: 2004-12-1215: 45: 43
-
12. There are 100 books in the library. The borrower needs to sign the book. It is known that 33, 44 and 55 books in 100 have the signatures of A, B and C respectively, among which 29 books have the signatures of A and B, 25 books have the signatures of A and C, and 36 books have the signatures of B and C. How many of these books have not been borrowed by any of A, B and C?
Solution: The number of books read by three people is: A+B+C-(A+B+C+C)+A, B, C =33+44+55-(29+25+36)+ A, B, C =42+ A, B, C, A, C is the most.
Three people will always read 42+25=67 (books) at most, and at least 100-67=33 (books) have never been read.
A: At least 33 books in this batch have not been borrowed by any of A, B and C.
________________________________________
-Author: abc
-Date of issue: 2004-12-1215: 46: 53
-
13, as shown in Figure 8-2, five equal-length line segments form a pentagram. If exactly 1994 points on each line segment are dyed red, how many red dots are there on this five-pointed star?
Solution: There are 5* 1994=9970 red dots on the right side of the five elements. If you put a red dot on all the intersections, then at least there are red dots. These five lines have 10 intersections, so there are at least 9970- 10=9960 red dots.
A: There are at least 9960 red dots on this five-pointed star.
The related pictures of this theme are as follows:
________________________________________
-Author: abc
-release date: 2004- 12- 12
-
14, A, B and C are watered at the same time 100 potted flowers. It is known that A poured 78 pots, B poured 68 pots and C poured 58 pots. So how many pots were watered by three people?
Solution: A and B must have 78+68- 100=46 pots * *, and C has 100-58=42, so all three people poured at least 46-42=4 pots.
A: All three people have watered at least four pots of flowers.
________________________________________
-Author: abc
-release date: 2004-12-1215: 52: 54.
-
15, A, B and C are all reading the same story book. There are 100 stories in the book. Everyone starts with a story and then reads it in order. It is known that A has read 75 articles, B has read 60 articles and C has read 52 articles. So how many stories have A, B and C read together?
Solution: B and C * * * have read at least 60+52- 100= 12 stories. This 12 story A must be read no matter where it starts.
A: A, B and C have read at least 12 stories.
________________________________________
-Author: abc
-Date of issue: 2004-12-1215: 53: 43
-
15, A, B and C are all reading the same story book. There are 100 stories in the book. Everyone starts with a story and then reads it in order. It is known that A has read 75 articles, B has read 60 articles and C has read 52 articles. So how many stories have A, B and C read together?
Solution: B and C * * * have read at least 60+52- 100= 12 stories. This 12 story A must be read no matter where it starts.
A: A, B and C have read at least 12 stories.
________________________________________
-Author: cxcbz
-release date: 2004-12-1321:53: 23.
-
The following is the quotation of abc in 2004-12-1215: 42:17:
8. How many natural numbers from 1 to 1000 are divisible by neither 5 nor 7?
Solution: multiples of 5 have 200 quotients 1000/5, multiples of 7 have quotients 1000/7 142, and multiples of 5 and 7 have 28 quotients 1000/35. The multiple of 5 and 7 * * * has 200+ 142-28=3 14.
1000-3 14=686
A: There are 686 numbers that are neither divisible by 5 nor divisible by 7.
The division in the title should be exactly division.
________________________________________
-Author: cxcbz
-release date: 2004-12-1321:56: 00.
-
The following is abc's quotation dated 2004-12-1215: 45: 02:
Grade four 1 class 1 1 There are 46 students taking part in three extracurricular activities. Among them, 24 students from the math group and 20 students from the Chinese group participated. The number of people who participated in the art group was 3.5 times that of those who participated in both the math group and the art group, and 7 times that of those who participated in all three activities. The number of people who participated in both the literature and art group and the Chinese group was twice that of those who participated in all three activities, and the number of people who participated in both the math group and the Chinese group was 10. The number of people seeking to join the art troupe.
Solution: Let the number of people participating in the art group be x, 24+20+x-(x/305+2/7 * x+10)+x/7 = 46, and the solution is X=2 1.
A: The number of participants in the art group is 2 1.
1. There are 19 people who subscribe to Juvenile Digest, 24 people subscribe to Learn and Play, and 13 people subscribe to both. Ask for a subscription "
How many people are there in Youth Digest or Learn and Play?
2. In the kindergarten, there are 58 people who learn piano, 43 people who learn painting and 37 people who learn piano and painting. How many people learn piano and painting respectively?
People?
3. Among the natural numbers from 1 to 100:
(1) How many numbers are multiples of 2 and 3?
(2) How many numbers are multiples of 2 or multiples of 3?
(3) How many numbers are multiples of 2 instead of multiples of 3?
4. The mid-term examination results of a class in mathematics and English are as follows: 12 Student English 100, 10 Student Mathematics 100, two subjects.
Three people got 100 in all courses, and 26 people didn't get 100 in all courses. How many students are there in this class?
5. There are 50 people in the class, 32 can ride a bike, 265,438+0 can skate, 8 can both, and how many can't both?
6. There are 42 students in a class, 30 students in sports teams and 25 students in literary and art teams, and each student should participate in at least one team. this
How many people are there in the two teams of the class?
Test answer
1. There are 19 people who subscribe to Juvenile Digest, 24 people subscribe to Learn and Play, and 13 people subscribe to both. Request to subscribe to Youth Digest
Or "learn and play"?
19+24— 13 = 30 (person)
A: There are 30 people who subscribe to Youth Digest or Learn and Play.
2. In the kindergarten, there are 58 people who learn piano, 43 people who learn painting and 37 people who learn piano and painting. How many people learn piano and painting respectively?
People?
Number of piano learners: 58-37 = 2 1 (person)
Number of people who only learn painting: 43-37 = 6 (people)
3. Among the natural numbers from 1 to 100:
(1) How many numbers are multiples of 2 and 3?
It is a multiple of 3 and 2 and must be a multiple of 6.
100÷6 = 16……4
So both 2 and 3 have multiples of 16.
(2) How many numbers are multiples of 2 or multiples of 3?
100÷2 = 50, 100÷3 = 33…… 1
50+33— 16 = 67 (piece)
Therefore, there are 67 numbers that are multiples of 2 or multiples of 3.
(3) How many numbers are multiples of 2 instead of multiples of 3?
50- 16 = 34 (piece)
A: There are 34 numbers that are multiples of 2, but not multiples of 3.
4. The mid-term examination results of a class in mathematics and English are as follows: 12 Student English 100, 10 Student Mathematics 100, two subjects.
Three people got 100 in all courses, and 26 people didn't get 100 in all courses. How many students are there in this class?
12+10-3+26 = 45 (person)
There are 45 students in this class.
5. There are 50 people in the class, 32 can ride a bike, 265,438+0 can skate, 8 can both, and how many can't both?
50-(30+2 1-8) = 7 (person)
A: There are seven people who can't do either.
6. There are 42 students in a class, 30 students in sports teams and 25 students in literary and art teams, and each student should participate in at least one team. this
How many people are there in the two teams of the class?
30+25-42 = 13 (person)
A: There are 13 students in this class.
The number of people who take the entrance examination in a class is as follows: 20 in math, 20 in Chinese, 20 in English, 8 in math English, 7 in math Chinese, 9 in Chinese English, and none of the three subjects. How many students are there in this class at most? How many people at least?
Analysis and solution as shown in Figure 6, students who get full marks in mathematics, Chinese and English are all in this class. Let's assume that there are y students in this class, which are represented by rectangles. A, B, and C stand for those who get full marks in mathematics, Chinese, and English, respectively, from A∩C=8, A∩B=7, and b ∩ c = 9.
According to the principle of inclusion and exclusion
Y=A+B+c-A∩B-A∩C-B∩C+A∩B∩C+3
That is, y = 20+20+20-7-8-9+x+3 = 39+x.
Let's look at how to find the maximum and minimum value of y.
It can be seen from y=39+x that when x takes the maximum value, y also takes the maximum value; When x takes the minimum value, y also takes the minimum value. X is the number of people who get full marks in mathematics, Chinese and English, so their number should not exceed the number of people who get full marks in two subjects, that is, x≤7, x≤8 and x≤9, from which we get x≤7. On the other hand, students who get full marks in mathematics may not get full marks in Chinese, that is to say, there are no students who get full marks in all three subjects, so x≥0.
When x takes the maximum value of 7, y takes the maximum value of 39+7 = 46, and when x takes the minimum value of 0, y takes the minimum value of 39+0 = 39.
A: There are at most 46 students and at least 39 students in this class.
Question 1. The clerk changed a 5 yuan RMB and a 50-cent RMB into 28 yuan RMB with face values of 1 yuan and 1 respectively. How much RMB do you want?
Question 2: There are 50 RMB * * with total face value 1 16 yuan. As we all know, one yuan is more than two yuan. How many RMB are there in three denominations?
Question 3: There are 400 movie tickets from 3 yuan, 5 yuan and 7 yuan, with a value of 1920 yuan, among which 7 yuan and 5 yuan have equal tickets. How many movie tickets are there for each of the three prices?
Question 4: Two kinds of cars are used to transport goods. Each car contains 18 boxes, and each car contains 12 boxes. Now there is a 18 car, worth 3024 yuan. If each case is cheap in 2 yuan, the goods are worth 2520 yuan. Q: How many cars are there?
Question 5. A truck can transport ore 20 times a day in sunny days and 12 times a day in rainy days. Transportation 1 12 times a day, with an average of 14 times a day. How many days are it rainy these days?
Question 6. A batch of watermelons has been delivered and will be sold in two categories, the large one in 0.4 yuan and the small one in 0.3 yuan. In this way, these watermelons are worth 290 yuan. If the price per kilogram of watermelons is reduced by 0.05 yuan, this batch of watermelons can only be sold in 250 yuan. Q: How many kilograms is the watermelon?
Question 7. In the darts competition, it is stipulated that each player gets 65,438+00 points, and each player misses the target and gets 6 points. Each player throws 10 times and scores * * * 152 points, in which player A scores more than player B 16 points. Q: How many times did each player win?
Question 8. There are 20 questions in the math contest. Every time he answers a question correctly, he gets 5 points. If he answers a wrong question, he will not only get no points, but also deduct 2 points backwards. Xiaoming got 86 points in this competition. Q: How many questions did he answer correctly?
1. solution: x sheets of 1 element and (28-x) sheets of 1 angle.
x+0. 1(28-x)=5.5
0.9x=2.7
x=3
28-x=25
A: There are three Zhang Yiyuan bills and 25 dimes.
2. Solution: Let 1 element have X, 2 yuan (x-2) and 5 yuan (52-2x).
x+2(x-2)+5(52-2x)= 1 16
x+2x-4+260- 10x = 1 16
7x= 140
x=20
x-2= 18
52-2x= 12
A: There are 20 1 yuan, 8 18 in 2 yuan and 2 12 in 5 yuan.
3. Solution: 7 yuan and 5 yuan have X pieces, and 3 yuan has (400-2x) pieces.
7x+5x+3(400-2x)= 1920
12x+ 1200-6x = 1920
6x=720
x= 120
400-2x= 160
A: 3 yuan has 160 and 7 yuan and 5 yuan have 120.
4. Answer: Total cargo: (3024-2520)÷2=252 (boxes)
There are x buses and (18-x) cars.
18x+ 12( 18-x)= 252
18x+2 16- 12x = 252
6x=36
x=6
18-x= 12
Answer: Bus No.6, 12.
5. Solution: Days = 1 12÷ 14=8 days.
It rained on day X.
20(8-x)+ 12x = 1 12
160-20x+ 12x = 1 12
8x=48
x=6
There are six rainy days.
6. Solution: Watermelon number: (290-250)÷0.05=800 kg.
There is a big watermelon x kg.
0.4x+0.3(800-x)=290
0.4x+240-0.3x=290
0. 1x=50
x=500
There are 500 kilograms of big watermelons.
7. Solution: A: (152+ 16)÷2=84.
B: 152-84=68 points.
Set armor x times
10x-6( 10-x)=84
10x-60+6x=84
16x= 144
x=9
Set b to y times.
10y-6( 10-y)=68
16y= 128
y=8
A: Nine times for A and eight times for B. ..
8. Answer: Suppose he answered question X correctly.
5x-2(20-x)=86
5x-40+2x=86
7x= 126
x= 18
A: He got it right 18.