Math problem (1) 1 in the second volume of grade six. Lili and her family go to the bookstore to buy books. They all fell in love with a book. Finally, Lili spent three-fifths of her own money and two-thirds of her own money at home. Lili's remaining money is five yuan more than that of each family. How much money do they each have? How much are these books?
Let the lily have X yuan, and everyone has Y yuan, and get: 3/5x=2/3y 2/5x= 1/3y+5 (lily leaves have 1/3 in families). Solve the quadratic equation and get x=50 y=45, that is, Lily 50 yuan's family has a book, 45 yuan, 30 yuan.
2. A car consumes 4/5 kilograms of fuel per line for 8 kilometers, and how many kilometers per kilogram of gasoline is feasible on average. How many kilograms does driving 1 km consume?
8 divided by 4/5= 10 (km /) 4/5 divided by 8=0. 1 (kg)
3. A motorcycle 1/2 hours for 30 kilometers. How many kilometers does it travel per hour? How many hours does it take him to drive 1 km?
30? 1/2=60 km 1？ 60= 1/60 hours
Four out of seven students reading in the reading room are boys. After five male students walked out of the reading room, twelve of the twenty-three were female students. How many students were reading in the original reading room?
There are x students, but the number of girls remains the same, so (1-4/7)x=(x-5)? Found x=28
There are 62 red, yellow and blue balloons, of which three-fifths of the red balloons are equal to two-thirds of the yellow balloons, and there are 24 blue balloons. How many are Red Balloon and Yellow Balloon?
62-24=38 (only) 3/5 red =2/3 yellow 9 red = 10 yellow red: yellow = 10:9 38/( 10+9)=2 red: 2? 10=20 Yellow: 2? 9= 18
There are 36 students reading in the school reading room, 4/9 of whom are female students. Later, several female students came. At this time, the number of female students accounted for 3/5 of the number of students. Later, several female students came.
Original girl: 36? 4/9= 16 (person) After the original boy: 36- 16=20 (person), the total number of students: 20? (1-3/5)=50 (people) There are girls: 50? 3/5=30 (person) Number of female students: 30- 16= 14 (person)
7. When water turns into ice, its volume is110, 2. 16 cubic meters of ice melts into water, what is its volume?
2.16/(1+11) =1.98 (m3)
8. Party A's grain is 560 tons. If 2/9 of Party A's grain is shipped to Party B, Party A's grain is exactly the same. How many tons of grain does Party A have? How many tons of grain does B have?
Now Party A and Party B each have 560? 2=280 tons, so A has 280? (1-2/9)=360 tons The original B has 560-360=200 tons.
9. The price reduction of TV sets in 200 yuan is 2/ 1 1. What's the price of this TV set now?
The original price is 200? 2/ 1 1=2200 yuan. The current price is 2200-200=2000 yuan.
10。 Car A has traveled more than 2/5 kilometers from A to B.. At this time, there are still 70 kilometers from B. How many kilometers are there between A and B?
1-2/5=3/5 The whole journey is 20+70 = 90km. The distance between a and b is 90? 3/5 =150km
1 1. Xiaoming reads books. On the first day, he read 28 pages. The next day, he read the whole book 1/5 (1). Last two days, * * * read 3/8 (8/3) of the whole book. How many pages does this book have?
What I read on the first day accounts for 3/8- 1/5=7/40 of the whole book. There are 28 books in this book. 7/40= 160 page
12. Both the master and the apprentice are processing a batch of parts. After a period of processing, the master processed 84 parts. The apprentice made 63 parts. The master works more than the apprentice, accounting for 1/28 of all tasks. How many parts are there in this batch?
Suppose there are x parts * * *1/28x = 84-631/28x =19x = 532, so there are 532 parts * * *.
13. A barrel of oil, after eating 7/ 10, added 15 kg. At this time, the oil in the barrel is exactly half of that in a barrel. How much does this barrel of oil weigh?
15? (7/ 10- 1/2)=75 (kg)
14. A train runs from Shanghai to Tianjin, accounting for 3/5 of the whole journey. If you drive at 106 km/h, you can reach Tianjin in five hours. How many kilometers is the railway from Shanghai to Tianjin?
( 106? 5)/(1-(3/5)) = 530/0.4 =1325 (km)
15. There are 46 students in grade six who participate in math interest groups, among which 4/5 girls are 3/2 times as many as boys. How many boys and girls joined the interest group?
The ratio of male to female students is 4/5: 3/2 = 8: 15. The number of boys is 46/(8+ 15)? 8= 16 Number of girls 46- 16=30 16. It takes Zhang Hong five hours to copy a manuscript. This manuscript has been copied by others 1/3, and the rest is given to Zhang Hong. How many hours does it take to copy it?
(1-1/3)/(1/5) =10/3 It takes 3 hours1/3 to complete the replication.
17. Two trains leave from two cities 600 kilometers apart at the same time. One train runs at 60 kilometers per hour, and the other train runs at 75 kilometers per hour. How many hours will the two trains meet?
600/(60+75)=40/9 (hours) After 40/9 hours, the two cars can meet.
18. A motorcycle travels 64 kilometers per hour. It takes 3/4 hours to find this speed from a to b. What is the distance between a and b?
64? 3/4=48 km
19. The fruit shop sold a batch of fruits in two days. On the first day, 3/5 of the total fruit weight was sold, 30 kilograms more than the next day. How many kilograms are there in this batch of fruit?
If you sell 3/5 of the total fruit weight on the first day, then you sell 2/5, 3/5-2/5= 1/5 on the second day, and the first day is more than the second day, 30? 1/5 = 150kg, and the formula is,1-3/5 = 2/5-2/5 =1/5 30? 1/5 =150kg
20. Jessie Primary School has 9 10 students, seven quarters of whom are girls. How many are girls? How many boys are there?
9 10? 4/7=(9 10? 4)/7=520 ... girls 9 10-520=390 ... boys
2 1. A rectangular piece of land is 60 meters long and 2/5 wide. What is the area of this land?
4/5? 5/8=(4? 5)/(5? 8)= 1/2(m)4/5- 1/2 = 8/ 10-5/ 10 = 3/ 10(m)
22. The ratio of red goldfish to black goldfish in the goldfish pond is 7:3. There are 9 black goldfish. How many red goldfish are there?
9? 3? 7=2 1
Grade 23.6 students 132, in which the ratio of male to female students is 6: 5. How many boys and girls are there in the sixth grade?
132? (6+5)= 12. Are there 12 male students? 6=72 female students have 12? 5=60 people
24. The ratio of A to B is 2:3, and the ratio of B to C is 4:5. Find the ratio of a to C.
A:B = 2:3 = 8: 12 B:C = 4:5 = 12: 15 A:B:C = 8: 12: 15 A:C = 8:65438。
The sixth volume of the sixth grade math problem (middle) 26. Last year, the ratio of color TV output to total TV output in a TV factory was 9/20. Last year, * * * produced 250,000 TV sets, including how many color TV sets?
250000? 9/20= 1 12500 units
27. Workers in a factory account for two-thirds of the total number of employees in the factory, technicians account for two-ninth of the total number of employees in the factory, and the rest are cadres. Write down the proportion of workers, technicians and cadres in this factory.
Cadres account for1-3,2-9 =1. The ratio of workers, technicians and cadres in this factory is 2-3, 2-9, 1 = 6:2: 1.
The number of students in a class is between 40 and 50, and the ratio of male to female is 5:6. How many boys and girls are there in this class? ..
Because the number of students is an integer, the class size can be divisible by 5+6 = 1 1, so the class size is 44. (5+6)? 5=20 girls have 44-20=24 girls.
29. The ratio of science and technology books to literature and art books in the library is 4: 5. After purchasing 300 works of art, the ratio of science and technology books to literature and art books is 5: 7. What percentage of literature and art books have increased?
Original literature: 300? (7/ 12-5/9)= 10800 (this) literature and art books increased by 300? 10800? 2.8% 30. 100g sugar water just fills a glass with 10g sugar. Pour 10g sugar water out of the glass and fill the glass with water. What's the ratio of sugar to water in the quilt?
It turns out that the water in it is 90 and the sugar is 10. Pour out10g, and there is still 90 in it, in which water 8 1, sugar 9 1 and sugar 9 are 9/9 1.
3 1. There are only 175 students in grades 5 and 6. Divide into three groups to participate in the activities. The ratio of the first group to the second group is 5: 4, and the third group has 67 people. How many people are there in the first and second groups?
(1) The first and second groups have 175 students -67 students = 108 students (2) The first group has 108 students? 5/9=60 students (3) There are 108 students in the second group? 4/9=48 people 3
2. There are 465 students in a school, of which 2/3 girls are 20 less than 4/5 boys. A man? How many women are there?
Two thirds of the girls are less than four fifths of the boys. Girls are twenty (4/5)/(2/3)=6/5 less than boys. 20/(2/3)=30 boys have (465+30)/( 1+6/5)=225 girls have.
33. For a manuscript, 1 7 was typed on the first day, and 2/5 was typed on the second day. The next day was nine pages more than the first day. How many pages are there in this manuscript?
9 divided by (5' s 2-7 1)= 9 divided by 35' s 9 = 35 (pages) A: This manuscript has 35 pages.
34. On a piece of land, the aspect ratio is 8: 5, and the length is 24 meters more than the width. How many square meters is this land?
If the length is 8 and the width is 5, there will be more: 3, which means 24 meters, so one is: 24/3=8 meters, which means the length is: 8? 8=64 meters, width: 8? 5=40 meters area is: 64? 40=2560 square meters
35. If there are 25% more boys than girls, how many girls are less than boys?
Girls 1, boys 1+25%= 125%. The number of girls is less than that of boys (125%- 1)? 125%=20%
36. This breeding factory has raised 65,438+0,987 pigs this year, which is three times less than that of last year, that is, 245 pigs. How many more pigs have been raised this year than last year?
Raising pigs last year: (1987+245)/3=744 There are more pigs this year than last year: 1987-744= 1243.
37. The ratio of Xiao Wei and Xiaoying's donation to Project Hope is 2:5. Xiaoying donated 35 yuan. How much did Xiao Wei donate?
Suppose Xiao Wei donated X yuan, then 2:5=X:35: X= 14 yuan. Donation from Xiao Wei 14 yuan.
38. All three averages are 8.4, of which the first number is 9.2, and the second number is 0.8 less than the third number. What is the third number?
Solution: Let the third number be x and the column equation be: [9.2+(x-0.8)+x]/3=8.4. The solution is x=8.4.
39. There are two ropes. The length of the first rope is 1.5 times that of the second rope, and the second rope is 3 meters shorter than the first rope. How long are these two ropes?
Let the second root be x meters long, so the second root is1.5xm1.5x-x = 30.5x = 3x = 66? 1.5=9 (m). The first one is 6 meters long and the second one is 9 meters long.
40. The construction team built a road, and the repaired length and the remaining ratio were 4: 5. If you build another 25 meters, it will just reach the midpoint of this road. What is the total length of this road?
Solution: 4+5=9 If the total length of this road is x meters, then (5/9-4/9) x = 251/9x = 25 x = 225, and the total length of this road is 225 meters.
4 1. There must be an algorithm to cut a circular piece of paper into several small sectors with equal areas along the radius, and then put them together to form an approximate rectangle. The circumference of the new pattern is longer than that of the circular paper 16 cm. What is the area of this round paper?
The newly added 16 cm is two widths of a rectangle, that is, two radii of a circle. So the radius is: 16/2=8, and the area of the circle is: 8? 8? 3. 14=200.96
42. The difference between the areas of two circles is 209 square centimeters. Given that the circumference of a big circle is 10/9 times that of a small circle, how many square centimeters is the area of the small circle?
The circumference of a big circle is 10/9 times that of a small circle, the radius is 10/9 times, and the area is (10/9) square = 100/8 1 times. The following is the problem of difference times, decimal = difference/(multiple -660).
43. A circle starts from a certain point on the circumference and is segmented with an arc length of 54 cm, which is exactly divided into integer segments. If we still start from that point and segment it with an arc length of 72 cm, it also happens to be divided into integer segments. If two line segments leave 60 points on the circumference, what is the circumference of the circle?
Let the circumference of a circle be c, then c is a multiple of 54 and c is also a multiple of 72, then c is a multiple of their least common multiple of 2 16. In 2 16cm, there are four points divided by 54 (excluding the last point, count this as the first point of the next 2 16), and divided by 72 from point 3, a * * * has 4+3- 1=6 points (the first point, two common points So there are 6 points every 2 16 cm, so the perimeter is (60/6)? 2 16=2 160 cm。
44. A puppy is tied to the top corner of a regular polygon. The rope is 6 meters long and the side of a regular Pentagon is 2.5 meters long, so that the dog's range can be found.
Solution: Each internal angle of a regular Pentagon is (5-2)/5= 108 degrees 6? 6? 3. 14? (360- 108)/360+(6-2.5)? (6-2.5)? 3. 14 ? ( 180- 108)/360? 2+(3.5-2.5)? (3.5-2.5)? 3. 14? ( 180- 108)/360? 2=95.77 square meters.
45. There is a 40-meter-long copper wire, which is wound around a circular tube 12 times, leaving 2.32 meters. Find the diameter of the circular tube?
1: If there is nothing left, there is still 40-2.32=37.68 (m) 2: A circle is: 37.68 divided by 12=3. 14 (m) 3: Find the diameter: 3.1.
Answer: diameter1m.
46. A batch of goods, the first shipment is 20%, the second shipment is 6 tons, and the third shipment is 2 tons, which is less than the first two neutralization. At this time, one third of the remaining goods have not been transported. How many tons are there in this shipment?
Suppose the total cargo volume is x tons, and the equation is x-20% x-6-1/3x = 20% x+6-2x = 37.5.
47. Cut the radius of a round eye and put it into an approximate rectangle. Given that the circumference of a rectangle is 4 1.4 cm, what is the circumference and area of this circle?
Solution: Let the radius be x cm, because the width of the rectangle is the radius of the circle and the two lengths of the rectangle are the circumference of the circle. The formula for the circumference of a circle is: radius? 2? 3. 14 (3. 14? 2x)+2x = 41.46.28x+2x = 41.48.28x = 41.4x = 5 circumference: radius? 2? 3. 14 5? 2? 3. 14=3 1.4 square centimeter area: radius? Radius? 3. 14 5? 5? 3. 14=78.5 square centimeters, that is, 20%X+6+(20%X+6)-2+x/3=x=37.5 tons.
48. A factory produced 350 products in the first half of the month, and the qualified rate was 90? ; 450 pieces were produced in the second half of the month, with a qualified rate of 96? What is the product qualification rate this month?
350? 90%=3 15 450? 96%=432 pieces (432+3 15)/(350+450)? 100%=747/800? 100%=93.375%
49. In two stores, the profit of store A increased by 25% and that of store B decreased by 25%, so the profits of these two stores are the same. What percentage was the profit of store B originally?
1? ( 1+25%)=4/5 1? ( 1-25%)=4/3 4/5? 4/3=60% 50. 8800 kilograms of apples and pears were harvested in the orchard, and apples were 20% more than pears. How much are these two fruits?
Pear 8800/(1+20%+1) = 4,000 Jin Apple 8800-4,000 = 4,400 Jin.
50. The road construction team planned to complete a road within 30 days, and 45% of the planned road was completed after 9 days of construction. How many days will this finish the task ahead of schedule?
30? 45%= 13.5 days means13.5/9 =1.530/1.5 = 20 30-20 =10 days.
? On the next page, more "math problems in the second volume of grade six"?