Let Lili have X yuan, and every family has Y yuan.
3/5 times = 2/3 years
2/5x= 1/3y+5 (Lily has 2/5 left, and 1/3)
X=50 y=45 when solving a quadratic equation, that is, Lily 50 yuan's 45 yuan book 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 = 60km1÷ 60 =1/60h.
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, and the number of girls remains the same, so (1-4/7) x = (x-5) *12/23.
Find 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: 20*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 female student: 36×4/9= 16 (person)
Former male classmate: 36- 16=20 (person)
Total number of employees: 20( 1-3/5)= 50 (persons)
Female: 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 both parties have their own.
560 ÷ 2 = 280 tons
It turns out that Jia has
280 ÷ (1-2/9) = 360 tons.
It turns out that b has it.
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?
Full time
1-2/5=3/5
be
20+70 = 90km
Distance between Party A and Party B
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 accounted for the whole book.
3/8- 1/5=7/40
This book * * * has
28/7/40 = 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 this batch has x parts.
1/28X=84-63
1/28X= 19
X=532
So there are 532 parts in this batch.
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
=1325km
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.
Number of boys: 46/(8+ 15)*8= 16.
The number of girls is 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 was given to Zhang Hong. How many hours does it take to copy it?
( 1- 1/3)/( 1/5)= 10/3
It takes 3 1/3 hours 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 = 48km
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 weight of fruit on the first day, you will sell 2/5 the next day.
3/5-2/5= 1/5, the first day is more than the second day,
30 ÷ 1/5 = 150kg，
The formula is,
1-3/5=2/5
3/5-2/5= 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 ...
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 people
Male students have
12× 6 = 72 people
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: 15
25. The number of trees planted in Jiefang Road Primary School this year is 65438+ 0.2 times that of last year. Write down the ratio between the number of trees planted in this primary school this year and the number of trees planted last year.
1.2: 1=6:5
Last year, the ratio of the output of color TV sets to the total output of TV sets in a TV factory was 9/20. Last year, * * * produced 250,000 TV sets, including how many color TV sets?
250000× 9/20 =112500 sets.
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 for 10% of the total factory employees.
1-2/3-2/9 = 65438/9+0
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 people is an integer,
So the class size can be divisible by 5+6 = 1 1.
So the class size is 44.
Boys have
44 ÷ (5+6) × 5 = 20 people
Girls have
44-20 = 24 people
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 literary works: 300 ÷ (7/12-5/9) =10800 (this).
The number of literary and artistic books increased: 300÷ 10800≈2.8%.
30.100g sugar water just fills a glass, including10g sugar. Pour out10g sugar water from the cup, and then fill the cup 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 out 10g, with 90 left, including 8 1 water and 9 sugar.
Fill it with water, the water is 9 1, and the sugar is still 9.
That is 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.
(2) A group has 108 students ×5/9=60 students.
(3) There are 108 people in the second group ×4/9=48 people.
32. There are 465 students in a school, of whom 2/3 are girls and 20 are less than 4/5 boys. How much is the male and female?
Two thirds of the girls are 20 less than four fifths of the boys.
Girls are less than boys by 20/(2/3)= 30(4/5)/(2/3)= 6/5.
Boys have
(465+30)/( 1+6/5)=225 (person)
Girls have
465-225=240 (person)
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 (2/5-65438/7+0)
=9 divided by 9 of 35.
=35 pages
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, it is more than 3, which is 24 meters.
Then one is: 24/3=8 meters.
That is, the length is 8 * 8 = 64m and the width is 8 * 5 = 40m.
Area: 64 * 40 = 2560m2.
35. If there are 25% more boys than girls, how many girls are less than boys?
Female students 1.
For 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.
Raise 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?
Let Xiao Wei donate X yuan.
So 2:5=X:35: X= 14 yuan Xiaowei donated 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?
The third number is 8.4.
Solution: Let the third number be x and the column equation be:
3*[9.2+(x-0.8)+x]=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?
If the length of the second root is x meters, the length of the second root is 1.5x meters.
1.5x-x=3
0.5x=3
x=6
6× 1.5 = 9 (m)
The first one is 6 meters long.
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?
4+5=9
Solution: Let this road be x meters long:
(5/9-4/9)x=25
1/9x=25
x=225
This road is 225 meters long.
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.
Then the radius is: 16/2=8.
The area of this circle is 3. 14*8*8=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) 2 =100/81times. Here is the problem of difference times, and the small number = difference/(multiple -0 times).
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.
Each internal angle of a regular Pentagon is 180*(5-2)/5= 108 degrees.
(360- 108)/360 * pi * 6 2+2 *( 180- 108)/360 * pi(6-2.5)2+2 *( 180-6508)
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: 40-2.32=37.68 (m) If not left.
2. One circle is: 37.68 divided by 12=3. 14 (meter).
3. Find the diameter: 3. 14 divided by 3. 14= 1 (m).
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?
Assuming that the total quantity of this batch of goods is x tons, the equation is given.
X-20%X-6- 1/3X=20%X+6-2
X=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 of the circumference is: radius ×2×3. 14.
(3. 14×2x)+2x=4 1.4
6.28x+2x=4 1.4
8.28x=4 1.4
x=5
Circumference: radius ×2×3. 14.
5× 2× 3. 14 = 3 1.4 cm2
Area of circle: radius × radius ×3. 14.
5×5×3. 14=78.5 square centimeters.
Namely: 20% x+6+(20% x+6)-2+x/3 = X.
X=37.5 tons
48. A factory produced 350 products in the first half of the month, with a qualified rate of 90 ‰; 450 pieces were produced in the second half of the month, and the qualified rate was 96‰. What is the product qualification rate this month?
350*90%=3 15 pieces
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. There are 20% more apples than pears. How much are these two fruits?
Pear 8800/(1+20%+1) = 4000 Jin.
Apple 8800-4000=4400 Jin
5 1. The road construction team plans to complete a road within 30 days, and 45‰ of the planned road will be completed after 9 days of construction. How many days will it finish the task ahead of schedule?
30*45%= 13.5 days
Description 13.5/9= 1.5
30/ 1.5=20
30-20= 10 days
52. How many grams of water do you need to add to make salt water with salt content of 5% with 20 grams of salt? (column calculation)
20 divided by 5%=400
400-20=380
53. Xiaoming deposited 1500 yuan in the bank for a fixed period of 3 years. How much interest can he get at maturity? (Recalculate the annual interest rate after investigation)
Annual interest rate 1 year 4. 14%.
3 years 5.4%
5 years 5.58
2 years 4.68%
Principal * Time * Interest Rate = Interest
1500*3*5.4%
= 4500 & amp5.4%
=243 (yuan)
A: He can get interest of 243 yuan at maturity.
54.A \ B Two people process 1 batch of parts at the same time, and several parts; After six hours, A did 20% more than B. How many hours did B do alone?
It takes 13.2 hours. Let the completion quantity of B be X, then A will complete (1+20%) X.
X+(1+20%) x =1x = 5/1,so b completed 5/1of the total in 6 hours.
The total amount of completion is 6 ÷ 5/11=13.2 hours.
55. Take 2500 grams of rice, and after drying, there is 1284 grams left. Find the drying speed and moisture content of rice.
Drying rate:1284/2500 *100% = 51. 36%
Water content: 1-5 1. 36%=48。 64%
56. The price of a blue cat coat after 4% reduction is the same as that of a pair of blue cat sports shoes after 20% increase, both of which are in 96 yuan. How much is the original price of the blue cat coat and sneakers?
Solution: blue cat coat x yuan, sports shoes y yuan.
0.96X=96
X= 100
1.2Y=96
Y=80
A: original price of blue cat coat 100 yuan, sneakers 80 yuan.
57. The garment factory planned to produce 2,000 sets of children's clothes in September, and as a result, 55% of the planned output was completed in the first half of the year, and the number completed in the second half was the same as that in the first half. How many sets were actually overproduced in September?
First half
:2000*55%= 1 100
The second half: 1 100
Actual in September: 2200 exceeded 200.
58. The Agricultural Machinery Factory produced 1500 seeders last year, 300 more than planned. What is the percentage of exceeding the plan?
The plan is 1500-300= 1200 units.
300/ 1200=25%
More than 25%
58. It is known that the sum of the original prices of aquatic products A and B in an aquatic product market is 100 yuan. Due to market changes, aquatic products A will be promoted at a 10% discount, while aquatic products B will be promoted at a 50% discount. After the price adjustment, the sum of the prices of aquatic products A and B is 2% higher than the sum of the original prices. How much is the original price of aquatic products A and B?
Solution: If the original price of A is X, then the original price of B is100-X.
0。 9X+( 100-X)*( 1+5%)= 100( 1+2%)
X=20
A: The original price is 20 yuan, and the original price is 80 yuan.
59. The length of a thick candle is the same as that of a thin candle. Thick candles can be lit for 5 hours, and thin candles can be lit for 4 hours. If these two candles are lit at the same time, after a period of time, the remaining thick candle is four times as long as the thin candle. How long have these two candles been lit?
Solution: let the blackout time be x.
1-X * 1/5 = 4[ 1-X * 1/4]
x= 15/4
That is, it stopped 15/4 hours.
60. The express train goes from A to B, and the local train goes from B to A. The two trains leave at the same time and meet eight hours later. After the two cars met, they continued to drive for 2 hours. At this time, the express train is 250 kilometers away and the local train is 350 kilometers away from A ... How many kilometers is there between A and B?
Let the total distance be s, and the sum of the speeds of the express train and the local train be a.
From the meeting after 8 hours, we can get: S=8A,
After driving for 2 hours, because the total distance remains unchanged, we can express S=350+250+2A again.
So there is 8A=350+250+2A. Connect the equations to get A= 100.
So the distance between the two places is s = 8a = 800km.
6 1. For three digits, the tenth digit is 3 larger than the hundredth digit and 1 smaller than the hundredth digit, and the sum of the three digits is 50 times smaller than the three digits. Find this three-digit number
Solution: let x be in the tenth place, X-3 in the first place, and X+ 1 in the hundredth place.
(X+X-3+X+ 1)* 50 = 100(X+ 1)+ 10X+(X-3)-2
X=5
A: This three-digit number is: 652.
62. Arbor Day, 170 Senior three students go to participate in voluntary tree planting activities. If boys can dig three tree pits a day and girls can plant seven trees a day, then only one tree will be planted in each tree pit. How many men and women are there in this grade?
Solution: There are X boys and (170-X) girls.
3X=7( 170-X)
X= 1 19
170-X=5 1
A: Boys 1 19, girls 5 1.
63. Four years ago, my sister was twice as old as her sister. This year, she is 1.5 times as old as her sister. How old is my sister this year?
Suppose: my sister was x four years ago.
Then four years ago, my sister X/2
Sister (X+4)÷(X/2+4)= 1.5 this year.
So X=8.
So this year X+4= 12 years old.
64. The sum of the number of excavators and the number of loading and unloading vehicles in a development zone site is 2 1. If each excavator digs an average of 750 cubic meters of soil every day, it will just allow the excavated soil to be shipped out in time. What are the number of excavators and loaders?
Set excavator x, and then install 21-x.
750*X=(2 1-X)*300
Then X= 14.
65. Last year, Factory A and Factory B completed 1 12% and 1 10% respectively, and * * * produced 4,000 tons of grain, 400 tons more than the sum of the original plans of the two factories. What is the initial production task of Factory A?
The original production task of a factory is X.
1 12% x+ 1 10%(3600-x)= 4000
1. 12x+3960- 1. 1x = 4000
0.02x=40
x=2000
A: The original production task of Factory A was 2000 tons.