( 12.4+8.6)*( 1- 1/5)
=2 1*4/5
= 16.8 (yuan)
During the winter vacation, Fang Li and three good friends went to the bookstore. The four of them came to the stationery bookcase of the bookstore and saw a notebook, the original price was 2.80 yuan, with a 20% discount on holidays, and there was a "buy three get one free" activity. I bought one each. How can I get a better deal?
Buy 3 copies and get 1 copy.
Hua 2.8*3/4=2. 1
One copy per person, 2. 1 yuan per person.
The football match has the reputation of "the first sport in the world". The height of the soccer goal is 6 1/25m, which is 1/3 of the width of the soccer goal. What is the circumference of the football goal?
(6 1/25)* 3+2 *(6 1/25)= 6 1/5m。
4. Wei 16 years old, grandpa 6 1 year old. A few years ago, Grandpa was exactly six times as old as Xiao Wei.
This year, the difference between grandpa and grandson is 45 years old, which is also 45 years ago. A few years ago, grandpa was six times older than his grandson, so grandpa was five times older than his grandson.
45/5=9, so it was 7 years ago, my grandson was 9 years old and my grandfather was 54 years old.
The ratio of boys to girls in class 6/kloc-0 is 3: 2. In the math unit exam, the average score of boys is 86 and that of girls is 89. 6 1 class What is the average score of this exam?
The average score of boys multiplied by the number of boys in the class is 86*3=258.
The ratio of the average score of girls multiplied by the number of girls in the class is 89*2= 178.
258+ 178=436 divided by the class size of 436/5=87.2, then the average score of this class is 87.2.
6.a. B has three people 185 yuan. The ratio of money between Party A and Party B is 3: 4, and Party A has less 5 yuan than Party C. How much money does Party A have?
Let A be 3X, then B is 4X. Then c is 3X+5.
They have 185.
Then it is 3X+4X+3X+5= 185.
X is 18.
So A has 54 yuan.
7. Cement in some building concrete. Yellow sand. The ratio of stones is 2: 3: 5. Now there are 4 tons of cement, 12 tons of yellow sand and 24 tons of stones on the construction site. Is it enough to be so specific? Why?
The proportion of cement, yellow sand and stones is 2; 3; five
So now there are 4 tons of cement, 6 tons of yellow sand, 10 tons of stone.
From the perspective of yellow sand, yellow sand is 12 tons, so cement should be 8 tons and stone should be 20 tons.
It can't be compared because the cement is only 4 tons.
From the perspective of stone, 24 tons of stone needs 9.6 tons of cement and 14.4 tons of yellow sand.
Cement and yellow sand are not enough.
The final result doesn't match.
8. A runs 13 km per hour, B runs 1 1 km per hour, and B runs 20 minutes longer than A. As a result, B runs 2 km longer than A. How many kilometers did B run?
General manager B ran away 14 19 km.
20 *11-2 = 218km is the time for A to run, and A runs more than B.
2 18/2= 109 hours (running time of a)
109+20= 129 hours (running time of b)
11*129 =1419 km.
There are 3 yellow balloons in 9.2 yuan and 2 flower balloons in 3 yuan. The school bought 32 balloons, of which 4 flower balloons are less than yellow balloons. What balloons do schools spend more money on?
It costs a lot of money to spend balloons
(32-4)/2= 14 flower balloon, * * with 3*( 14/2)=2 1 yuan.
Yellow balloon 14+4= 18, * * with 2*( 18/3)= 12 yuan.
10. Struggle Primary School organized sixth-grade students to go camping and training in Baihua Mountain, and the trip increased by 2 kilometers every day. I went for four days and came back for three days. How many kilometers is the school from Baihua Mountain?
The school is 84 kilometers away from Baihua Mountain.
The first day's trip = 8+10+12-(2+4+6) =18.
18 * 4+(2+4+6) = 84km.
1 1. Hong Guang Primary School donated money to Project Hope. The donations from students in grade 5.6 account for 55% of the whole school, among which the donations from students in grade 5 contribute to 720 yuan, and the donations from students in grade 6 account for 1/4 of the whole school. How much did the school donate?
Let the sixth grade donation be X.
Then: 720+X=4X(55%) A number plus 1 is a multiple of 2, plus 2 is a multiple of 3, plus 3 is a multiple of 4, and plus 4 is a multiple of 5. What is the minimum number except 1?
Solution: X=600
So the whole school donation is: 4 * 600 = 2400.
12. There is a cuboid with a bottom area of 200 square centimeters and a height of 12 centimeters, which contains water with a depth of 5 centimeters. Now put a stone into the water, and the water level will rise by 7.5 cm. What is the volume of this stone?
It should be raised to 7.5 cm, otherwise 5+7.5= 12.5 will be full.
If it rises to 7.5 cm, the volume is 200*(7.5-5)=500 cubic centimeters =0.5 cubic decimeter.
13. Party A has deposits in 520 yuan and Party B has deposits in 240 yuan. After both of them withdraw the same amount of money, the remaining amount of A is five times that of B. How much do they withdraw?
The difference between them is 520-240=280 yuan.
After withdrawing money, b should be 280÷(5- 1)=70 yuan.
So, B takes out 240-70= 170 yuan.
Total * * * take out 170+ 170=340 yuan.
14. A store buys a batch of tapes at the price of every three 16 yuan, and buys the previous batch of tapes at the price of 2 1 yuan every four. If they all get 20% investment at the price of K yuan for every three sets, find the K value.
Let the first batch be close to X, then the second batch is 2x, the total cost is 16x\3+42x\4, and the sales volume is 3kx\3=kx. Then according to the profit of 20%, we can get an equation, 5kx=32x+63x, k= 19.
15. The distance between Party A and Party B is 496 kilometers. Car A travels from A to B at a speed of 32 kilometers per hour. Half an hour later, car B travels from B to A at twice the speed of A. How many hours after car B leaves, will the two cars meet?
Suppose two cars meet in x hours.
32×0.5+32x+32×2x=496
x=5
16. Mingming and Liangliang go shopping, and the ratio of money they bring is 7:6. 50 yuan was obviously used, and 60 yuan was used, and the ratio of their remaining money was 3:2. How much money do they have left?
Let's make it clear that there is X yuan, then there is 6x/7 yuan.
(x-50)3 =(6x/7-60)2
x= 140
Obviously, it is 140 yuan, and Liangliang is 120 yuan. 90 yuan and 60 yuan are left.
17. Warehouse A has 132 tons of grain, and Warehouse B has 74 tons of grain. Now 34 tons of grain will be transferred to two warehouses, making warehouse A twice as big as warehouse B. How many tons will warehouse A and warehouse B transfer?
If x tons are transferred to warehouse a, warehouse b is 34-x tons.
132+x=(74+34-x)×2
x=28
28 tons will be transferred to A and 6 tons to B.
18. A project will be completed by one person in team A 12 days and one person in team B 15 days. How many days can the two teams work together?
1/(115+112) = 20/3 (days)
19. A number plus 1 is a multiple of 2, plus 2 is a multiple of 3, plus 3 is a multiple of 4, and plus 4 is a multiple of 5. What is the minimum number except 1?
=60
60+ 1=6 1
In order to sign a purchase and sale contract with Wang Laohan, he needs to estimate the total weight of fish in his fish pond. For the first time, he fished out 100 fish, weighing 184 kg, and put each fish into the water. When they were completely mixed with fish, he fished out 200 fish, weighing 465,438+06 kilograms. How many kilograms does the marked fish weigh?
200/20 * 100 = 1000 articles
184/ 100 = 1.84kg。
4 16- 1.84 * 20 = 379.2kg。
(379.2+ 184)/( 100+200-20)≈2.0 1 14kg
1000 * 2.0 1 14 = 20 1 1.4kg。
A: It is estimated that there are 1000 fish in the fish pond, ***20 1 1.4 kg.
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: 30010800 ≈ 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 plan 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.