Solution: suppose everyone is allowed to carry one kilogram, and the overweight part is B yuan per kilogram.
According to the meaning of the question
90-2a=(5.6+4.4)/b( 1)
90-a= 14/b(2)
By (1)
90-2a= 10/b(3)
(3)/(2)
(90-2a)/(90-a)= 10/ 14
14×90-28a = 10×90- 10a
18a=360
A = 20kg kg
Substitute (3)
10/b=90-40
10/b=50
b=0.2
The weight of free luggage per person on the train is 20kg.
22. Red Star Factory plans to recruit two types of workers 150. The monthly salary of Class A workers is 600 yuan, Class B workers 1000 yuan, and Class II workers 1000 yuan. Can you help the factory director figure out how many people will be recruited for Type A and Type B respectively?
Solution: Recruit Class A workers and Class B workers150-a.
According to the meaning of the question
600 a+ 1000( 150 a)= 100000
6a+ 1500- 10a = 1000
4a=500
A= 125 people
Class a 125 students, class b 150- 125=25 students.
Or: Let's recruit a class A, a class B and a class B..
a+b= 150
600a+ 1000b= 100000
solve
a= 125
b=25
23, there are one or two digits, divided by the sum of their numbers, the quotient is 5, after exchanging two digits, divided by the difference between the single digits of the original number and the ten digits, the quotient is 9, and the two digits are found.
Solution: Let this two-digit number be10A+B.
According to the meaning of the question
10a+b=(a+b)×5
10b+a=(2b-a)×9
simplify
5a=4b
a=4b/5
b=0， 1，2，3，…9
Therefore, only when b=5 and a=4 can the question be answered.
This two-digit number is 45.
24. The circular track of the stadium is 400 meters long. Party A and Party B conduct long-distance running and bicycle practice at a certain speed respectively. If they go in the opposite direction, then they meet every 30 seconds. If you go in the same direction, then B will catch up with A every 80 seconds. What are the speeds of A and B respectively?
Solution: Let the speed of A be a meter/second and the speed of B be b meter/second.
According to the meaning of the question
(a+b)×30=400
(b-a)×80=400
simplify
a+b=40/3( 1)
b-a=5(2)
( 1)+(2)
2b=55/3
B = 55/6m/s
( 1)-(2)
2a=25/3
A = 25/6m/s
The speed of a is 25/6 m/s, which is 250 m/min.
The speed of B is 55/6 m/s, which is 550 m/min.
25. From City A to City B, the waterway is 40 kilometers closer than the land. In the morning 1 1, a ship sailed from city a to city b at a speed of 24 kilometers per hour. At 2 o'clock in the afternoon, a car traveled from city A to city B at a speed of 40 kilometers per hour. The ship and the car arrive at city b at the same time. How long is the waterway and land from city A to city B?
Solution: The water is one kilometer, and Lu Dingyi is one kilometer.
a+40=b( 1)
a/24-3=b/40(2)
(1) into (2)
a/24-3=(a+40)/40
1/60a=4
A=240 km
B = 240+40 = 280
240 kilometers by water and 280 kilometers by land.
Note: 165438+ The difference between 0 am and 2 pm is 3 hours.
1. The distance between the two stations is 275 kilometers. The local train goes from Station A to bilibili at a speed of 50 kilometers per hour. 1h later, the express train runs from bilibili to Station A at a speed of 75km/ h. How many hours after the local train leaves, will you meet the express train?
Set the local train to meet the express train in an hour.
50a+75(a- 1)=275
50a+75a-75=275
125a=350
A=2.8 hours. 2. A car travels from place A to place B at a speed of 40 kilometers per hour. After 3 hours, due to the rain, the average speed was forced to drop 10km. The result arrived at B 45 minutes later than expected. Find the distance between a and b.
Set the original time to one hour.
45 minutes =3/4 hours
According to the meaning of the question
40a = 40×3+(40- 10)×(a-3+3/4)
40a= 120+30a-67.5
10a=52.5
A=5.25=5, 1/4 hours =2 1/4 hours.
So the distance between Party A and Party B is 40×2 1/4=2 10 km.
The locksmith class in a workshop is divided into two teams to watch the tree planting work. The number of people in Team A is twice that of Team B. If 16 people are transferred from Team A to Team B, the number of people left in Team A is three less than that of Team B. What about the original numbers of Team A and Team B?
Solution: Team B originally had A, while Team A had 2a.
Then according to the meaning of the question
2a- 16 = 1/2×(a+ 16)-3
4a-32=a+ 16-6
3a=42
a= 14
Then team B was originally 14, and team A was originally 14×2=28.
At present, team B 14+ 16=30 people, and team A = 28- 16= 12 people.
4. It is known that the profit of a store in March is 654.38+10,000 yuan, and the profit in May is1320,000 yuan. The month-on-month growth rate in May was 654.38+00 percentage points higher than that in April. Find the monthly growth rate in March.
Solution: Let April profit be X.
Then x * (1+10%) =13.2.
So x= 12 let the growth rate in March be y.
Then10 * (1+y) = X.
Y=0.2=20%, so the growth rate in March is 20%.
5. The school arranges dormitories for boarding students. If there are 7 people living in each dormitory, 6 people can't arrange it. If there are 8 people living in each dormitory, then there are only 4 people living in one dormitory, and there are 5 empty dormitories. How many people are there?
Solution: There is room A, with 7a+6 people in total.
7a+6=8(a-5- 1)+4
7a+6=8a-44
a=50
Someone =7×50+6=356 people
6. One kilogram of peanuts can fry 0.56 kilograms of peanut oil, so how much peanut oil can be fried in 280 kilograms?
Proportional solution
Suppose you can fry one kilogram of peanut oil.
1:0.56=280:a
A = 280× 0.56 = 156.8kg Complete formula: 280 ÷/kloc-0 /× 0.56 =156.8kg.
7. A batch of books are distributed to Class 1 10 and Class 2 15. How many books have been distributed in both classes now?
Solution: Let's assume that there are a total of books.
Class number =a/ 10
Number of Class Two =a/ 15
Then they are evenly divided into two categories, each of which is a/(a/10+a/15) =10×15/(10+15) =/kloc.
8. The tree planting team of June 1st Squadron went to plant trees. If everyone plants five trees, there are still 65,438+04 seedlings left. If each race has seven trees, there will be six fewer seedlings. How many people are there in this team? A * *, how many seedlings?
Solution: There is one person.
5a+ 14=7a-6
2a=20
a= 10
A * * * has 10 people.
There are 5× 10+ 14=64 saplings.
9. A barrel of oil weighs 50 kilograms. Half of the soybean oil poured out for the first time was less than 4 kilograms, and the remaining three-quarters were two and two-thirds kilograms more for the second time. At this time, the barrel filled with oil weighs one third of a kilogram. How much oil was there in the original barrel?
Solution: Let the oil weigh one kilogram.
Then the barrel weighs 50-a kilograms.
Pour out 1/2a-4kg for the first time, leaving 1/2a+4kg.
Pour out 3/4× (1/2a+4)+8/3 = 3/8a+17/3kg for the second time, leaving1/2a+4-3/8a-17/3 =/kloc.
According to the meaning of the question
1/8a-5/3+50-a= 1/3
48=7/8a
A = 384/7kg
There used to be 384/7kg of oil.
10, use a bundle of 96m cloth to make clothes for the students in Class 1, Grade 6, 15 use 33m cloth. According to this calculation, which class is the most suitable for these fabrics to make school uniforms? (1 class 42, class 2 43, class 3 45)
Give person a 96 meters.
According to the meaning of the question
96:a=33: 15
33a=96× 15
A about 43.6
So it is suitable for Class 2, with a surplus, but not much. It is not enough to do it for Class Three.
1 1, a fraction. If the numerator adds 123 and the denominator subtracts 163, the new fraction is 3/4; If the numerator adds 73 and the denominator adds 37, then the new score is reduced to 1/2, and the original score is found.
Solution: Add 123 to the original fractional numerator and subtract 163 from the denominator to get 3a/4a.
According to the meaning of the question
(3a- 123+73)/(4a+ 163+37)= 1/2
6a- 100=4a+200
2a=300
a= 150
Then the original score = (3×150-123)/(4×150+163) = 327/763.
12. The fruit shop sent a batch of fruits. On the first day, it sold 60 kilograms, which is exactly two-thirds of the sales the next day. In two days, it sold a quarter of the fruit. How many kilograms is this batch of fruit (equation solved)?
Suppose the fruit used to have a kilo.
60+60/(2/3)= 1/4a
60+90= 1/4a
1/4a= 150
A=600 kg
This kind of fruit used to weigh 600 kilograms.
13. There is a batch of goods in the warehouse. After three-fifths of the goods were shipped out, 20 tons were brought in. At this time, the goods are exactly half of the original. How many tons are there in the warehouse? (Equation solving)
Suppose there was a ton.
a×( 1-3/5)+20= 1/2a
0.4a+20=0.5a
0. 1a=20
a=200
It used to be 200 tons.
14, Uncle Wang enclosed a rectangular vegetable field with a 48-meter-long fence. The length-width ratio of this rectangle is 5: 2. What is the area of this vegetable field?
Solution: Let the length and width be 5m and 2m respectively.
According to the meaning of the question
5a+2a×2=48 (wall as width at this time)
9a=48
a= 16/3
Length = 80/3m
Width = 32/3m
Area = 80/3×16/3 =1280/9 m2.
or
5a×2+2a=48
12a=48
a=4
Length = 20m
Width = 8m
Area = 20× 8 = 160m2.
15, a city mobile phone has the following two charging methods:
The first one: Pay 22 yuan's fee every month, and then charge 0.2 yuan's phone bill in cents.
The second type: no monthly fee, call charge per minute, 0.4 yuan.
If you talk for 80 minutes a month, which billing method is cheaper? If you talk for 300 minutes a month, which billing method is cheaper?
Set the monthly call for one minute.
When the two charges are the same
22+0.2a=0.4a
0.2a=22
a= 1 10
So when the call is 1 10 minutes, the charge is the same.
When talking for 80 minutes, it takes 22 seconds+0.2× 80 = 38 >; 0.4×80=32
When passing 300 minutes, use the first 22+0.2× 300 = 82.
I need references.