Application problems and answers of solving equations in seventh grade mathematics: 1-5.
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 drives 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. As a result, it arrived at B 45 minutes later than expected, so we can 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 a and b is 40? 21/4 = 210km.
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?
There used to be A in Team B, and 2a in Team A..
Then according to the meaning of the question
2a- 16= 1/2？ (a+ 16)-3
4a-32=a+ 16-6
3a=42
a= 14
So team B has 14 people and team A has 14 people? 2=28 people
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, and the monthly growth rate in May is 10 percentage point higher than that in April.
Let the profit in April 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 was 20%
5. The school arranges dormitories for boarding students. If there are seven people living in each dormitory, no six 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?
There is room A, a total of 7a+6 people.
7a+6=8(a-5- 1)+4
7a+6=8a-44
a=50
Someone =7? 50+6=356 people
The seventh grade math equation solving application problems and answers: 6- 10.
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? 1? 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?
There is usually a book.
Class number =a/ 10
Number of Class Two =a/ 15
Then they are divided into two categories on average, each of which is a/(a/10+a/15) =10? 15/(10+15) =150/25 = 6 copies.
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?
There's a man
5a+ 14=7a-6
2a=20
a= 10
A * * * has 10 people.
There are saplings 5? 10+ 14=64 trees.
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?
Set the weight of oil to one kilogram.
Then the barrel weighs 50-a kilograms.
Pour out 1/2a-4kg for the first time, leaving 1/2a+4kg.
Three quarters for the second time? (1/2a+4)+8/3 = 3/8a+17/3kg, leaving1/2a+4-3/8a-17/3 =1/8a.
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.
Application problems and answers of solving equations in seventh grade mathematics: 10- 15.
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
Answer? 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 1/2. Find the original score.
Let the numerator of the original fraction add 123 and the denominator subtract 163 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
So 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.
Answer? ( 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?
Set the length and width to 5m and 2m respectively.
According to the meaning of the question
5a+2a？ 2=48 (the wall is used as the width at this time)
9a=48
a= 16/3
Length = 80/3m
Width = 32/3m
Area =80/3? 16/3 =1280/9m2
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 you talk for 80 minutes, use 22+0.2 seconds? 80=38 >0.4? 80=32
After 300 minutes, use the first 22+0.2? 300=82