It can be solved by binary linear equations.
There are x kilograms of apples in basket A and y kilograms of apples in basket B.
X+Y= 100
( 1+2/9)( 1-25%)X = Y+25% X
Solving this equation group can get X=60, and there are 60 kilograms of apples in a basket.
1. It takes 30 seconds for the train to completely pass the 300-meter-long iron bridge, and it takes 10 seconds to completely stay on the bridge. The length and speed of the train.
Solution:
l+300=30v
300-l= 10v
v= 15m/s
L =150m
Answer: vehicle length150m, speed15m/s. ..
2. A class of students went to Beishan for an outing, 18km. There is only one car, so it needs to be divided into two groups. Group A takes the bus first, and Group B walks. The bus goes to Group A, Group A gets off and walks, and the bus goes back to Group B. Finally, the two groups arrive at Beishan at the same time. Given the car speed of 60km/h and the walking speed of 4 km/h, find the distance from point A to Beishan.
Let the speed of a be x and the speed of b be y.
80x+80y=400
80y-80x=400
So x=0 y=5 (the time of this question is 80 seconds, which is not true)
3. Let the distance from point A to Beishan be X, and when the car returns to group B, the distance from point B to the starting point is Y..
Then [x-4 * (18-x-y)/60]/4 = (18-y)/60.
y/4 =( 18-x)/60+( 18-x-y)/60
So x=2 y=2.
Point A is 2 kilometers away from Beishan.
3. Peony Cup football match 1 1 round (that is, each team needs to play 1 1 game). If you win a game, you will get 3 points, if you draw a game, you will get 1 point, and if you lose a game, you will get 0 point. The team of Guoxing Sangao Club won four times as much as it lost, and the result was * * * 25 points. The team won the trophy.
Let x win and y lose, then 1 1-x-y will be even.
x=4y
3x+ 1 1-x-y=25
x=8
y=2
Eight wins and two losses 1 draw.
In extracurricular activities, some students take part in group activities. Originally, there were 8 people in each group, and then they were regrouped, and each group had 12 people, which decreased by 2 groups. How many students are there?
Suppose there is an X organization. So the number of people is 8x.
(x-2) 12=8x
x=6
* * * There are 48 people.
5. There is a high-speed wind belt above the surface 10 km. Suppose there are two planes flying at the same speed in this wind belt, and one of them flies from A to B, the distance is 4000 meters, which takes 6.5 hours; At the same time, another plane flew from B to A in only 5.2 hours. What is the average speed of the plane and the wind?
Let the average speed of the aircraft be xkm/h and the wind speed be ykm/h.
From the meaning of the question, we can see that there is headwind from A to B and tailwind from B to A, and the countable equation is:
x+y=4/5.2
x-y=4/6.5
Solution: x = 9/ 13, y =113.
6. A team travels at a speed of 5 kilometers per hour. Twenty minutes later, a correspondent caught up with the team at a speed of 15 km/h. How many hours will it take him to catch up with the team?
5*( 1/3)+5*X= 15*X
x= 1/6
6. A harvester harvests 12 hectares of wheat every day. Cutting 2/3 of the wheat field improved the efficiency to 5/4 times of the original, so it was completed 1 day ahead of schedule. How many hectares of wheat fields are there?
Assuming that the wheat field is x hectares, because two thirds of it has been cut, there is still 1/3 left, and the equation is obtained:
( 1/3)x/ 12 =( 1/3)x/[ 12 *(5/4)]+ 1
Simplify:
(5/3)x=(4/3)x+60
( 1/3)x=60
x= 180
So the wheat field has 180 hectares.
7. Party A and Party B invest in the company according to the ratio of 2: 5, and agree to share the profits according to the investment ratio. If the profit in the first year is 14000 yuan, how much should Party A and Party B share respectively? Solutions of equations
Solution: let every minute be divided into X.
2X+5X= 14000
7X= 14000
X=2000
2X=4000
5X= 1000
So A gets 4000 yuan and B gets 10000 yuan.
8. According to the regulations of civil aviation, an ordinary class passenger can carry up to 20 kilograms of luggage for free, and the excess can be purchased at the ticket price of 15% with the baggage ticket. A passenger carries 35 kilograms of luggage, pays the air ticket and baggage ticket 1323 yuan, and asks for the passenger's air ticket fee.
Please do equations to solve application problems.
Set the fare to x yuan.
x+(35-20)* 1.5% x = 1323 x = 1080
(It should be 1.5% per kilogram, not 15%) It is impossible to charge that high. If it is so high, the calculation result is not an integer, which is not in line with the actual fare of the air ticket. If it is charged according to 15%, the answer is 407; if it is charged according to 1.5%, the answer is 6544.
9. When a store sells two goods with the same price, one of them gains 25% and the other loses 25%. Is it a profit or a loss to sell these two goods?
Solution: Suppose the prices of these two commodities are both X yuan.
Because the purchase price is x/(1+25%)+x/(1-25%) = 4/5x+4/3x = 32/15x.
The price is, x+x=2x.
32/ 15x & gt； 2x instant purchase price > price
So lose money
10. It takes 30 seconds for the train to completely pass the 300-meter-long iron bridge, and it takes 10 seconds to completely stay on the bridge. The length and speed of the train.
Solution:
l+300=30v
300-l= 10v
v= 15m/s
L =150m
Answer: vehicle length150m, speed15m/s. ..
1 1. An intelligence test with 20 multiple-choice questions. The grading standard is: 1 5 points for the question, 2 points for the wrong 1 question, no points or points for not answering the question. Xiao Ming has two unanswered questions. Answer at least a few questions correctly, and the total score will not be less than 60 points.
12. Always working, Party A needs to do it alone 15 days, and Party B needs to do it alone 12 days. Party A and Party B will cooperate in this work. During the construction period, Party B will rest for 7 days and finish it in a few days.
13. Given (x+3) \ (x+2) = 1 \ (root 3+ root 2+ 1), find (x-3) \ (2x-4) ÷ [5 \ (x)
14. The scale in a store is not allowed (the arms are not equal), and the weight is 1kg. A customer wants 2 kilograms of candy. The salesman put the weight of 1kg on the left plate, balanced the candy on the right plate and handed it to the customer, then put the weight of 1kg on the right plate, and balanced it and handed it to the customer.
15. A computer company sells two kinds of computers, A and B. It sold 2,200 computers the year before last. Last year, 6% more computers A were sold than the previous year, and 5% fewer computers B were sold. The total sales of the two computers increased by 1 10. How many computers did A and B buy the year before last?
16. A clothing factory accepts a batch of clothing orders and produces according to the planned number of days. If 20 sets of clothes are produced every day, the production is less than the ordering task 100 sets; If we produce 23 sets of clothes every day, we will produce 20 sets more than the ordering task. What is the ordering task of this batch of clothes? How many days was originally planned to be completed?
17. A cargo ship has a deadweight of 400 tons and a volume of 860 cubic meters. There are two kinds of goods to be loaded now, pig iron and cotton. The volume of each ton of pig iron is 4 cubic meters. How many tons of pig iron and cotton can be loaded separately to make full use of the load and volume of the ship?
18. For every 2,500 yuan increase in the original price of a refrigerator in a store, it is now sold at a 20% discount. What is the current price of each elevator? If you want the sales before and after the price reduction to be 500,000 yuan, how many sets of sales must you increase?
19. The purchase price of a commodity is 1000 yuan, and the price is 1500 yuan. The store requires a discount at the selling price, and the profit rate is not less than 5%. How much discount can the salesperson give to sell this product?
20. The purchase price of commodity A is 1400 yuan, and it is sold at a 10% discount on the list price of 1820 yuan; Commodity B is sold at 20% off the bid price in 400 yuan and 560 yuan. Which profit margin is higher?