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Practical problems of Grade 7 (solved by equation) 1. Ask the child's age, and answer: "9% less than half of my father's age", ask the father's age, and answer: "3 times older than my child's age", and ask the child's age? 2. The price of a commodity is increased by 50% of the cost price, and then 20% off (80% of the price). The price is 240 yuan. How much is the profit of this commodity? 3. There is a train passing through the first and second tunnels at the speed of 600 meters per minute. It is known that it takes 5 seconds more to pass through the second tunnel than the first tunnel. The length of the second tunnel is twice that of the first tunnel, and it is 50 meters shorter. What is the length of each tunnel? (write steps or equations)
1. Suppose the child's age is x, then the father's is 3x + 3
x=(3x+3)/2-9
The solution is x = 15
2. Suppose the cost price is X
x(1+50%)*80%=240
x=200
Profit: 240-200 = 40 yuan
3. If the first tunnel is x m, the second tunnel is 2x-50 m, including:
600 meters per minute = 10 meters per second
It is known that the second tunnel takes 5 seconds more than the first tunnel = 5 * 10 = 50 meters more
So:
2x-50=x+50
x=100
The second tunnel is 100 meters, and the first one is 100-50 = 50 meters
Solving two practical problems with equations
1. The master and apprentice have to process 360 parts, 240 parts in the first four hours. How many hours will it take to finish the rest of the parts?
2. A workshop needs to process 1440 parts, which was originally planned to be completed in 20 days, but actually 360 parts were processed in the first 4 days. How many days ahead of time can the task be completed according to this efficiency?
1. It will take x hours to finish processing
240+(240/4)*x=360
x=2
2. Set X days in advance
1440/(360/4)+x=20
x=4
Two equations to solve practical problems
1. When the dog jumps for 6 times, the rabbit can only jump for 4 times. The distance of the dog jumping for 3 times is equal to that of the rabbit jumping for 7 times. The rabbit runs 5.5m first, and then the dog starts to chase. How many meters is the rabbit overtaken?
2. There are 10 instruments in Beijing and 4 instruments in Shanghai. At present, Chongqing needs 8 instruments and Wuhan needs 6 instruments. It costs 400 yuan to transport from Beijing to Wuhan and 800 yuan to transport to Chongqing. It costs 300 yuan to transport from Shanghai to Wuhan and 500 yuan to Chongqing. How to design it?
1. When the dog jumps for 6 times, the rabbit can only jump for 4 times. The distance of the dog jumping for 3 times is equal to that of the rabbit jumping for 7 times. The rabbit runs 5.5m first, and then the dog starts to chase. How many meters is the rabbit overtaken?
In this way, the rabbit runs twice as many times as the dog, and the distance is 3 / 7. When the dog overtakes the rabbit from 0, the rabbit runs 2 / 3 * 3 / 7 of the dog
So: 5.5 / (1-2 / 3 * 3 / 7) - 5.5 = 2.2m
A: the rabbit is overtaken by another 2.2m
2. Set up station x from Beijing to Chongqing and 8-x from Shanghai to Chongqing
800X+500(8-X)+400(10-X)+300[4-(8-X)]=8000
X=6
A: six from Beijing to Chongqing and two from Shanghai to Chongqing
Four from Beijing to Wuhan, two from Shanghai to Wuhan
RELATED INFORMATIONS
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