Passengers are waiting for ticket checking in the waiting room of the station, and the number of passengers queuing is increasing at a certain speed. It takes half an hour to check all the passengers who want to check the ticket at the station. Open two ticket gates at the same time, and all passengers can enter the station in ten minutes. There is an extra train to transport passengers across the border, and all passengers must check in within five minutes. How many ticket gates should this station open at least at the same time?
Analysis:
(1) This question is practical, and the quantitative relationship given is somewhat obscure. After careful reading, it is found that the number involved is: the original queue number, the number of passengers increasing at a certain speed, the ticket checking speed at each ticket gate and so on.
(2) Give a representative symbol to the quantity analyzed: set the number of passengers waiting for ticket checking at the beginning of ticket checking as X, increase the queue by Y every minute, and check Z at each ticket gate every minute. At least n ticket gates will be opened at the same time, so that all passengers can enter the station within 5 minutes.
(3) translating essential content into mathematical language;
It takes half an hour to open a ticket gate, so x+3y = z.
If it takes 10 minutes to complete the inspection by opening two ticket gates, then x+ 10y=2× 10z.
Open n ticket gates and complete the inspection in 5 minutes at most, then x+5y≤n×5z.
X= 15z and y=0.5z can be solved.
Bring the above two expressions into n≥3.5z, ∴n=4.
A: You need to open four ticket gates at the same time.
The price of buying food, paying utilities and so on. Can be transformed into a mathematical model.
The simplest thing is the lucky money for the New Year, how to use it and so on. You definitely need to do a detailed calculation, or you can use it casually. You don't even know when your money will run out.