In the math activity group, I met such a real-life problem:
Two advertisements were reported in the newspaper. There are prizes for sale in a commercial building: first prize 10000 RMB 1, first prize 1000 RMB 2, second prize 100 RMB 10, third prize 200 5 yuan, and 15% discount for second-class commercial buildings. Please think about it; Which sales method is more attractive? Which commercial building is of great benefit to consumers?
We can't see the problem at a glance. So we made a random survey first. Taking the whole group 16 students as the survey object, 8 of them are willing to go to A's home, 6 like to go to B's home, and 2 think they can go to both. The survey results show that the sales model of a shopping mall is more attractive, but is this the case?
In practical problems, there is no limit to the turnover of each group of prize-winning sales and the number of people participating in the lucky draw. So we think there should be several answers to this question.
1. Kujia Commercial Building has determined that awards should be given to each group. When the number of participants is small, less than 213 (112+10+200 = 213), people will think that the chances of winning the prize are greater and a sales model of a commercial building will attract customers more.
Second, if the volume of each group of a commercial building is large, then the preferential margin it gives customers is correspondingly small. Because the preferential amount provided by a commercial building is fixed, * * 14000 yuan (10000+2000+1000 =14000). Assuming that the discount offered by two commercial buildings is 14000 yuan, the turnover of the second commercial building can be 280000 yuan (14000 ÷ 5% = 280000).
So from this point of view:
(l) When the turnover of the two commercial buildings is 280,000 yuan, the two commercial buildings will give the same amount of preferential treatment.
(2) When the turnover of both shopping malls is less than 280,000 yuan, the discount of shopping mall B is less than10.4 million yuan, so the discount provided by shopping mall A is still10.4 million yuan, which is a big discount.
(3) When the turnover of both companies exceeds 280,000 yuan, the discount of the second commercial building exceeds 14000 yuan, while the discount of the first commercial building remains at 14000 yuan, and the second commercial building provides great benefits.
Problems like this can be seen everywhere in our daily life. For example, there are two liquefied gas stations. It is known that the quality and quantity of each bottle of liquefied gas are the same, and the initial price is the same. In order to win more users, the two stations have introduced preferential policies respectively. The method of Station A is 25% off sales, and the method of bilibili is 30% off sales to customers after the second ventilation. The preferential period of both stations is one year. As a user, which one should you choose? This question is very similar to the last one. As long as you analyze and discuss how many cans you need, the problem will be solved. With the gradual improvement of market economy, economic activities in people's daily life are becoming more and more colorful. Trading, deposits and insurance, stocks and bonds, ... all come into our lives. At the same time, mathematics, profit ratio and proportion, interest and interest rate, statistics and probability are all related to this series of economic activities. Operations research and optimization, as well as system analysis and decision-making, will all become "guests" in mathematics courses.
As cross-century middle school students, we should not only learn mathematics knowledge, but also apply it to analyze and solve problems encountered in life, so as to better adapt to the development and needs of society.