In the hot summer, the difficulty students encounter is drinking water. In order to let the students have a clean summer, the class decided to pay for a water dispenser. How much should each person pay? Even if you buy a water dispenser, is it more economical than every student buying mineral water every day in the past? Let's answer this question.

First, the cost of student mineral water

There are 37 classes in Wenzhou Jingshan Middle School. Assuming that the average number of students in each class is 60, the whole school has 60×37=2220 (people). In a year, students spend about 240 days in school (excluding weekends in winter and summer vacations), and 60 days in spring, summer, autumn and winter. When you don't buy a water dispenser in the class, students usually buy mineral water to quench their thirst. Each bottle of mineral water is set at one yuan, and each student has 60 bottles in spring and autumn 1 bottle of mineral water. In summer, * * * is 60 bottles per person per day 1 bottle, and in winter, * * * is 1 bottle every four days, so the average annual water fee is 60+60+(60 ÷ 4) ×1=. The mineral water cost of the whole class 135×60=8 100 yuan; The cost of mineral water for all students: 8100× 37 = 299,700 yuan.

Second, the use cost of drinking fountains.

The price of a hot and cold water dispenser is around 750 yuan, one barrel 1 brand mineral water barrel 10 yuan. Now each class is equipped with a water dispenser. If each shift 1 barrel needs 60 barrels every two days in spring and season, 2 barrels every day in summer, 120 barrels and 20 barrels every six days in winter, then each shift needs "60+1 20+200 = 200 (one academic year). The electricity fee is converted into 300 yuan for each class in each academic year. The water and electricity fee for each class of water dispenser is 2300 yuan per school year. Therefore, the total number of drinking fountains per class in a school year is about 2300+750÷3=2550 yuan; The average annual water and electricity fee for each student is 2500÷60=42.5 yuan; The annual cost of drinking fountains in Jingshan Middle School is about 37×2550=94350 yuan;

Obviously, through the calculation and comparison of the two expenses, it is much more economical to buy a water dispenser in each class, and each student can save one school year: 135-42.5=92.5 yuan; Each class can save one academic year: 92.5×60=5550 yuan; The whole school can save: 5550×37=205350 yuan.

205,350 yuan, an amazing figure, and we can drink mineral water in a sanitary and clean water dispenser every day. When we graduate, we can give the water dispenser to the next class. Why not? I propose to Changle No.2 Middle School that each classroom should be equipped with a water dispenser.

Using mathematics skillfully to see reality

In real life, people's lives tend to be economic and rational. But how to achieve this goal?

Two advertisements were reported in the newspaper. A shopping mall is selling with prizes: the first prize 10000 yuan 1, the first prize 1000 yuan 2, the second prize 100 yuan 10, the third prize 200 won 5 yuan, and the second-class shopping mall was sold at a 15% discount. 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.