(1) In response to the call to save water, a family plans to use 4 cubic meters less water every month than in the past, which makes 480 cubic meters of water more than in the past for 4 months. What is the planned average monthly water consumption of this family?
(2) If the average monthly water consumption of the household actually exceeds 40% of the planned average water consumption for four months in a year, and the remaining eight months use water as planned, how much water fee does the household need to pay a year according to the new payment method?
2. Put some birds in some cages. If there are only four birds in each cage, then there is no cage for a bird. If you put five birds in each cage, there will be no birds in one cage. How many birds are there at least? How many birdcages?
3. There are 3,500 bicycles in a bicycle storage station on a Sunday, of which the storage fee for variable-speed vehicles is once in 0.5 yuan and the general storage fee for vehicles is once in 0.3 yuan.
(1) If the number of cars parked in general is X and the total storage fee income is Y yuan, try to write the relationship between Y and X;
(2) If 3,500 bicycles are expected to be parked, and the number of variable-speed vehicles is not less than 25%, but not more than 40%, try to find the range of the total storage fee income of this storage station this Sunday.
4. A factory has 360 kilograms of raw materials A and 290 kilograms of raw materials B, and plans to produce 50 products A and B with these two raw materials. It is known that using 9 kilograms of raw materials A and 3 kilograms of raw materials B to produce a product can make a profit in 700 yuan; The production of product A and product B uses 4kg of raw material A and10kg of raw material B, and the profit can be 1.200 yuan.
(1) Is there any plan to arrange the number of production pieces of products A and B as required? Please design it;
(2) Let the total profit of producing two products, A and B, be RMB, and the number of pieces produced by one product be RMB. Try to write the functional relationship between and, and use the properties of the function to explain which scheme is the most profitable. What is the maximum profit?
In order to expand its business, a company decided to buy six machines to produce some kind of piston. There are two kinds of machines to choose from. The price of each machine and the number of pistons produced by each machine are shown in the following table. After the budget, the funds for purchasing the machine this time can't exceed 340,000 yuan. (1) According to the requirements of the company, how many procurement schemes can there be? (2) If the daily production capacity of the company's six machines is not less than 380, which procurement scheme is more economical?
Jiayi
Price (ten thousand yuan/set) 7 5
Daily output per unit (unit) 100 60
6. The diagram of the relationship between the operating profit y (ten thousand yuan) and the time x (months) of a product of a private enterprise in our city in 2005, in which the two variables meet the inverse proportional function relationship in the first few months and the two variables meet the linear function relationship in the last few months.
(1) Find the relationship between two functions;
(2) When was the lowest profit in that year? What is the minimum profit?
(3) If the monthly profit of the enterprise does not exceed 6.5438+0.2 million yuan, it is said to be the off-season. Which months in the same year are the off-season of surgery?
7. In June this year, fruit farmers in a city collected 30T litchi and 3t banana/kloc-0. It is planned to rent two kinds of trucks *** 10 to transport all fruits to Shenzhen. It is known that each car of Class A can carry 4T litchi and 1T banana, and each car of Class B can carry 2T litchi and 2t banana. (1) * * There are several different transportation schemes, please help design them. (2) If the freight of car A is 2000 yuan and the freight of car B is 1.300 yuan, which scheme has the least freight? How much is the minimum?
8. There are more and more tourists visiting Jiangyan, and a scenic spot attracts a large number of tourists every day. Facts show that too many tourists are not conducive to the protection of precious cultural relics. In order to implement sustainable development and give consideration to social and economic benefits, the scenic spot plans to control the number of tourists by floating ticket prices. Given the original price of each ticket in 40 yuan, the current floating ticket is RMB 40 < x & lt70. Through market research, it is found that there is a linear functional relationship between the number of visitors a day and the ticket price as shown in the figure.
(1) Find the functional relationship between and according to the image;
(2) Set the ticket income of this scenic spot as RMB for one day.
(1) Trial algebraic expression;
② Question: What is the highest ticket income of this scenic spot in a day when the ticket price is set? What is the highest ticket income?
9. At the price of per kilogram 18 yuan, 8 kilograms of 20 yuan's type A candy was mixed with several kilograms of type B candy. To make the total price not exceed 400 yuan and the total weight of candy not less than 15 kg, what is the maximum dosage of the second candy? What's the minimum?
10. A plant is suitable for growing in mountainous areas with the temperature of 18 ~ 20. It is known that the temperature drops by 0.55 for every elevation increase of 100 meters in mountainous areas, and now the temperature at the foot of the mountain is 22. Where in this mountain is suitable for this kind of plant to grow?
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