2. A bicycle factory plans to produce n bicycles every day on average, but the actual output is different from the planned output. The following table records the actual output of a certain five working days every day (if it exceeds the planned output, it will be recorded as positive, and if it is less than the planned output, it will be recorded as negative):
Monday, Tuesday, Wednesday, Thursday and Friday.
Actual output +5 -2 -4+13 -3
(1) Use an algebraic expression containing n to represent the total number of bicycles produced in the first three days of this week;
(2) The factory implements the daily piecework wage system, and every car produced can be taken to 60 yuan. If the task is overfulfilled, each vehicle will be awarded 15 yuan. If 20 yuan produces one less car, when n= 100, what is the total wages of the workers in this factory this week?
(3) If the "piece-by-day wage system" in the above question (2) is changed to "piece-by-week wage system", and other conditions remain unchanged, when n= 100, which is more? Please explain the reason.
3. The fruit price of a supermarket is shown in the following table:
Variety apple watermelon orange pear banana
Price (RMB/kg) 4.0 3.2 1.8 2.0 3.6
(1) Xiao Minghua 15 yuan buys fruit, and the equation15-(3.2x+2.0× 2) =1.4 is obtained. According to the price of fruit in the supermarket, please describe the practical significance of this equation and then solve this practical problem.
(2) Please put forward a similar practical problem according to the information provided in the table and solve it with the relevant knowledge of the equation.
4.27. In order to solve the problem of migrant workers' children's difficulty in enrolling in school, Beijing has established a set of schooling guarantee mechanism for migrant workers' children since 2009, one of which is to exempt them from paying "borrowing fees". According to statistics, in the autumn of 2009, there were 15000 children of migrant workers studying in primary and secondary schools in a certain district of Beijing. By the autumn of 2065, 438+065,438+0, the number of children of migrant workers studying in primary and secondary schools in this district has increased compared with 2009, including 20% in primary schools and 32% in secondary schools. In this way, 2065,438+065,438+
(1)20 1 1 Among the 3,600 new students in autumn, how many are primary school students and middle school students respectively?
(2) If 40 primary school students need more teachers, the same number of middle school students need more teachers than primary school students 1 teacher. 20 1 1 After entering school in autumn, according to the calculation of 3,600 new students of children of migrant workers in primary and secondary schools in this area, a * * needs to be equipped with 3 10 primary and secondary school teachers.
5.29. A clothing factory produces suits and ties, each set costs 200 yuan and each tie costs 40 yuan. In the promotion activities, the factory provides customers with two preferential schemes:
Buy a suit with a tie;
Pay for the suit and tie at 90% of the list price.
Now a customer wants to buy 20 suits and X ties (x > 20) from this clothing factory.
(1) If the customer purchases according to scheme ①, it needs to pay (40x+3200).
Element (represented by an algebraic expression with x);
If the customer purchases according to Scheme ②, payment is required.
(3600+36x)
Element (represented by an algebraic expression with x);
(2) If x=30, through calculation, which scheme is more cost-effective?
6. A deck of playing cards is arranged in the following order: the first card is king, the second card is Xiao Wang, and then it is arranged in the order of A, 2, 3, …, J, Q and K. The number of each card is arranged in four colors: spades, hearts, diamonds and clubs. Someone threw the first card from top to bottom, put the second card at the bottom, and then put it at the bottom.
A.k.b. of hearts J.c. of hearts. Hearts 10 D Box 3.
7. Someone left 1, 2 1 km by bus, which took 3 hours. The first section travels 24 kilometers per hour, the second section travels 38 kilometers per hour, the third section travels 40 kilometers per hour, and the third section travels 20 kilometers per hour. How many kilometers are the first and second sections?
8. Let A, B and C be unequal nonzero real numbers, and prove that the equations ax2+2bx+c=0, bx2+2cx+a=0 and cx2+2ax+b=0 cannot all have two equal real roots.
9. In order to encourage residents to save electricity, a certain place has made the following provisions on the charging standard for residents' electricity consumption: if the monthly electricity consumption of each household does not exceed 100 kWh, it will be charged at 0.50 yuan per kWh; If it exceeds 100 degrees and does not exceed 200 degrees, the excess will be charged at 0.65 yuan per degree; If it exceeds 200 degrees, the excess will be charged at 0.75 yuan per degree.
(1) If the electricity consumption of each household is 90 degrees in June of 5438+00, how much electricity will he pay this month?
(2) If a household pays the electricity bill to 76 yuan on June 5438+065438+ 10, how many kWh did he use this month?
(3) If the monthly electricity consumption exceeds 200 kWh, assuming that the electricity consumption is t kWh, can the algebraic expression containing t be used to express the electricity bill that should be paid?
10. There is a typhoon center 200 kilometers south of a coastal city B, with the maximum wind force at the center 12. Every 20 kilometers away from the typhoon center, the wind will weaken by one level. The current speed of the typhoon center is15km per hour, and it moves 30 northeast to C. The wind force of the typhoon center remains unchanged. If the urban wind reaches or exceeds level 5,
(1) During the movement of the typhoon center, the nearest distance between the typhoon center and City A is100km.
(2) The distance affected by typhoon in City A is
140km
(3) Is this city affected by the typhoon? Please explain the reasons;
(4) If it will be affected by a typhoon, how long will it affect the city?
Answer and process
1. Solution: Let the raw water flow in the pond be A, the water inflow in the mountain spring be B, 1 the water pumping in the Jinwei water pump be C, then there are
A+60b = 60c 1a+20b = 2× 20c② ①-② c=2b，a=60b ③。
Suppose it takes x minutes to pump the water out of the pool with three pumps, then a+bx=3? x？ ④
Substituting ③ into ④ gives 60b+bx=6bx, that is, 60+x=6x.
∴x= 12.
A: It takes 12 hours to pump the water out of the pond.
2. Solution: (1) (n+5)+(n-2)+(n-4) = 3n-1(vehicle);
(2) The daily piecework wage is (n+5+n-2+n-4+n+13+n-3) × 60+18×15-9× 20.
= 300 N +630
=300× 100+630
=30630 (yuan);
(3) Pay more per week.
* piece rate per week is:
(5n+5-2-4+ 13-3)×60+(5-2-4+ 13-3)× 15
= 300 N +675
=300× 100+675
=30675>30630,
Pay more weekly.
3. Solution: (1) For example, I bought a watermelon and 2 kilograms of pears with 15 yuan in the supermarket, and there was 1.4 yuan left. How many kilograms of watermelon did I buy?
(2) For example, Xiao Ming has only 20 yuan in his pocket. He has bought 2 kilograms of bananas in the supermarket. How many kilograms of apples can he buy?
Suppose you can buy x Jin of oranges.
According to the meaning of the question: 3.6×2+4.0x=20,
Solution: x = 3.2.
4. Solution: (1) Suppose 20 1 1 There are X children of migrant workers in primary school and Y children in middle school in autumn.
From the meaning of the question: x+y= 15000 20%x+32%y=3600,
X= 10000 y=5000，
∴ 20% x = 20% x10000 = 2000 (person),
32%y=32%×5000= 1600 (person)
A: Among the 3,600 students added in the autumn of 2065,438+065,438+0, there are 2,000 primary school students and 0,600 middle school students/kloc-0.
(2) 40 primary school students need a teacher and 40 middle school students need (a+ 1) teachers.
2000/40 a+ 1600/40 *(a+ 1)= 3 10，
Solution: A = 3.
A: Forty pupils need three teachers.
5. Solution: (1) The cost of scheme ① is: 200×20+(x-20)×40=(40x+3200) yuan;
The cost of the second scheme is: (200×20+40x)×0.9=(3600+36x) yuan;
② When x=30 yuan,
The payment of scheme ① is: 40x+3200 = 40x30+3200 = 4400 yuan.
The expenses to be paid for the second scheme are: 3600+36x = 3600+36x30 = 4680 yuan.
∵4400 100。
(4) crossing point A as AD⊥BC and crossing point BC at point D,
Suppose that when the typhoon center moves to point E, the city happens to be affected by the typhoon, and at this time AE= 140 km,
DE= radical symbol (140~2- 100~2) =40 radical symbol (6),
EF=40 radical (6) ×2=80 radical (6),
80 root number (6) ÷ 15= 16 /3 root number (6).
The duration of typhoon affecting our city is 16/ 3 (6) hours.
∴a=b=c, which contradicts that A, B and C are mutually unequal non-zero real numbers.
So it is impossible for all three equations in the problem to have two equal real roots.
I found it myself, I hope to adopt it ~O(∩_∩)O Thank you ~