① Assemble 30 minutes after departure;
(2) A immediately returned to town B, and it took another 30 minutes to catch up with B;
(3) When A catches up with B, they are still 4 kilometers away from Town A, so find X, U and V..
According to the meaning of the question, according to the condition ③, the four students each draw the following third equation, and the wrong one is ().
A.x=u+4 B.x=v+4 C.2x-u=4 D.x-v=4
2. Xiao Min bought 12 pencils and 5 exercise books in the shop, of which each pencil was RMB X and each exercise book was RMB Y, and * * spent 4.9 yuan.
(1) List binary linear equations about x and y;
(2) It is known that it takes 2.2 yuan to buy the same six pencils and the same two exercise books, and to list the binary linear equations about X and Y 。
Solution: (1) Each pencil is X yuan and each exercise book is Y yuan, so the total price of 12 pencils is 12x yuan, and the total price of five exercise books is 5y. The listed equation is:12x+5y = 4.9;
(2) Each pencil is X yuan and each exercise book is Y yuan, so the total price of six pencils is 6x yuan and the total price of two exercise books is 2y yuan. The equation listed is 6x+2y = 2.2.
3. According to the following statements, set appropriate unknowns and list binary linear equations:
The number of (1)A is 3 times less than that of B 7;
(2) The sum of twice the number A and five times the number B is 4 4/5;
(3) The difference between 15% of a number and 23% of b number is11;
(4) The sum of number A and number B is one third of the difference between number B and number A multiplied by 0.25.
Solution: (1) Let B be X and A be Y, then 3x-Y = 7；;
(2) let a be x and b be y, then 2x+5y = 445；;
(3) Let a be x and b be y, then15% x-23% y =11;
(4) Let the number A be x and the number B be y, then 2 (x+y)- 13 (y-x) = 0.25.
4. Let the number A be X and the number B be Y, and list the binary linear equation according to the following statement:
(1) The sum of half of the number A and two thirds of the number B is100;
(2) The sum of twice the number A and the number B is-5;
(3) The difference between twice the number A and half the number B is-1;
(4) Half of the difference between the doubled number A and the doubled number B is equal to 9.
Solution: If the number A is X and the number B is Y, then:
(1) If half of A is 12x and 23 of B is 23y, then the equation can be listed as12x+23y =100;
(2) If the numbers A and B are x and 2y respectively, the equation can be listed as x+2y =-5;
(3) Twice the number A and 12 of the number B are 2x and 12y respectively, so the equation can be listed as 2x-12y =-1;
(4) If the number A is 2x after doubling, and half of the difference between the number A and the number B after doubling is 12(2x-y), the equation can be listed as: 12 (2x-y) = 9.
5. (Question) Several tourists want to take a cruise ship, and each cruise ship is required to have the same number of passengers. If each cruise ship takes 12 passengers, the rest 1 passengers fail to board; If a cruise ship is empty, all tourists can sit on other cruise ships equally. It is known that each cruise ship can accommodate at most 15 people. Please calculate how many tourists there are.
Solution: suppose there are x cruise ships at the beginning, and after leaving an empty cruise ship, each cruise ship takes y tourists on average.
From the meaning of the title, there is12x+1= y (x-1).
That is y =12x+1x-1=12+13x-1.
∫y is a positive integer,
∴ 13x- 1 is an integer,
And ∵x are integers,
X- 1 = 1 or 13,
X = 2 or x = 14.
When x=2, y = 25 > 15 is irrelevant.
When x= 14, y = 13.
At this time, the number of tourists is 13× 13 = 169.
A: Tourists 169.
A city agricultural machinery company raised 6.5438+0.3 million yuan to buy 30 AB harvesters at one time. According to the market demand, these harvesters can be sold, and the profit after all sales is not less than 6.5438+0.5 million yuan. Among them, the purchase price and selling price of the harvester are shown in the following table:
A-type harvester b-type harvester
Purchase price (ten thousand yuan/set) 5.3 3.6
Price (ten thousand yuan/set) 6 4
The design company plans to buy X Type A harvesters. After all harvesters are sold, the company will make a profit of y million yuan.
(1) Try to list the binary linear equations about the letters X and Y;
(2) What kinds of schemes does the city agricultural machinery company have to buy harvesters?
Solution: (1) y = (6-5.3) x+(4-3.6) × (30-x) = 0.7x+12-0.4x = 0.3x+12;
(2) In terms of meaning, {5.3x+3.6 (30-x) ≤1300.3x+12 ≥15,
The solution is10 ≤ x ≤121617.
∴x can adopt three schemes: 10, 1 1 2.
Answer: A 10 and B20 can be purchased; A 1 1，b 19； A 12，B 18。
A correction is actively promoting the "Sunshine Sports" project. This semester, the ninth grade 1 1 class will hold a basketball single-cycle competition (each class will play one game with other classes, and each class needs to play 10). According to the rules of the game, you must win every game, winning 3 points and losing-1 point.
(1) If all the competitions in a class are only 14, what are the winning and losing competitions in this class?
(2) Assuming that after the game, Class A scored three times as much as Class B, Class A won no more than five games, and Class A won more games than Class B, please find out how many games Class A and Class B won respectively.
Solution: (1) If the class wins X games, the class loses (10-x).
3x-( 10-x)= 14。
The result of the solution is x=6(3 points)
So the class won 6 games and lost 4 games;
(2) Set Class A to win X games and Class B to win Y games. According to the meaning of the question:
3x-( 10-x)= 3[3y-( 10-y)]，
To simplify, you get 3y=x+5,
That is y = x+5/3.
Because x and y are non-negative integers, and 0≤x≤5, x > y,
∴x=4,y=3.
So Class A won four games and Class B won three games.
Answer: (1) This class has 6 wins and 4 losses. (2) Class A won 4 games and Class B won 3 games.