"Application of linear equations of two variables - chicken and rabbit in the same cage" System of linear equations of two variables PPT courseware 2

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"Application of linear equations of two variables - chicken and rabbit in the same cage" System of linear equations of two variables PPT courseware 2

"A chicken and a rabbit live in the same cage" is a famous ancient Chinese arithmetic problem. It was first seen in "The Pheasant and the Rabbit in the Same Cage" in Volume 2 of "Sun Zi Suan Jing", Question 31. It is widely circulated, and many mathematical application problems can be transformed into this type of problem. Solve the problem, or use the solution to the "chicken and rabbit in the same cage" problem.

Total number of feet ÷ 2 - total number of heads = number of rabbits

It can be calculated in this way mainly because the number of rabbit and chicken feet is 4 and 2 respectively, and 4 is a multiple of 2. But when other problems are transformed into this kind of problem, the number of feet is not necessarily 4 and 2, and the above calculation method will not work.

1. What does "there are 35 heads on the mountain" mean? What about "94 feet underneath"?

2. Can you formulate an equation based on the quantitative relationship in (1)?

3. Can you solve this interesting problem?

Quick response:

1: Suppose number A is x and number B is y, then the sum of 2 times of number A and 3 times of number B is 15. The equation listed is ________.

2: A cricket has 6 legs and a spider has 8 legs. There are 10 crickets and spiders in total, with a total of 68 legs. If there are x crickets and y spiders, then the system of equations is ________ .

3: Xiaogang has 8 50-cent coins and 8 one-yuan coins. The coins value ________ are 6 yuan and 50 cents. Suppose there are x coins of 50 cents and y coins of one yuan. The listed equation system is ________.

(4): Two people, A and B, participated in a tree planting activity. They planted 20 trees in total. It is known that the number of trees planted by A is 1.5 times that of B. If A plants x trees and B plants y trees, then the system of equations that can be formulated is ( )

x+y=20 x=20+y

x=2.5y x=1.5y

x+y=20 x+y=20

x=1.5y x=y+1.5

Summary and harvest

1: What have you gained from studying this lesson?

2: General steps for solving practical problems by formulating a system of linear equations in two variables:

(1) Examine the question; (2) Suppose two unknowns and find two equivalence relations; (3) Sequence equations based on the equivalence relations and establish a system of simultaneous equations;

(4) Solve the system of equations; (5) Check and answer.

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For more information about the PPT courseware "A system of linear equations of two variables and the application of linear equations of two variables, a chicken and a rabbit in the same cage", please click the "System of linear equations in two variables ppt application of a system of linear equations of two variables and a chicken and a rabbit in the same cage" ppt tag.

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Update Time: 2024-11-03

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