"Application of linear equations of one variable" PPT courseware 6

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"Application of linear equations of one variable" PPT courseware 6

create situations

If the sum of a day and the adjacent dates above and below it is 42, what is the date of this day?

According to the meaning of the question, answer the following questions orally

(1) Suppose the middle number is x, then the other two numbers are __________, _____

(2) The equivalence relationship in the question is___________;

(3) Based on the equality relationship, list the equation___________.

Example 2 Two warehouses A and B co-store 40 tons of fertilizer. If warehouse A ships out 3 tons of fertilizer, and warehouse B ships out 5 tons of fertilizer, and the mass of fertilizer stored in the two warehouses is exactly the same, how many tons of fertilizer were originally stored in each of the two warehouses?

If x tons is used to represent the quality of the original fertilizer inventory in warehouse A, fill in the following table.

The equivalence relationship in the question is;

Quality of fertilizers in stock after changes in warehouse A = Quality of fertilizers in stock after changes in warehouse B

Solution Assume that warehouse A originally stocks x tons of fertilizer, then warehouse B stocks (40-x) tons of fertilizer.

According to the meaning of the question, we get

x+3=(40-x)-5

Solving this equation, we get x=16

After testing, x=16 (tons) is consistent with the meaning of the question.

40-16=24

Therefore, warehouses A and B originally stocked 16 tons and 24 tons of fertilizers respectively.

Are there any other solutions?

Challenge yourself

Solution: Suppose the number in the mind of the person who showed 11 is x, then the number in the mind of the person who showed 9 is 14-x, and the number in the mind of the person who showed 8 is 20-x. According to the meaning of the question, we get

(20-x)+(14-x)=2×4

Solve for x=13

Answer: The number in the person's mind when showing 11 is 13.

Expand and improve

To participate in voluntary labor, there are 27 people in place A and 19 people in place B. Now 20 people are sent to support the two places, making the number of people in place A twice that of place B. How many people should go to place A? How many people should go to place B?

Analysis: If you go to place A and x people, then you should go to place B - people. Now there are - people in place A, and there are - people in place B.

Equivalent relationship: Number of people in place A = Number of people in place B × 2

Solution: Suppose x people should go to place A, then (20-x) people should go to place B. According to the meaning of the question, we have

27+x=2 (19+20-x)

Solution: x=17

20-x=3

Answer: 17 people should go to place A, then 3 people should go to place B.

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