"Solving word problems using linear inequalities in one variable" PPT courseware 3

Description

"Solving word problems using linear inequalities in one variable" PPT courseware 3

Scenario import

A certain town is rich in wind resources. In order to achieve "low carbon and environmental protection", the town decided to develop wind power generation and planned to purchase 10 wind turbines. There are two types of units, A and B. The price of type A unit is 120,000 yuan/unit, and the average monthly power generation is 24,000 kw.h; the price of type B unit is 100,000 yuan/unit, and the average monthly power generation is 2 10,000 kw.h.

It is estimated that the township's funds for purchasing wind turbines will not exceed 1.05 million yuan.

(1) Please design several purchase plans for this township;

(2) If the electricity consumption of the township is not less than 204,000 kw.h/month. Which purchase option should you choose to save money?

Ideas: When solving the problem, pay attention to the key words in the question design, "not higher than" and "not lower than". The key to this question is that the funds required to purchase a wind power generation set shall not exceed 1.05 million yuan.

(1) What are known quantities? What are the unknown quantities? What is the relationship between quantities and quantities? Communicate with classmates.

(2) If the unknown quantity in the problem is represented by x, how can we use mathematical symbols to express the relationship between the known quantity and the unknown quantity in the problem?

Suppose x units of type A units are purchased, then (10-x) units of type B units are purchased. According to the restriction that the funds of the two units shall not exceed 1.05 million yuan, a linear inequality of one yuan can be listed

12x+10（10-x）≤105

Solve to get x≤2.5

Its non-negative integer solution is x=0, 1, 2.

Therefore, there are three options that meet the purchase conditions:

①To purchase 10 B-type units, the cost is 10x10=100 (10,000 yuan);

② To purchase 1 type A unit and 9 type B units, the cost is 12x1+10x9=102 (10,000 yuan);

③To purchase 2 A-type units and 8 B-type units, the cost is 12x2+10x8=104 (10,000 yuan).

In conclusion

General steps for solving word problems using linear inequalities of one variable:

(1) Review: Review the question, analyze the known quantities and unknown quantities in the question, and clarify the relationship between the quantities.

(2) Suppose: Let one of the unknown quantities be recorded as x, and the other unknown quantities be expressed as the algebraic expression of x;

(3) Find: Find the unequal relationship in the question;

(4) Column: column inequality

(5) Solution: Find the solution set of the inequality

(6) Answer: Write an answer that conforms to the meaning of the question, and check whether the solution set of the inequality conforms to the meaning of the question.

The general ticket price for a certain tourist attraction is 30 yuan per person, and the ticket price for groups of 20 people or more is 25 yuan per person.

(1) A tour group has a total of 18 tourists visiting the scenic spot. Which method of purchasing tickets is cheaper for them?

Solution: (1) The cost for 18 tourists to purchase ordinary tickets is

18x30=540 (yuan)

If you purchase group tickets for 20 people, the cost is

20x25=500 (yuan)

At this time, it is cheaper to buy group tickets than to buy ordinary tickets.

(2) If the group is less than 20 people, for what number of passengers is it cheaper to buy a group ticket for 20 people than to buy a general ticket?

Solution: (2) Assuming that there are

20x25＜30x

Because x<20, we get x=17, 18, 19.

After testing, the integer solution of the above inequality is consistent with the meaning of the question.

Therefore, when the number of tourists is 17, 18 or 19, it is cheaper to buy a group ticket for 20 people.

consolidate new knowledge

1. Our school is going to hold an art festival. My classmates are responsible for making 240 ribbons to decorate the venue. They plan to complete it in 4 days of spare time. We actually produced 42 ribbons on the first day. How many ribbons should we produce on average every day in the future to complete the task on time or ahead of schedule?

2. There are 20 questions in a certain knowledge competition, and the following scoring rules are adopted: 10 points are awarded for each correct answer, and 5 points are deducted for incorrect answers or no answers. How many questions does Xiaoliang need to answer correctly at least for his total score to be no less than 80?

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For more information about the PPT courseware "Solving Word Problems by Listing First-degree Inequalities in One Variable", please click the "Solving Word Problems by Listing First-degree Inequalities in One Variable" ppt tag.

"Solving word problems using linear inequalities in one variable" PPT courseware 2:

"Solving word problems with linear equations of one variable" PPT courseware 2 Steps for solving word problems with linear equations of one variable: (1) Review: Review the question, analyze what is known in the question, what is sought, and clarify the relationship between the quantities; (2) Find: Find the word that can express the full meaning of the word question..

"Solving word problems using linear inequalities in one variable" PPT courseware:

"Solving word problems with linear inequalities of one variable" PPT courseware. Review the past and learn new things. What are the steps for solving linear inequalities of one variable? What should we pay attention to when solving problems? Can you tell me the steps to solve word problems using equations? Test you. Can you form inequalities? 1. The unit price of a certain commodity is a...

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Update Time: 2024-07-06

This template belongs to Mathematics courseware Qingdao Edition Eighth Grade Mathematics Volume 2 industry PPT template

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