"Practical problems and linear inequalities of one variable" PPT courseware on inequalities and inequality groups

Description

"Practical problems and linear inequalities of one variable" PPT courseware on inequalities and inequality groups

learning target

①Be able to convert practical problems into linear inequalities of one variable; be able to formulate linear inequalities of one variable based on the quantitative relationships in specific problems.

② Summarize the basic steps for solving practical problems with linear inequalities of one variable and cultivate students' mathematical modeling abilities.

③ By solving practical problems, we can realize the application value of linear inequalities of one variable in life and cultivate students' interest in learning mathematics.

Analysis: Consumption in Store B > Consumption in Store A

Solution: Suppose the cumulative shopping is x yuan (x>100). If the shopping cost in store A is small, then

50+0.95(x-50)>100+0.9(x-100)

Remove the brackets and get 50+0.95x-47.5>100+0.9x-90

Move the items and combine them to get 0.05x>7.5

The coefficient is changed to 1, and X >150

∴When the cumulative shopping exceeds 150 yuan, the shopping cost at store A is small.

If we want to travel in a group (no less than 10 people), use the knowledge we have learned to analyze, which method will you choose to buy tickets?

A 20% off for all

B One person is free and the rest are 15% off

Group purchase discount method

(No discount will be given for less than 10 people)

Famous mountain pass 60 yuan/person

Solution: Suppose the number of people in the group is

When the fees for both methods A and B are the same:

60 ×0.8x= 60 ×0.85(x-1)

When method A is cheaper than method B:

60 ×0.8x <60 ×0.85(x-1)

When method B is cheaper than method A:

60 ×0.8x >60 ×0.85(x-1)

Answer: When the number of people is 17, choose either method A or B; when the number of people exceeds 17, method A is appropriate; when the number of people is less than 17 but not less than 10, method B is appropriate.

Operation

Required questions: Questions 5 and 9 of P141.

Optional questions: 1. Go home and help your parents calculate which consumption method should be chosen to save money on mobile phones.

2. There are two charging methods for personal Internet access: the first one: 2 yuan/hour; the second one: no more than 30 hours, 1.5 yuan/hour; more than 30 hours, 2.5 yuan/hour.

Please design an optimal consumption plan for consumers.

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Update Time: 2024-10-02

This template belongs to Mathematics courseware People's Education Press Seventh Grade Mathematics Volume 2 industry PPT template

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