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

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

List the steps to solve word problems using 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 an equality relationship that can express the full meaning of the word problem;

(3) Assume: Assume the unknown number (generally, let x be whatever you want);

(4) Column: List the required algebraic expressions based on this equality relationship, and then list the equations;

(5) Solution: Solve the listed equations and find the values ​​of the unknowns;

(6) Answer: Check whether the solution is consistent with the meaning of the question, and write the answer (including the name of the unit).

learning target

1. Be able to use linear inequalities of one dollar to solve discounting, plan design and other problems in life.

2. Understand the practical value of linear inequalities of one variable in life by doing the questions.

Example explanation

Example 1 The purchase price of each electronic keyboard is 1,800 yuan. If the store sells it at 20% off the listed price, and the profit is still not less than 10% of the actual selling price, then what is the range of the listed price of each electronic keyboard?

Solution: Assume that the price of each electronic keyboard is x yuan, then the profit from selling an electronic keyboard is not less than (10% × 80%x) yuan. According to the meaning of the question, we get

80%x-1800≥10%×80%x.

Solving this inequality, we get x≥2500.

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

Therefore, the price tag of each electronic keyboard is no less than 2,500 yuan.

Situational Navigation Questions and Answers

In questions (1) (2) in this chapter's "Situational Navigation", what are the known quantities? What are the unknown quantities? What is the equality or inequality relationship between quantities? Communicate with classmates.

Known quantities: the total number of generator sets of two types, A and B; the price and average monthly power generation of type A unit; the price and average monthly power generation of type B unit; the monthly electricity consumption of the township; the total funds to purchase the generator set.

Unknown quantity: A and B models and how many generator sets are each.

Equality relationship: The total number of generator sets of two models A and B is 10.

Unequal relationship: The total capital of model A and B generator sets is not more than 1.05 million yuan; the power generation capacity is not less than 204,000 kw·h/month.

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

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

12x+10（10-x）≤105.

The solution is x ≤ 2.5, and its non-negative integer solution is x= 0, 1, 2.

Therefore, there are three eligible options for purchasing equipment:

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

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

③Purchase 2 A-type units and 8 B-type units, the cost is 12×2+10×8=104 (10,000 yuan)

List the steps to solve word problems with linear inequalities of one variable:

(1) Review: Review the question carefully, distinguish between known quantities and unknown quantities and their relationships, and look for words in the question that express unequal relationships;

(2) Assume: Assume appropriate unknowns;

(3) Column: List the inequalities based on the inequality relationships in the question;

(4) Solution: Find the solution set of the listed inequalities;

(5) Answer: Write the answer and check whether the answer is consistent with the meaning of the question.

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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.

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Update Time: 2024-07-30

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

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