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"Practical problems and linear inequalities of one variable" Inequalities and Inequality Groups PPT Courseware 4
Question 1: In 2002, the ratio of the number of days with good air quality (level 2 or above) in Beijing to the number of days in the whole year was 55%. If the ratio exceeds 70% by 2008, then the number of days with good air quality in 2008 will be at least 10% higher than in 2002. How much increase?
Analysis: Number of days with good air quality in Beijing in 2002__________
Let x represent the increased number of days with good air quality in 2008, then the number of days with good air quality in Beijing in 2008 is ________
Which expression related to x should have a value exceeding 70�?
Tip: There are 366 days in 2008 365×0.55+x/366
Solution: Suppose the number of days with good air quality in 2008 increased by
365×0.55+x/366>70�
Remove the denominator and get x+200.75>256.2
Move items and combine to get x>55.45
Since x should be a positive integer, x≥56
Answer: The number of days with good air quality in 2008 must be at least 56 more days than in 2002, so that the number of days with good air quality in this year can exceed 70% of the total number of days in the whole year.
Question 2: In a knowledge competition, there were 10 quick-answer questions. 10 points were awarded for each correct answer, 5 points were deducted for each incorrect answer, and 0 points were awarded for no answer. Xiaoling did not answer one question, and her score was still no less than 60 points. , at least how many questions did she answer correctly?
Analysis: Score for correct answers - Points deducted for wrong answers ≥ 60 points
Solution: Suppose the number of questions that Xiaoling answered correctly is x, then the number of questions that Xiaoling answered incorrectly is 9-x. According to the meaning of the question, we get
10x-5(9-x) ≥60
Solving this inequality, we get x ≥ 7
Answer: She answered at least 7 questions correctly
Question: How many possibilities does Xiaoling have to answer the question?
Steps to apply linear inequalities of one variable to solve practical problems:
Practical problems----Assume unknowns----Find inequality relations----Line inequalities----Solve inequalities----Determine the answer based on actual conditions
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