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"Application of linear equations of one variable" PPT courseware 4
Warm up before class
A water company charges water fees as follows: if the water consumption does not exceed 10 tons per month, it is charged at 1.5 yuan per ton; if the water consumption exceeds 10 tons per month, the excess is charged at 2 yuan per ton.
Xiao Ming's family uses 15 tons of water in September. Xiao Ming's water bill in September is _________ yuan.
Xiao Ming's family uses water at(a 10) in October. Xiao Ming's water bill in October is _________ yuan.
Basic steps to solve practical problems using linear equations of one variable:
1. Review: review the question and analyze the quantitative relationship in the question;
2. Assume: Assume appropriate unknowns and represent the unknowns;
3. Column: Make a series of equations based on the quantitative relationships in the question;
4. Solution: Solve this equation;
5. Answer: Check and answer.
Use your brain
In order to encourage residents to save water, a certain city has introduced a new household water charging standard, which stipulates that the water fee to be paid is divided into a standard water fee of 1.96 yuan/t, and an excess water fee of 2.94 yuan/t. A certain family used 12 tons of water in June. A water fee of RMB 27.44 is required. Find the standard monthly household water consumption stipulated by the city.
Analysis: This question must first analyze whether the water fee of 27.44 yuan paid contains excessive parts.
Since 1.96×12 = 23.52 (yuan), which is less than 27.44 yuan,
Therefore, the water fee paid contains the excess water fee, that is,
The monthly standard water fee + the excess water fee = the water fee paid for the month.
Solution: Suppose the monthly standard household water consumption is x t. According to the equivalent relationship, we can get
1.96x +(12-x)×2.94 = 27.44
Solve to get x = 8.
Answer: The standard monthly household water consumption in this city is 8 t.
Example 4 There are several existing saplings, which are planned to be planted on one side of a section of road.
It is required to plant one tree at each end of the road, and the intervals between every two trees are equal. Option 1: If one tree is planted every 5m, there will be a shortage of 21 saplings; Option 2: If one tree is planted every 5.5m, then there will be a shortage of 21 saplings. Just finished planting. Based on the above plan, please calculate the number of original saplings and the length of this road.
Analysis Look at the tree planting diagram above and think about it:
(1) What is the relationship between the distance between two adjacent trees and the number of trees that should be planted?
(2) What is the quantitative relationship between the distance between two adjacent trees, the number of trees that should be planted, and the length of the road?
The equivalence relationships involved in this question are: the road length of option 1 = the road length of option 2
Exploration and innovation
Xiao Ming's father wanted to test Xiao Ming and said: "Which business will save more money?" So Xiao Ming made a correct plan for his father through thinking and calculation, which saved his father a lot of phone bills. Students, do you know this plan?
Because when there are 250 minutes of calls in a month, the call charges of the two services are the same. On the basis of 250 minutes, for every additional (or decreased) minute of calls, the call charges of "Global Telecom" and "China Travel" will increase (or decrease) by 0.4 and 0.4 respectively. 0.6 yuan.
Therefore, when the monthly call time exceeds 250 minutes, it will save more money to choose "Global Telecom";
On the contrary, when the monthly call time is less than 250 minutes, it will save more money to choose "China Travel".
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"Application of linear equations of one variable" PPT courseware 9:
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