"Practical Problems and Systems of Linear Equations of Two Variables" System of Linear Equations of Two Variables PPT Courseware 3

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"Practical Problems and Systems of Linear Equations of Two Variables" System of Linear Equations of Two Variables PPT Courseware 3

1. Review exchanges and introduce topics

Preparation before class: A certain art group purchased a total of 20 acrobatic tickets worth 3 yuan and 5 yuan each, spending 76 yuan. How many 3 yuan tickets and 5 yuan tickets were there?

Solution: Suppose there are x 3-yuan tickets and y 5-yuan tickets. According to the question, we get:

x+y=20 3x+5y=76

Solution: x=12 y=8

Answer: There are 12 3-yuan tickets and 8 5-yuan tickets.

1. What are the steps to solve word problems using a system of equations?

Review: Review the question, analyze what is known in the question, what is sought, and clarify the relationship between the quantities.

(Find: Find two equality relations that can express the full meaning of the word problem)

Assume: Assume the unknown number (generally, let x and y be whatever you want, pay attention to the units)

Column: List the required algebraic expressions based on these two equality relationships, and then list two equations to form an equation.

Solution: Solve the listed equations to obtain the values ​​of the unknowns

Verification: Verify whether the obtained value is correct and consistent with the actual situation

Answer: Write the answer (including the name of the unit)

2. What is the key to solving word problems using a system of equations? Or what is the most difficult and confusing part for everyone?

The relationship between known quantities and unknown quantities

Railway freight of raw materials + road freight of raw materials = freight per ton of raw materials

Railway freight of the product + road freight of the product = freight per ton of product

Solution: Assume that the railway freight is x yuan (ton·km) and the road freight is y yuan (ton·km). According to the question, we get:

120x+10y=159

110x+20y=162

Arrange the system of equations to get:

120x+10y=159

55x+10y=81

Solving the system of equations gives:

x=1.2 y=1.5

Answer: The railway freight is 1.2 yuan (ton·km), and the road freight is 1.5 yuan (ton·km).

3. Classroom exercises, feedback and regulation

1. The meaning of peak and valley in the electric power industry is to use mountain peaks and valleys to vividly describe the change range of electricity load characteristics. Generally, electricity consumption is relatively concentrated and the electricity consumption is relatively large during the day, while electricity consumption is relatively small at night when people are resting, so usually Electricity consumption during the day is called peak electricity consumption, that is, from 8:00 to 22:00. Electricity consumption in the middle of the night is from 22:00 to 8:00 the next day. If the peak electricity price in a certain place is 0.56 per kilowatt hour yuan; the low-peak electricity price is 0.28 yuan per kilowatt hour. The total electricity consumption of Xiaobin's home in August was 125 kilowatt hours, and the total electricity bill was 49 yuan. Do you know how many kilowatt hours his home's peak electricity consumption and trough electricity consumption are?

2. A certain melon and fruit base produces a special fruit. If the profit per ton in the market is 1,000 yuan; after rough processing and sale, the profit per ton is 4,500 yuan; after fine processing and sale, the profit per ton can reach 7,500 yuan. A food company purchased 140 tons of this fruit and prepared to process it and sell it on the market. The company's processing capacity is: it can finish 6 tons or rough process 16 tons per day, but the two processing methods cannot be carried out at the same time. Due to seasonal and other conditions, the company must sell or process all this batch of fruits within 15 days. To this end, the company has developed three feasible plans:

Option 1: Roughly process all the fruits;

Option 2: Process as many fruits as possible and sell the fruits that have not been processed in the market;

Option 3: Some fruits will be finely processed and the rest will be roughly processed, and it will be completed in exactly 15 days.

Which option do you think will be the most profitable? Why?

4. Class summary and knowledge sorting

1. General steps for solving word problems using a system of equations

2. Find equivalence relationships in word problems from lists

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Update Time: 2024-09-05

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

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