"Application of linear equations of two variables - increasing income and reducing expenditure" System of linear equations of two variables PPT courseware 3

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"Application of linear equations of two variables - increasing income and reducing expenditure" System of linear equations of two variables PPT courseware 3

Don’t forget: growth part = original total × growth rate

1. The total output value of a factory last year was x million yuan. This year’s total output value increased by 20% compared with last year. Then this year’s total output value is __________ million yuan;

2. If the factory’s total expenditure last year was y million yuan, and this year’s total expenditure is 10% less than last year, then this year’s total expenditure is __________ million yuan;

3. If the factory’s profit this year is 7.8 million yuan, then from 1 and 2, we can get the equation _______________________.

Supplementary examples

There are two solutions, A and B. Solution A is prepared from 1 liter of alcohol and 3 liters of water; solution B is prepared from 3 liters of alcohol and 2 liters of water. Now we need to prepare 7 liters of alcohol solution with a concentration of 50%. How many liters of each solution should be taken?

Analysis: From the conditions, the concentration of solution A is 1÷(1+3)=25%

The concentration of solution B is 3÷(3+2)=60%

If solution A requires x liters and solution B requires y liters

Additional exercises:

1. A person saves 8,000 yuan in two forms. One type of savings has an annual interest rate of 10%, and the other type of savings has an annual interest rate of 11%. After one year of maturity, he earns a total of 855 yuan in interest (without deducting interest tax). , asked how much he had saved in each of the two savings?

Suppose you deposit x yuan with an annual interest rate of 11% and deposit y yuan with an annual interest rate of 10%.

Then:X + y=8000

11%x+10%y=855

2. A company spent 30,000 yuan to purchase two types of goods, A and B. After the goods were sold, the profit for type A was 10%, and the profit for type B was 11%, with a total profit of 3,150 yuan. How much did each of the two goods cost? goods?

Suppose that goods of type A are purchased for x yuan, and goods of type B are purchased for Y yuan.

X + Y=30000

10%X + 11%Y=3150

Summary and harvest

1: What have you gained from studying this lesson?

2: General steps for solving practical problems by formulating a system of linear equations in two variables:

(1) Review the question, clarify the quantitative relationship in the question, find the unknowns, and use x and y to represent the two required unknowns.

(2) Find two equivalence relations that can express the full meaning of the word problem;

(3) According to the series of equations of equivalent quantities, the system of simultaneous equations;

(4) Solve the system of equations;

(5) Check and answer.

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Update Time: 2024-10-06

This template belongs to Mathematics courseware Beijing Normal University eighth grade first volume mathematics industry PPT template

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