"Application of linear equations of two variables - increasing income and reducing expenditure" System of linear equations of two variables PPT courseware 4

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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 4

Introduction before class

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 _______________________.

A factory's profit (total output value - total expenditure) last year was 2 million yuan. This year's total output value increased by 20% compared with last year, and total expenditure decreased by 10% compared with last year. This year's profit was 7.8 million yuan. How many thousand yuan were the total output value and total expenditure last year?

Key: Find the equivalence relationship.

Last year’s total output value – last year’s total expenditure = 2 million yuan

This year’s total output value – this year’s total expenditure = 7.8 million yuan

This year’s total output value – this year’s total expenditure = 7.8 million yuan

This year’s total expenditure = last year’s total expenditure × (1-10%)

The hospital uses raw materials A and B to prepare nutritional supplements for patients after surgery. Each gram of raw material A contains 0.5 units of protein and 1 unit of iron, and each gram of raw material B contains 0.7 units of protein and 0.4 units of iron. If a patient needs 35 units of protein and 40 units of iron per meal, how many grams of each of ingredients A and B in each meal will exactly meet the patient's needs?

The amount of protein in ingredient A per meal + the amount of protein in ingredient B in each meal = 35

The mass of iron contained in raw material A per meal + the mass of iron contained in raw material B per meal = 40

The amount of protein contained in each meal of raw materials = 0.5 × the mass of each meal of raw materials

The mass of iron contained in raw material A per meal = 1 × the mass of raw material A per meal

The amount of protein contained in raw material B per meal = 0.7 × the quality of raw material B per meal

The mass of iron contained in raw material B per meal = 0.4 × the mass of raw material B per meal

Class summary

1. Learn to use tables to analyze the equivalence relationships of issues such as increasing revenue and reducing expenditure.

2. Sometimes indirect assumptions (unknown numbers) can bring convenience to problem solving.

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Update Time: 2024-09-05

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

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