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Mathematical principle and practical application of cross method
Principle: It's just a solution of binary linear equation. X+y = 1, ax+by = c, where c is between a and b, and the solution is x: y.

For binary linear equation: Ax+By=(x+y)C can be changed to? :?

xC - B

- ? = -

y? A - C

This formula is the principle of cross method. Simplifying this formula can be written as:

Application example 1. A city now has a population of 700,000. If the urban population increases by 4% and the rural population increases by 5.4% in five years, the population of the whole city will increase by 4.8%. Now the urban population has (? ) ten thousand.

Application example 2. A university in 2006? 7650 graduate students? Name, an increase of 2% over the previous year. Among them, undergraduate graduates decreased by 2% compared with the previous year. The number of graduate students increased by 10% over the previous year. So, the undergraduate who graduated from this university this year is ()

Application example 3. A city collects gas fees according to the following regulations: if the gas consumption is 60 cubic meters, it will be charged according to the 0.8 yuan per cubic meter; If the gas consumption exceeds 60 cubic meters, the excess will be charged per cubic meter 1.2 yuan. The average gas fee paid by a user in August is 0.88 yuan per cubic meter. So the user's gas bill in August is (? )。

Extended data:

The cross method is actually the cross comparison method, which is a graphic method. In fact, the cross diagram method is a simple algorithm to replace the summation formula. It is especially suitable for calculating the mixture of two quantities and two relationships (that is, the calculation of 2-2 mixture) and calculating the ratio of two components in the mixture.

Cross elimination method, referred to as cross elimination method, is a solution to the problem of ion inference. Using "cross-elimination method" can narrow the range of unknown substances, so as to determine substances under given conditions and find out the correct answer.

References:

Baidu encyclopedia-cross multiplication