An elementary three one variable quadratic equation mathematics application problem! A company requires its 350 employees to work overtime, and promises to pay each male employee $10 for overtime work, while each female employee gives $8.15. According to this proposal, all female employees work overtime, but some male employees refuse to work overtime, The sum of overtime pay has nothing to do with the number of male employees in the whole company? I don't know how to find the equivalent relation. I attach the detailed formula, process and result. The process is the most important. Then I explain it in words be deeply grateful!

An elementary three one variable quadratic equation mathematics application problem! A company requires its 350 employees to work overtime, and promises to pay each male employee $10 for overtime work, while each female employee gives $8.15. According to this proposal, all female employees work overtime, but some male employees refuse to work overtime, The sum of overtime pay has nothing to do with the number of male employees in the whole company? I don't know how to find the equivalent relation. I attach the detailed formula, process and result. The process is the most important. Then I explain it in words be deeply grateful!

There are x male employees and Y employees who refuse to work overtime
The sum of wages is 8.15 × (350-x) + 10 × (X-Y) = 1.85x-10y + 8.15 × 350
The sum of wages has nothing to do with the number of male workers, that is, there are no indefinite terms X and Y in the above formula, 1.85x = 10Y, y = 0.185x. It can be concluded that the number of male workers who refuse to work overtime is 18.5% of the total number of male workers, which has nothing to do with the total number of male workers. In fact, it is equivalent to treating all male workers as if Chengdu is willing to work overtime. Because there is 0.185 people who do not work overtime, the average overtime pay of male workers is the same as that of female workers, This has nothing to do with the total number of male workers, so what matters is the proportion of male workers who work overtime or not
At the same time, X and y are people, they must be positive integers and less than 350, X can only be 200, so the number of female employees is 150, so the total overtime pay of female employees is 8.15 × 150 = 1222.5 US dollars, or 1222 US dollars and 50 cents

The relationship between the root and coefficient of higher order equation?

If the equation of higher degree has rational root, then the rational root P / Q, P is the constant term divisor and Q is the highest term divisor
If the root of the equation is 1 and the sum of the coefficients is 0, the polynomial has the factor X-1

The relationship between the real root of equation and coefficient
A linear equation with one variable has real roots as long as the coefficient of the first term is not 0. A quadratic equation can know whether it has real roots or imaginary roots according to the discriminant. So what is the relationship between the coefficient of the cubic equation and the number of real roots?
In addition, the same problem of quartic equation is added
What I want to know is the relationship between the coefficient and the root of the equation. For example, when the square of the quadratic equation B - 4ac > 0, there are two unequal real roots, etc., it's better to bring the process, which is a little harsh, sorry

Cubic equation (real coefficient) or three real roots (including multiple roots), or one real root and a pair of conjugate complex roots
There are only three possibilities for quartic equation (real coefficient)
Or four real roots, or two real roots and a pair of conjugate complex roots, or two pairs of conjugate complex roots
There is no simple relation between the coefficient and the number of real roots for cubic and above equations, except for very special equations

The clothes produced by the garment factory are 1.8 meters for each adult's clothes and 1 meter for each child's clothes. At present, there are 20 meters of cloth. They are ready to be made into x adult's clothes and Y child's clothes. The cloth is just ready to be used up
1. List the equations according to the meaning of the question
2. There are several different solutions? Write them all

1.x+1.8y=20
2. X, y are integers
So y is a multiple of 5
When y = 5, x = 11
When y = 10, x = 2

A binary math problem of grade one in junior high school
Xiaoming's family contracted an orchard. Last year, the balance of the orchard was 12000 yuan. This year's fruit harvest is good. It is estimated that the income can be increased by 15% compared with last year. Moreover, due to the improvement of planting technology, the expenditure will be reduced by 5% compared with last year. Therefore, the balance of this year is expected to be 11400 yuan more than last year. Please calculate the income and expenditure of Xiaoming's family this year
I have listed the equation 1.15/x + 0.95/y = 12000 x + y-12000 = 11400. The main problem is that the equations are very difficult to solve

Balance = income expenditure
Income = x
Expenditure = y
X - y = 12000 (last year)
X * 1.15 - y *. 95 = 12000 + 11400 (this year)
Two equations, two unknowns. Now it should be easy to solve!

Mathematical problems of the first grade in junior high school
In the following equations, there are ()
1、（1/2）x+（3/4）= （2/3）y 2、（2/x）+y-2=0
3、 xy-3y+x=0 4、 3x2-2y-3=0 5、 x+2y-1=z
(A) 1 (b) 2 (c) 3 (d) 4
It's better to explain why

1、（1/2）x+（3/4）= （2/3）y
2、（2/x）+y-2=0
It's binary once
(B) 2
]3,4 is 2 yuan twice, 5 is 3 yuan once

After a shopping mall bought two kinds of clothing, they all increased the price by 40%. During the Spring Festival, the shopping mall made a preferential promotion and decided to sell them at 20% and 10% discount of the price. A customer paid 182 yuan for the two kinds of clothing, and the sum of the two kinds of clothing price was 210 yuan?

If the price of a clothing is x yuan, the price is x1.4 yuan according to the title; if the price of B clothing is y yuan, the price is y1.4 yuan according to the title. According to the title equation system, the price is x + y = 21080% x + 90% y = 182, and the solution is x = 70Y = 140 Price is 70 yuan, B clothing price is 100 yuan, price is 140 yuan

It's better to be binary
The length of an express train is 168 meters, and that of a local train is 184 meters. If two trains are running in opposite directions, it takes 4 seconds from meeting to leaving. If they are running in the same direction, it takes 16 seconds from the express train chasing the slow lane to leaving,

Set the fast speed as X and the slow speed as y
（X+Y）4=168+184
（X-Y)16=168+184
Solution x = 55
Y=33

(one yuan twice or two yuan once is OK)
A. B is 60 kilometers away. A bicycle starts from a and B motorcycle starts from B. A starts one hour and 40 minutes earlier than B. then a starts three hours later and meets B. after meeting, the two continue to move forward. When a arrives at B, B just arrives at a and asks for the speed of a and B

Let the speed of two persons be x, y km / h respectively
According to the theme
3x+(3-5/3)y=60
60/x=60/y+5/3
From Formula 1, we can get 9x + 4Y = 180, and then we can solve the quadratic equation of one variable by substituting it into formula 2~

Mathematical problems (on linear equation of two variables)
For a three digit number, the number on the ten digit is equal to the sum of the number on the one digit and the number on the hundred digit, and the sum of the number on the one digit and the number on the ten digit is 9. If the hundred digit number of the three digit number is exchanged with the one digit number, the new three digit number is 297 larger than the original three digit number, so the original three digit number can be obtained. "

Let the hundred, ten, and one digit of the three digit number be a, B, and C respectively, then the number is 100A + 10B + C. then B = a + C, C + B = 9, substitute the former formula into the latter formula, and get C + (a + C) = 9, that is, a + 2C = 9, exchange the hundred digit and one digit of the three digit number, and get the new three digit number is 100C + 10B + A, and have (100C + 10B + a)