How does the mathematics of the third grade of junior high school work out easily? How to make equations for the application of money

This question is too general to answer. Just ask some specific questions

When a farmer planted peanuts, the yield of peanuts was 200 kg / mu, and the oil yield was 50% (that is, every 100 kg of peanuts can be processed into 50 kg of peanut oil). Now after planting new varieties of peanuts, the peanut harvested per mu can be processed into 132 kg of peanut oil, and the growth rate of peanut oil yield is 12% of the growth rate of yield per mu
A. 20%B. 30%C. 40%D. 120%

Suppose that the growth rate of yield per mu of new peanut variety is x.200 (1 + x) × 50% (1 + 12x) = 132x = 15 or x = - 165 (rounding off) x = 15 = 20%, so a

Mathematical problems of quadratic equation of one variable in the third grade of junior high school
The trunk of a plant grows several branches, and each branch grows the same number of small branches. The total number of small branches of the trunk is 91. How many small branches does each branch grow?

Suppose each branch grows x small branches, then the branch also has x branches
1+x+x^2=91
x^2+x-90=0
(x-9)(x+10)=0
X = 9 or x = - 10 (rounding off)
So each branch grows nine small branches

The system of linear equations of two variables is known as equation 1 / 2 + 3Y = 5. Please write a system of linear equations of two variables and make it consist of the known equations
The solution is x = 4, y = 1

1/2x+3y=5
2X + y = 9 is the solution

When we use the method of addition, subtraction and elimination to solve a system of linear equations of two variables, we must make () a of the two equations unknown
When we use the method of addition, subtraction and elimination to solve the linear equations of two variables, we must make ()
A the coefficient of an unknown is 1
B the coefficients of the same unknown are equal
C the coefficients of the same unknown are opposite to each other
D the absolute values of the coefficients of an unknown number are equal

As shown in the figure, the length of a rectangle is reduced by 4cm and the width is increased by 2cm. The result is a square whose area is equal to that of the original rectangle. Find the length and width of the original rectangle

Let the length and width of the original rectangle be xcm and YCM respectively. According to the meaning of the title, we get x − 4 = y + 2, ① xy = (x − 4) (y + 2) ②. From ②, we get: xy = XY + 2x-4y-8, that is, x-2y = 4, x = 2Y + 4, substituting into ①, we get: 2Y + 4-4 = y + 2, solving y = 2, substituting y = 2 into ①, we get: x = 8, the solution of the equations is: x = 8y = 2, so the original rectangle is 8cm in length and 2cm in width

If pipe a injects water for 40 minutes and pipe B injects water for half an hour at the same time, it can inject water for half of the pool. How many hours does it take for pipe a and pipe B to fill the pool?

Let a be x and B be y. {60 / x + 60 / y = (1-1 / 8) 1
40/X+30/Y=1/2 2
1 integral: multiply both sides by X, Y: 60y + 60x = 7 / 8xy 1
2 integral: multiply both sides by X, Y: 40y + 30x = 1 / 2XY 2
The two sides of formula 2 multiply by 2 to get: 80y + 60x = XY 2, formula 2 minus 1:
20Y=1/8XY 1/8X=20 X=20÷1/8 X=20×8/1 X=160
Substituting x = 160 into formula 2: 80y + 60 × 160 = 160y 80y = 9600
Y = 120 x = 160 (minutes) y = 120 (minutes)
A: 160 ／ 60 = 2 and 2 / 3 hours; B: 120 ／ 60 = 2 hours
A: a needs 2 and 2 / 3 hours to fill a pool, B needs 2 hours to fill a pool

Binary linear equations
When students a and B solve the equations: 3x + by = 5, ax + by = 1, a misinterprets A and gets x = 3, y = 2; B writes B as an opposite number and gets x = 1, y = - 1. The values of a and B

X = 3, y = 2, B = - 2
And then x = 1, y = - 1 is brought into the equation, a = 3

The school applied to the bank for two kinds of loans, a and B, totaling 680000 yuan, with an annual interest of 84200 yuan. It is known that the annual interest rate of a loan is 12%, and that of B Loan is 13%. Q: how many yuan are the two kinds of loans?

If a school bank applies for a loan of RMB x 10000, it will apply for a loan of RMB (68-x) 10000. According to the Title Meaning: 12% x + 13% × (68-x) = 8.42 & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; 12% x + 8.84-0.13x = 8.42 & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; 0.01x = 0.42 & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; X = 4268-42 = 260000 yuan. A: the school applied for 420000 yuan of type a loan and 260000 yuan of type B Loan from the bank

I don't know how to write the problem of binary linear equations,
1. The two objects a and B respectively make uniform circular motion on a circular orbit with a circumference of 600 meters. When the two objects move in the opposite direction, they meet once every 15 seconds. In the same time, the ratio of the distance between the two objects a and B is 5:3. What is the speed of the two objects
2. There are two kinds of aluminum sheets of different specifications. One type a aluminum sheet can make 15 aluminum box bodies and 7 aluminum box covers, and one type B aluminum sheet can make 12 aluminum box bodies and 16 aluminum box covers. Now to make 1950 boxes, how many aluminum sheets should be taken from type A and type B aluminum sheets to save the most materials?
The deadline is today.

1. Let the velocity of a be XM / s and that of B be YM / s
X / y = 5 / 3 (the same time, then the distance ratio is the speed ratio)
(x + y) 15 = 600
2. Set X sheets for a and Y sheets for B
15x + 12Y = 1950 (since it is said to take two kinds of a and B, then there is no need to take only one kind, then a skin and B skin make a total of 1950 boxes)
7x + 16y = 1950

How does the mathematics of the third grade of junior high school work out easily? How to make equations for the application of money