Application of unary equations in the second semester of the sixth grade

Solution: Let the first purchase price be x1 and the second purchase price be x2, and the system of equations can be obtained.

64-x1=60%x1 ；64-x2=-20%x2, the solution is x1=40, x2=80, then each sells one is s=60%*40-20%*80=8, so that the store makes a profit of 8 yuan.

Solution: Let the first purchase price be X yuan, and the second purchase price is 2X yuan.

64-x1=60%x1

64-x2=-20%x2

Solution x=40

So 2x=2*40=80

80-64)*1 2=8 (yuan).

Answer: The store makes a profit of 8 yuan.

1.An equation is an equation with unknowns. There are many types of equations, and the unary equations we are studying now belong to integral equations, that is, both sides of the equation are integers.

Unary means that the equation contains only one unknown, and the number of times that the number of unknowns is 1, and the coefficient of the unknown is not 0. We call ax+b=0 (where x is an unknown number, a, b are known numbers, and a≠0) as the standard form of a unary linear equation. Here a is the coefficient of the unknown number and b is the constant.

Since we will have to learn other types of equations in the future, we must understand what kind of equations are unary equations.

Example 1Determine 3x+5=7x+2, 2x+3y=6, y2+2y+1=0, 2x2+9=3x+2x2, which are unary equations?

Analysis: To determine whether an equation is unary or not, it is important to determine whether it has only one unknown, and the highest order of the unknown is one. In fact, the "element" and "degree" of an integer equation can only be determined after the equation has been reduced to its simplest form.

Solution: 3x+5=7x+2 is simplified to get 4x=3, which contains an unknown x, and the number of unknowns x is 1, so 3x+5=7x+2 is a univariate equation.

2x+3y=6 contains two unknowns x and y, which is a binary equation, not a univariate equation.

y2+2y+1=0, although the equation contains only one unknown y, the highest order of the unknown y is 2. So y2+2y+1=0 is a unary quadratic equation, not a unary quadratic equation.

2x2+9=3x+2x2 is a quadratic equation in form, but after simplification, 3x=9 is obtained, and the highest order of the unknown x is not 2, but 1, so 2x2+9=3x+2x2 is actually a unary quadratic equation.

Test 1: 7 8=8 7 does not contain unknowns, so it is an equation, not an equation; 2x2-x-1 is an algebraic formula, not an equation, so it is not an equation. The discrimination method of , is the same as the example question, choose B.

Solution: If the planting area of tomatoes is x hectares, then the planting area of greens is hectares, and the planting area of celery is hectares.

x+x=250

A: Tomatoes are planted on an area of 250 hectares, greens are planted on 375 hectares, and celery is planted on 350 hectares.

It is set to plant greens 15x, tomatoes 10x, celery 14x15x+10x+14x=975

Find x=25 then greens 15x=375, tomatoes 10x=250 celery 14x=350

Let's say the tomato is b

Greens are 3b 2

Celery is 7b 5

Therefore, 3b 2 + b + 7b 5 = 975

This gives b=250

Therefore, the greens are 375, the tomatoes are 250, and the celery is 350

Let green cabbage x, tomato y, celery z, x+y+z=975, x:y=3:2, y:z=5:7

3 2y+y+7 5y=975, y=9750 49,x,z,

1. There are 42 students in the sixth grade (1) class, of which 4 boys are more than girls, if there are x boys in this class, then the equation can be listed according to the meaning of the question: :(x-4)+x=42

2. A column of engineering team A can be completed in 10 days alone, team B can be completed in 15 days alone, and two days of cooperation can be completed in x days, and the column equation is: 1 10 + 1 15 = 1 x

Set up x blanks of type A and Y blanks of type B.

The equation is that x and y are integers, so we get x=3, y=10 or x=9, y=5

Solution: Set to x, to y

5x+6y=75

When x=3, y=10

When x=9, y=5

When x=15, y=0

Use column **, it's okay.

Meter of the X segment of the Y segment of the meter.

If the steel is not wasted, the values of x and y are integers.

The possible value of x can only be 1 15

where there is x=3 y=10

x=9 y=5

x=15 y=0

The three truncation methods do not make the waste just now.

The state stipulates that the tax calculation method for individuals who publish articles and books is as follows: (1) no tax is paid if the manuscript fee is not higher than 800 yuan; (2) 14% of the part of the manuscript fee that exceeds 800 yuan if the manuscript fee is higher than 800 yuan but not more than 4000 yuan; (3) If the manuscript fee is higher than 4,000 yuan, 11% of the total manuscript fee shall be paid. Professor Ding received a manuscript fee and should pay personal income tax of 420 yuan, how much is this manuscript fee?

The manuscript fee is $x.

14%（x-800)=420

x=3800

A: The manuscript fee is 3,800 yuan.

What's the question? Give questions and ask questions.

Xiao Ming's father is 23 years older than Xiao Ming, Xiao Ming is 10 years old this year, ask Xiao Ming's father how old is it?

1) There are 5x buses, 7x trucks and 6x cars.

According to the title, 20*5x+10*7x+5*6x=48000200x=48000

x=2405x
x
x=1440

Therefore, there are 1,200 passenger cars, 1,680 large trucks, and 1,440 cars.

2) Xie Zhen Pon's: If you answer x questions correctly, you will answer (40-x) questions incorrectly or not, according to the meaning of the question: 4x-3 (40-x) = 62

Dissolve: x=26

Answer: I answered 26 questions correctly.

There are 5x buses, 7x trucks, and 6x cars. 20 * 5 x + 10 * 7 x + 5 * 6 x = 48000200x = 48000x = 2405x x x = 1440 So, 1200 buses, 1680 large trucks, and 1440 cars were sold.

Set up bamboo poles x meters long.

x/5+2x/5+1+1=x

x=5 bamboo poles are 5 meters long.