A few math problems for junior high school, and one math problem for junior high school

(1) According to the known conditions, the column equation is.

600x+120*(15-x)≤5000

x≥(15-x)/2

Solution 5 x So there are two kinds of purchase schemes: 5 tickets and 10 B tickets; 6 tickets and 9 B tickets.

2) The cost of option 1 is:

The cost requirements for option II are:

So option 1 is more cost-effective!

Pay attention to reciprocity, disorder.

To be continued. When a set is a subset of another set, first consider the case where the set is empty. Because an empty set is a subset of any collection.

For reference, please smile.

The answer is 1, and the answer is as follows:

Original = ABC+BCD+CDA+DAB

ab(c+d)+cd(a+b)

ab(-a-b)+cd(a+b) (this step gives c+d=-a-b from known a+b+c+d=0).

a+b)(cd-ab)

Then, it is known that a+b+c+d=0 can be obtained.

a+b=-c-d, cube both sides of the equation at the same time.

a+b) =c-d).

a +b +c +d +3a b +3ab +3c d +3cd =0, i.e.

3+3a b+3ab +3c d+3cd =0, so (this step is obtained from the known a +b +c +d =3).

3a²b+3ab²+3c²d+3cd²=-3,a²b+ab²+c²d+cd²=-1

ab(a+b)+cd(c+d)=-1

ab(a+b)+cd(-a-b)=-1 (this step gives c+d=-a-b from the known a+b+c+d=0).

ab(a+b)-cd(a+b)=-1

a+b)(ab-cd)=-1

a+b)(cd-ab)=1 (compared to the original simplification results).

So, the original = 1

Percentage practice questions.

1. (Solve the practical problem of "finding how many percent more than one number" is).

Xiangyang Bus Factory originally planned to produce 5,000 buses, but actually produced 5,500 buses. How many percent more production than planned?

2. (Solve the practical problem of "finding how many percent of one number is less than another").

Xiangyang Bus Factory originally planned to produce 5,000 buses, but actually produced 5,500 buses. How many percent less is planned to produce than it actually is?

3. (Breakthrough of difficulties).

A basket of apples weighs 20 more than a basket of pears, so a basket of pears is 20 lighter than a basket of apples

4. (Test center perspective).

The original price of an electronic product was 5,000 yuan per unit, but now it has been reduced to 3,000 yuan. What percentage of the price reduction?

5. (Test center perspective).

A project was originally planned to be completed in 10 days, but the task was actually completed in 8 days, and the actual daily repair was several percent more than the original plan?

6. (Calculation method of tax payable).

Yimin Hardware Company's total turnover last year was 4 million yuan. If you pay business tax according to 3% of the turnover, how many yuan should you pay business tax last year?

7. (Simple practical issues related to tax payable).

Uncle Wang bought a motorcycle worth 16,000 yuan. According to the regulations, the purchase of a motorcycle is subject to a vehicle purchase tax of 10%. How much does Uncle Wang cost to buy this motorcycle?

8. A scenic spot in Yangzhou received 90,000 tourists in the "Eleventh" week in 2007, and the ticket revenue reached 270

10,000 yuan According to the calculation of the business tax paid on the 5th of the ticket, the business tax should be paid during the "Eleventh" ** week.

Xiao Ming has 3 apples, gave one to Xiaohong, and one to Xiaojun, how many do he have left?

Let the father's age be 4 times the son's age in x years, then 4(x+13)=40+x, and the solution is x=-4, that is, the father's age 4 years ago was 4 times the son's age

Suppose the father's age at x years is 4 times the son's age, then there is (40+x)=4*(13+x), and the solution is x = -4, that is, when the son is 9 (13-4) years old, the father's age (40-4 36 years) is 4 times that of the son.

This is because the difference in age between father and son does not change over time.

Let the son = x years old and the father = 4x years old, then there is.

4x-x=40-13

x = 9 or 40-13 = 27

x+y+xy=5 (1)(x 2)y+x(y 2)=6 (2)(2).

xy(x+y)=6 （3）

and (1) to solve the system of equations.

xy)^2+5xy+6=0

Think of xy as an unknown solution to a quadratic equation.

Get xy=2 or xy=3

When xy=2 (4).

x+y)=3 (5)

Solution (4) (5).

There is no real solution. When xy=3 (6).

x+y=2 (7)

The solution yields x=1, y=2

or x=2 , y=1

(x+y+xy)x=5x 1(x+y+xy)y=5y 2 condition: 1=x 2+xy+(x 2)y=5x

Condition 2 = xy + y 2 + x (y 2) = 5y, so condition 1 + condition 2 = (x + y) 2+ (x 2) y + x (y 2) = 5x + 5y

i.e. =(x+y) 2+6=5(x+y) then you can do the math yourself)

The easy way to do this should be this: Move item to get.

1 (x+3)-1 (x+4)=1 (x+1)-1 (x+2) The left and right sides are divided into the right and left sides

1 (x+3)(x+4)=1 (x+1)(x+2)j i.e.: (x+3)(x+4)=(x+1)(x+2) so there is 7x+12=3x+2

So x=-5 2

Multiply the common denominator on both sides.

x+1)(x+3)(x+4) +x+1)(x+2)(x+4) = (x+2)(x+3)(x+4) +x+1)(x+2)(x+3)

And then directly. 2 x^3+15 x^2+33 x+20 = 2 x^3+15 x^2+37 x+30

Can be solved. x = -5/2.

I don't know if it's right or not, I think I've completely forgotten...(Solution: 1 (x+2+x+3)=1 (x+1+x+4); 1/(2x+5)=1/(2x+5)=1/(2x+5); 0=1/(2x+5)-1/(2x+5);0=1/[(2x+5)-(2x+5)];0=1/(2x+5-2x-5);0=0.

Go to the denominator to get:

x+1)(x+3)(x+4) +x+1)(x+2)(x+4) = (x+2)(x+3)(x+4) +x+1)(x+2)(x+3)

Using the multiplicative distributive property and merging similar terms, we get:

2 x^3+15 x^2+33 x+20 = 2 x^3+15 x^2+37 x+30

Since there are 2 x 3+15 x 2 on both sides, it can be made to go, so that there is: -4x=10

Therefore x=-5 2

Move the item first, then pass the divide, and cross out the denominator to calculate.

Get rid of all the denominators, and then you're going to do it with the commutation method.

When x > 0, it is possible to convert the original to 1+1 x, where 0<1 x < 1, so, 1

Primitives are 1 x+11 x is an inverse function, when x is greater than 0, the value range is greater than 0, plus the previous 1, the value range of the original formula is greater than 1.