2 math problems (solution)! (1) A store will first increase the original price of a certain type of color TV by 40%, and then write "big reward" in the advertisement, with 20% discount. After customers complain, the law enforcement department will impose a fine of 2700 yuan per set according to 10 times of the illegal income, and ask for the original price of the color TV (2) When a shopping mall sells a certain product at a fixed price, it gets a profit of 45 yuan per gram. Now, the profit from selling 8 pieces of the product at 85% of the fixed price is the same as the profit from selling 12 pieces at a price reduction of 35 yuan per piece

2 math problems (solution)! (1) A store will first increase the original price of a certain type of color TV by 40%, and then write "big reward" in the advertisement, with 20% discount. After customers complain, the law enforcement department will impose a fine of 2700 yuan per set according to 10 times of the illegal income, and ask for the original price of the color TV (2) When a shopping mall sells a certain product at a fixed price, it gets a profit of 45 yuan per gram. Now, the profit from selling 8 pieces of the product at 85% of the fixed price is the same as the profit from selling 12 pieces at a price reduction of 35 yuan per piece

(1) If the original price is x, the illegal income is 270 yuan, that is, X * (1 + 40%) * 80% - x = 270, so x = 2250 (2) if the purchase price is x yuan, then the original price is x + 45 yuan, so ((x + 45) * 85% - x) * 8 = (x + 45-35-x) * 12, so x = 155

Solve by equation
2. A cuboid 8 decimeters long, 6 decimeters wide and 4 decimeters high has the same volume as a cone. If the height of the cone is 1 / 4 higher than that of the cuboid, calculate the bottom area of the cone
1. A 5-meter-high cylindrical tank is full of water. The daily average water consumption is 10 tons. After 10 days, the water in the tank is reduced by 40%. What is the bottom area of the tank? (1 cubic meter of water weighs 1 ton.)

Height of cone = 4 * (1 + 1 / 4) = 5
Set the bottom area as S
8*6*4= 1/3 *S *5
S = 576 / 5 = 115.2 square decimeter
Set the bottom area as s and the total volume as 5S,
5S * 40% =10*10
S = 50 square meters

Two mathematical problems, to solve equations
1. A ship sails downstream from wharf a to wharf B, and then reverses to wharf C for 9h. It is known that the speed of the ship in still water is 7.5km/h, and the speed of water flow is 2.5km/h. The distance between wharf A and wharf C is 15km. What is the distance between wharf a and wharf B?
2. On May 12 this year, Wenchuan County, Sichuan Province, 8.0 earthquake, a middle school teachers and students voluntary donations, known as the first day donation 4800 yuan, the second day donation 6000 yuan, the second day donations than the first day of 50 more people, and the two days of the same amount of per capita donations, then the two days of the total number of people to participate in donations? Per capita donations how many yuan?

Let AB distance x km
x÷(7.5+2.5)+（x-15）÷(7.5-2.5)=9
1/5x+1/10x=9+3
3/10x=12
x=40
If the number of donors on the first day is x, then the number on the second day is (x + 50)
4800÷x=6000÷（x+50）
6000x-4800x=240000
x=200
200 + 50 = 250 people
200 + 205 = 405
4800 △ 200 = 24 yuan

For a six digit number headed by 1, if 1 is put at the end, the new number is three times the original number. What is the new number? What is the original number?
Be sure to use the equation solution!
Be sure to use the equation solution!

Let the last five digits be X
The original six digits are 100000 + X
The new number is 10x + 1
10X+1=3(100000+X)
X=42857
The new number is 428571
The original number was 142857

A mathematical problem of equation
1.8-x of 0.01 = (x of 0.02) - 1
process
That's right

(1.8/0.01)-x=(x/0.02)-1
180-x=50x-1
51x=179
x=3.51
(1.8-x)/0.01=(x/0.02)-1
180-100x=50x-1
150x=179
x=1.193

1 math problem, equation solution, please<
1. The number of peach trees in the orchard is 2.5 times that of pear trees, 75 more than pear trees, and how many peach trees and pear trees are there respectively?
Equation solution, > 0<
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If x pear trees are set, the number of peach trees is 2.5x
2.5X-X=75
1.5X=75
X=50
Pear trees = 50
Peach trees = 50 * 2.5 = 125

Solving the equation
The average price of a kind of raw material with a total value of 2000 yuan and B kind of raw material with a total value of 4800 yuan is 3 yuan less than that of a kind of raw material per 0.5kg and 1 yuan more than that of B kind of raw material per 0.5kg

The unit price after mixing is x yuan per 0.5 kg
2000/（x＋3）＋4800/（x－1）＝（2000＋4800）/x
It is reduced to 3x = 51
x＝17
The test shows that x = 17 is the solution of the original equation

Solving a mathematical problem exponential equation
2 under the root minus the x power of the root 3 plus the x power of 2 under the root plus the x power of the root 3 equals 4 to find X

√[2-√3]^x+√[2+√3]^x=4
Let a = √ (2 - √ 3),
b=√(2+√3)
Then AB = 1
The equation is a ^ x + B ^ x = 4
a^x+1/a^x=4
a^2x-4a^x+1=0
The solution is a ^ x = 2 + √ 3, or 2 - √ 3
So x = - 2 or 2

First drop of a mathematical problem. Please help, to use the equation solution
(ancient problems) (those who can use equations can use equations to solve them, but it's better to use equations.) an old man's tablet said:
One sixth of life is a happy childhood,
One twelfth of life is bearded,
One seventh of LA's life is spent in marriage,
Five years later, he had a son,
But the son lived only half of his father's life,
Son walk pull, he is very painful pull, 4 years later also walk pull
(1) The life span of an old man
(2) The age of an old man as a father
(3) The age of the old man at the time of his son's death

Let the life span of the elderly be X
1/6x+1/12x+1/7x+5+2/2x+4=x
-3/28x=-9
x=84
Age at the time of death: 84-4 = 80

There is a mathematical problem to be solved by equation
There are 100g of 8% salt water in container a and 40g of 10% salt water in container B. pour in the same amount of clean water to make the salt water concentration of the two containers the same. How many grams of water should be poured in each container?

Let's pour in X grams of water each
100*8%/(100+x)=40*10%/(40+x)
8/(100+x)=4/(40+x)
4(100+x)=8(40+x)
400+4x=320+8x
8x-4x=400-320
4x=80
x=20
A: pour in 20 grams of water each