A new six digit number is obtained by transposing the last three digits and the first three digits. Six times of the new number is equal to seven times of the original number,

A new six digit number is obtained by transposing the last three digits and the first three digits. Six times of the new number is equal to seven times of the original number,

Suppose X and y are two three digit numbers
So 1000x + y is a six digit number. The first three digits are x and the last three digits are y
If you swap the last three digits with the first three, the new six digits will be
1000y+x
So the equation can be listed
7(1000x+y)=6(1000y+x)
5993y=6994x
x/y=5993/6994=461/538
It can't be simplified any more
Because XY must be an integer, there is only one solution, that is
x=461,y=538
That six digit number is 461538

The sum of a two digit number and a ten digit number is 7. Two plus 45 are equal to the two digit number formed by the transposition of a single digit number and a ten digit number
A single digit and a ten digit number plus 45 are equal to the two digit number formed by the transposition of a single digit and a ten digit number

The answer is 25, and the method is as follows: if the individual bit is x, then the ten bit is 7-x. after adding 45, it is 52. After transposition, the sum of two digits is 10x + (7-x). So the equation is 10x + (7-x) = 52, and the solution is x = 5. So the individual bit is 5, and the ten bit is 2

The sum of a three digit number, a single digit number and a hundred digit number is equal to a ten digit number. Seven times the sum of a hundred digit number is two times larger than that of a single digit number and a ten digit number. The sum of a single digit number, a ten digit number and a hundred digit number is 14

This three digit number is x on the one digit, y on the ten digit, and z.x + Z = y on the hundred digit. ① 7z = x + y + 2x + y + Z = 14. ③ substitute ① into ③ to get y = 7. Substitute y = 7 into ① to get x + z = 7. ④ substitute ② to get 7z = x + 9. ⑤ ④ - ⑤ to get z = 2, ｜ x = 5. This three digit number is 2 × 100 + 7 × 10 + 5 = 275. Answer: this three digit number is 275

There is 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; the number on the ten digit minus the number on the one digit is equal to 2; the number on the hundred digit and the number on the one digit are exchanged with each other, and the three digit number is 99 larger than the original three digit number
There's another one
In order to encourage the students, Mr. Chen decided to go to the store to buy some notebooks. The price of the notebooks is known to be 2.5 yuan. If you pay 14 yuan, you will get a few yuan more. If you pay 12 yuan, you will not be able to buy so many notebooks. How many notebooks did Mr. Chen plan to buy?

Let the hundreds of digits be x, the tens be y, and the ones be Z
From the meaning of the title, we can get: y = x + Z, Y-Z = 2100x + 10Y + z-100z-10y-x = 99 --- 99x-99z = 99 --- x-z = 1
z=y-2,y=x+y-2------x=2-----z=1----y=3
The original number is 231
5 copies, 5 * 2.5 = 12.5 (> 12, < 14)