Let's know that the sum of the number on the ten and the number on the single digit of a two digit number is 9. If we insert a '0' between the ten and the single digit, the three digit number obtained is six times of the original two digit number. What is the original two digit number? Quadratic equation of two variables! Complete process

Let's know that the sum of the number on the ten and the number on the single digit of a two digit number is 9. If we insert a '0' between the ten and the single digit, the three digit number obtained is six times of the original two digit number. What is the original two digit number? Quadratic equation of two variables! Complete process

Let X be the number of tens and y be the number of ones
X + y = 9 (1) 100x + y = 6 (10x + y) (2)
From (1) we can get: x = 9-y (3) from (2) we can get 100x + y = 60x + 6y -------- 40x = 5Y -------- y = 8x (4)
(4) Substituting (3), we can get x = 9-8x, and the solution is x = 1 -------- y = 8
The original number is 18

For a six digit number, the number of one digit is 5, the number of ten digit is 9, and the sum of any three adjacent digits is 17

The hundred digit number is: 17-5-9 = 3
The thousand digits are: 17-3-9 = 5
The ten thousand digit number is: 17-5-3 = 9
The 100000 digit number is: 17-9-5 = 3
This six digit number is 395395

There is a three digit number. Now move the leftmost digit to the rightmost digit, which is 45 times smaller than the original number. It is also known that the ratio of 9 times of the number on the hundred digit is composed of 10 digits and one digit

Let X be the number of hundreds and y be the number of tens and ones
From the meaning of the title: 100x + y-45 = 10Y + X ①
9x+3=y ②
Substituting (2) into (1) gives the following result:
100x+9x+3-45=10+x
109x-42=90x+30+x
18x=72
x=4
Substituting x = 4 into 2 gives y = 39
That is: the original three digit number is 439

It is known that axbxab = BBB, where a and B are numbers from 1 to 9, AB means that the single digit is B, the ten digit is the two digit of a, BBB means the single digit, the ten digit and the hundred digit are the third digit of B
So a = (), B = ()

bbb=111*b
111=3*37
So AB can only be 37
A is 3, B is 7
3*7*37=777
Then a = (3), B = (7)