For a two digit number, the ten digit number is 5 less than the single digit number. If the number of the two digit number is exchanged, a new two digit number will be obtained. The new number is 45 larger than the old number. What is the original number? Please use the equation of one variable to solve it

For a two digit number, the ten digit number is 5 less than the single digit number. If the number of the two digit number is exchanged, a new two digit number will be obtained. The new number is 45 larger than the old number. What is the original number? Please use the equation of one variable to solve it

Let X be the number of bits
x+10(x-5)=10x+(x-5)-45
11x-50=11x-50
Solution
X = any number
Because x is a positive integer and 10 (X-5) is a positive integer
So x = 6 7 8 9
So the corresponding ten is 1 2 3 4
So the original number is 16 or 27 or 38 or 49

A two digit number, the sum of one digit number and ten digit number is 8. After exchanging the position of one digit number and ten digit number, the new number is 36 more than the original number, and the two digit number can be obtained

If the single digit of the original number is x, then the ten digit is 8-x
10X+（8-X)-36=10（8-X)+X
9X-28=80-9X
18X=108
X=6
8-X=2
So the original number is 26

If a and B are used to represent a two digit ten digit number and a single digit number respectively, after exchanging the two digit ten digit number and a single digit number,
If we get a new two digit number, the sum of the two digits must be ()
A9 B10 C11 D12

The original number is 10A + B, and the new number is 10B + a
The sum is: 10A + B + 10B + a = 11 (a + b)
Then the new number must be divisible by 11. Choose C11