Question

The tens digit of a two-digit number exceeds twice the units digits by 1. If the digits are reversed, the sum of the new number and the original number is 143. What is the original number?

Answer 1

The original number is `94`.

Explanation:

If a two-digit integer has `a` in the tens digit and `b` in the unit digit, the number is `10a+b`.

Let `x` is the unit digit of the original number.
Then, its tens digit is `2x+1`, and the number is `10(2x+1)+x=21x+10`.

If the digits are reversed, the tens digit is `x` and unit digit is `2x+1`. The reversed number is `10x+2x+1=12x+1`.

Therefore,
`(21x+10)+(12x+1)=143`
`33x+11=143`
`33x=132`
`x=4`

The original number is `21*4+10=94`.