In a two digit number the digit in the unit place is 6 less than twice the digit in the tenth place. When tha digits are reversed th number increases by 9. Find the number

Answer 1

let the tenth digit be x
then the unit digit is 2x-6

the number is 10x + (2x-6)
the number reversed is 10(2x-6) + x
10(2x-6) + x - (10x + (2x-6)) = 9
20x - 60 + x - 10x - 2x + 6 = 9
9x = 63
x=7
then 2x-6 = 8
then number is 78

check:
87-78 = 9 , looks good

Answer 2

u = 2t - 6

10u + t = 10t + u + 9

substituting
... 20t - 60 + t = 10t + 2t - 6 + 9

solve for t, then substitute back to find u

Answer 3

Amazing!