classic puzzles in two variables

I'll explain how I got it.....

So I focused on the numbers that have their digits as a sum of 8 first

8,17,26,35,44,53,62,71,80

I added 16+8=24

You know CPhill?!?!  8 is also correct!!!!   There is nothing to swap....unless you put a 0 at the beginning, which I never do

17+16=33

71 is the swapped 17

26+16=42

62 is the swapped 26

35+16=51

53 is the swapped 35

44+16=60

44 is the swapped 44

53+16=69

35 is the swapped 53

62+16=78

26 is the swapped 62

71+16=89

17 is the swapped 71

80+16=96

8 is the swapped 80

First time around....I stared at my work and saw well 26*3=78 so that's the only answer

Now I see 8 could be correct too!!!!

62 is the answer

The sum of the digits of a two-digit number is 8. If 16 is added to the original number, the result is 3 times the original number with its digits reversed. Find the original number.

Let x be the first digit and y be the second digit.....so we have......

x + y = 8   (1)

And the original numbe can be represented as 10x + y

And we have

10x + y + 16 =  3(10y + x)

And using (1)   we have that y = 8 - x

So we have

10x + (8 - x) + 16 = 3[10(8-x) + x]

9x + 8  + 16 = 3 [[80 - 10x -+ x]

9x + 24 = 3 [ 80 - 9x ]

9x + 24  = 240 - 27 x     subtract 24 from both sides and add 27x to both sides

36x = 216

So....x = 6     and y = [8 - x ] → [8 - 6]  = 2

So the original number is 62

And adding 16 to this = 78

And this is 3 times the original number with the digits reversed, i. e.,   26 * 3  = 78

So I am right???????

You're correct, happy7, but we need to see some math.......nobody will be able to figure out how you got your answer, otherwise.......

8 would be OK, except that the problem speicified a "two digit number." But, technically, you would be correct - (we would just have a  "0" in the "tens" place !!! )

Good spot on that !!!