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
