Question

The sum of the of a two-digit number is 15. One third of the number diminished by 12 is 17. Find the number.

Answer 1

Did you mean the "sum of the digits of a two-digit number is 15" ?
if so, then
let the unit digit be x
let the tens digit be y
so the value is 10y + x

"One third of the number diminished by 12 is 17"
---> (1/3)(10y+x) - 12 = 17
(1/3)(10y+x) = 29
multiply by 3
10y+x = 87
x = 87 - 10y

also x+y = 15
by substitution:
87-10y + y = 15
-9y = -72
y = 8
x = 87 - 80 = 7

the number is 87

check the properties stated.