Exploring mathematics elementary algebra
posted by Joe Mhar Plaza .
The sum of the of a twodigit number is 15. One third of the number diminished by 12 is 17. Find the number.

Did you mean the "sum of the digits of a twodigit 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:
8710y + y = 15
9y = 72
y = 8
x = 87  80 = 7
the number is 87
check the properties stated.