Can someone smart me here?

solve the mathematical puzzle.

s is a three digit number.
determine the digits of s from the clues.

all the digits are odd.
the last two digits add to make ten.
the first and last digits add to make eight.
the first two digits add to make twelve.

s is

The answer is 573

S is the three digit number.
h - a number of hundreds
t - a number of tens
o - a number of ones

S = 100h + 10t + o

The last two digits add to make ten: t + o = 10
The first and last digits add to make eight: h + o = 8
The first two digits add to make twelve: h + t = 12

t + o = 10          ⇒ o = 10 - t
h + o = 8           ⇒ o = 8 - h

10 - t = 8 - h
h + t = 12          ⇒ h = 12 - t

10 - t = 8 - (12 - t)
10 - t = 8 - 12 + t
10 - t = -4 + t
10 + 4 = t + t
2t = 14
t = 14/2 = 7


h = 12 - t = 12 - 7 = 5


o = 8 - h = 8 - 5 = 3

S =  100h + 10t + o
h = 5
t = 7
o = 3

S = 100*5 + 10*7 + 3
   = 500 + 70 + 3
   = 573