let x represent number of 16-cent stamps and
let y represent number of 7-cent stamps
we can write equation:
16*x + 7*y = 129
Now, the problem is that we need both x and y to be whole numbers for obvious reasons. you cant put half a stamp.
We can do this by iteration and check for results. Obviously x cant be larger than 8 because:
8*16 = 128 and there is no room for 7-cent stamp
lets try 7:
7*16 = 112. remainder is 17 which isnt divisable by 7
for 6:
6*16 = 96. remainder is 33 which again isnt divisable by 7
but for 5 we get good result.
5*16 = 80. remainder is 49 which divided by 7 gives us 7
that means 5x 16 cent stamps and 7x 7 cent stamps