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Verified Answer :

Lampa20

let x represent number of 16-cent stamps and 
let y represent number of 7-cent stamps

we can write equation:
16x + 7y = 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:
816 = 128 and there is no room for 7-cent stamp

lets try 7:
716 = 112. remainder is 17 which isnt divisable by 7

for 6:
616 = 96. remainder is 33 which again isnt divisable by 7

but for 5 we get good result.

516 = 80.  remainder is 49 which divided by 7 gives us 7

that means 5x 16 cent stamps and 7x 7 cent stamps