Then:

2i + 9n + 12t = 120 and i + n+ t = 20, where i > 0; n > 0; t > 0.

Multiplying the second equation by 2 and subtracting the new equation from the first:

7n + 10t=80

Thus 7n = 10(8-t)

Therefore n is a multiple of 10 and since 1 £ n < 20, n=10

Hence 8-t=7 and therefore t=1