Let the number of ivy, nightshade and triffid plants be i, n and t respectively.

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.