Day of the Triffids

Answer: $1$ triffid


Buy $i$ ivy plants, $n$ nightshades and $t$ triffids.

$2i + 9n + 12t = 120$ and $i + n+ t = 20$
                                $\Rightarrow 2i + 2n + 2t = 40$

Subtract:
             $\begin{align} 2i+9n+12t=120&\\ -\underline{\quad 2i+2n+\ 2t\ =\ 40\ }\ &\\ 7n+10t=\ 80\ &\end{align}$

$t$ must be between $1$ and $7$ (because $n$ must be at least $1$)

$t$	$7n = 80-10t$
$1$	$70\Rightarrow n=10$
$2$	$60$ - not a multiple of $7$
other	This will always be a multiple of $10$, getting smaller   $50, 40, 30, 20, 10$ are not multiples of $7$

Only option for $t$ is $1$

Check this works: $t=1$ gives $n=10$ so the other $9$ plants must be ivy
$2\times9 + 9\times10 + 12\times1 = 18 + 90 + 12 = 120$