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'Day of the Triffids' printed from https://nrich.maths.org/
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
$2\times9 + 9\times10 + 12\times1 = 18 + 90 + 12 = 120$