Day of the Triffids
Jasmine buys three different types of plant. How many triffids did she buy?
Age
14 to 16
Challenge level
Problem
Jasmine spends exactly £120 on three types of plants.
Poison ivy plants cost £2 each.
Deadly nightshade plants cost £9 each.
Triffids plants cost £12 each.
She buys twenty plants in total, including at least one of each type.
How many triffids did she buy?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
Student Solutions
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
$2\times9 + 9\times10 + 12\times1 = 18 + 90 + 12 = 120$