Answer
Originally stolen $=36$ plants.
Work Step by Step
Let the number of stolen plants $=x$.
The thief is forced to give $\frac{1}{2}$ of stolen plant $+2$.
For the first thief:
He gave $\frac{x}{2}+2$.
Remaining number of plants.
$=x-(\frac{x}{2}+2)$
Simplify.
$=x-\frac{x}{2}-2$
$=\frac{x}{2}-2$
For the second thief:
He gave $=\frac{1}{2}(\frac{x}{2}-2)+2$.
Simplify.
$=\frac{x}{4}-1+2$
$=\frac{x}{4}+1$
Remaining number of plants.
$=\frac{x}{2}-2-(\frac{x}{4}+1)$
$=\frac{x}{2}-2-\frac{x}{4}-1$
Simplify.
$=\frac{x}{4}-3$
For the third thief:
He gave $=\frac{1}{2}(\frac{x}{4}-3)+2$.
Simplify.
$=\frac{x}{8}-\frac{3}{2}+2$
$=\frac{x}{8}+\frac{1}{2}$
Remaining number of plants.
$=\frac{x}{4}-3-(\frac{x}{8}+\frac{1}{2})$
Simplify.
$=\frac{x}{4}-3-\frac{x}{8}-\frac{1}{2}$
$=\frac{x}{8}-\frac{7}{2}$
After the third thief remaining number of plants $=1$.
$\Rightarrow \frac{x}{8}-\frac{7}{2}=1$
Add $\frac{7}{2}$ both sides.
$\Rightarrow \frac{x}{8}-\frac{7}{2}+\frac{7}{2}=1+\frac{7}{2}$
Simplify.
$\Rightarrow \frac{x}{8}=\frac{9}{2}$
Multiply by $8$ on both sides.
$\Rightarrow 8\cdot \frac{x}{8}=8\cdot \frac{9}{2}$
Simplify.
$\Rightarrow x=36$.
