Question

There are $1800$ apple trees in Tanya's orchard now. One year after starting the orchard, she had added $200$trees to the ones which were already there. Then $3$ years later, she added twice the number of trees she had at that time. How many apple trees did she plant originally?

Answer 1

Let number of trees she plant originally be $\mathrm{x}$.

But one year after starting the orchard, she had added $200$ tress, i.e., $\mathrm{x}+200$.

Then $3$ years later, she added twice the number of trees she had at that time, i.e., $2(\mathrm{x}+200)$.

At present Number of trees $=1800$

So,

$$\begin{gathered} (\mathrm{x}+200)+2(\mathrm{x}+200)=1800 \\ \Rightarrow \mathrm{x}+200+2\mathrm{x}+400=1800 \\ \Rightarrow 3\mathrm{x}+600=1800 \\ \Rightarrow 3\mathrm{x}=1800-600 \\ \Rightarrow 3\mathrm{x}=1200 \\ \Rightarrow \mathrm{x}=\frac{1200}{3} \end{gathered}$$

$\Rightarrow \mathrm{x}=400$

Hence, she plant originally $400$ trees of apples.