Question

there are 1800 apple trees in Tanya's orcard now. one year after starting the orchard she had added 200 trees to the ones which were already there. then three years later she added twice the number of trees she had at that time. how many apple trees did she plant originally?

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{number}\mathrm{of}\mathrm{trees}\mathrm{she}\mathrm{planted}\mathrm{originally}=\mathrm{x} \\ \mathrm{Now},\mathrm{number}\mathrm{of}\mathrm{trees}\mathrm{in}\mathrm{orchard}\mathrm{after}1\mathrm{year}=\mathrm{x}+200 \\ \mathrm{Number}\mathrm{of}\mathrm{trees}\mathrm{in}\mathrm{the}\mathrm{orchard}3\mathrm{years}\mathrm{later}=2\left(\mathrm{x}+200\right)=2\mathrm{x}+400 \\ \mathrm{Now},\mathrm{according}\mathrm{to}\mathrm{question}: \\ \mathrm{x}+\mathrm{x}+200+2\mathrm{x}+400=1800 \\ \Rightarrow 6\mathrm{x}+600=1800 \\ \Rightarrow 6\mathrm{x}=1800-600 \\ \Rightarrow 6\mathrm{x}=1200 \\ \Rightarrow \mathrm{x}=\frac{1200}{6}=200 \\ \mathrm{So},\mathrm{number}\mathrm{of}\mathrm{trees}\mathrm{she}\mathrm{planted}\mathrm{originally}=200 \end{gathered}$$