Question

If $35\%$ of a natural area is to be developed, leaving $500$ $acres$ untouched, how many acres are to be developed?

Answer 1

Step-1: Solve for the total natural area:

Given that $35\%$ of a natural area is to be developed, leaving $500$ $acres$ untouched
Let the natural area be $A$$acres$
Percentage of area left untouched $=100\%-35\%$
$=65\%$
$\therefore$ $65\%$ of $A=500\mathrm{acres}$
$$\begin{gathered} \Rightarrow \frac{65}{100}\times A=500 \\ \Rightarrow A=500\times \frac{100}{65} \\ =769.23\mathrm{acres} \end{gathered}$$

Step-2: Solve for the area to be developed:
$35\%$ of $769.23\mathrm{acres}$ is to be developed
$$\begin{gathered} \Rightarrow \frac{35}{100}\times 769.23=269.23 \\ \approx 269\mathrm{acres} \end{gathered}$$

Hence, the land to be developed is $269\mathrm{acres}$.