###### The problem

In an engineering factory, the production line takes up $\frac{2}{3}$ of the floor area.

Out of the remaining floor area ,a total of $\frac{3}{5}$ is taken up by the office space and the canteen.

The rest is warehouse space.

The warehouse space occupies 2000 ${m}^{2}$.

Work out the floor area of the production line.

###### The solution

$\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}Solution:\phantom{\rule{0ex}{0ex}}Letthefloorareabex{m}^{2}.\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}Productionline=x-\frac{2x}{3}=\frac{x}{3}\phantom{\rule{0ex}{0ex}}Totalareaofofficespaceandcanteenisgivenas\frac{3}{5}outofremainingarea\phantom{\rule{0ex}{0ex}}\Rightarrow \frac{3}{5}\left(\frac{x}{3}\right)=\frac{x}{5}\phantom{\rule{0ex}{0ex}}Warehousespace=\frac{x}{3}-\frac{x}{5}=\frac{5x-3x}{15}=\frac{2x}{15}\phantom{\rule{0ex}{0ex}}\Rightarrow \frac{2x}{15}=2000{m}^{2}\Rightarrow x=15000\phantom{\rule{0ex}{0ex}}Productionline=\frac{2x}{3}=\frac{2x15000}{3}=2x5000=10,000{m}^{2}.$