Wallpapering a room

The walls of a room are to be covered with wallpaper from floor to ceiling. The room is rectangular. It is 3 m wide, 5 m long, and 2.5 m high. In one wall there is a door, which together with the frame occupies a rectangle with dimensions 80 cm and 2 m. In the room there is also one window. Together with the frame, it forms a rectangle with dimensions 12 dm and 2 m. How many crowns will the wallpapering of the room cost if for 1 m² of wallpapered wall the owner pays 80 Kč?

Final Answer:

x =  2880 Kc

Step-by-step explanation:

$$\begin{gathered} a=3\text{m} \\ b=5\text{m} \\ c=2.5\text{m} \\ {x}_1=80\text{cm}\to \text{m}=80:100\text{m}=0.8\text{m} \\ {y}_1=2\text{m} \\ {x}_2=12\text{dm}\to \text{m}=12:10\text{m}=1.2\text{m} \\ {y}_2=2\text{m} \\ {S}_1=x_1\cdot y_1=0.8\cdot 2=\frac{8}{5}=1.6{\text{m}}^2 \\ {S}_2=x_2\cdot y_2=1.2\cdot 2=\frac{12}{5}=2.4{\text{m}}^2 \\ S=2\cdot (a+b)\cdot c-S_1-S_2=2\cdot (3+5)\cdot 2.5-1.6-2.4=36{\text{m}}^2 \\ x=80\cdot S=80\cdot 36=2880\text{Kc} \end{gathered}$$

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