Going to paint

The dimensions of the room are 3.8 and 3.4 m. The height is 2.6 m. The doors and windows together have 3.5 m². We are going to paint. The first coat with white basic we apply on the walls and ceiling. We paint with colour only the walls. Calculate how much we will pay for the purchase of paint if one bucket of white paint lasts for 150 m² and costs 24.50 eur, one bucket of coloured paint costs 33 eur and also lasts for 150 m². Calculate how many m² the floor has.

Final Answer:

S₁ =  12.92 m²
x =  57.5 Eur

Step-by-step explanation:

$$\begin{gathered} a=3.8\text{m} \\ b=3.4\text{m} \\ c=2.6\text{m} \\ {S}_2=3.5{\text{m}}^2 \\ {S}_1=a\cdot b=3.8\cdot 3.4=12.92{\text{m}}^2 \end{gathered}$$

$$\begin{gathered} c_1=24.50/150=\frac{49}{300}\doteq 0.1633{\text{Eur/m}}^2 \\ {c}_2=33/150=\frac{11}{50}=0.22{\text{Eur/m}}^2 \\ {S}_3=2\cdot (a+b)\cdot c-S_2=2\cdot (3.8+3.4)\cdot 2.6-3.5=\frac{1697}{50}=33.94{\text{m}}^2 \\ {x}_1=c_1\cdot (S_1+S_3)+c_2\cdot S_3=0.1633\cdot (12.92+33.94)+0.22\cdot 33.94=15.1206\text{Eur} \\ x=24.50+33=57.5\text{Eur} \end{gathered}$$

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