Roof repair

We need 15 pieces of boards 6 m long, 15 cm wide, and 25 mm thick to repair the roof. How many euros will we pay for all boards if 1 m³ of boards costs 500 euros?

Correct answer:

x =  168.75 Eur

Step-by-step explanation:

$$\begin{gathered} n=15 \\ a=6\text{m} \\ b=15\text{cm}\to \text{m}=15:100\text{m}=0.15\text{m} \\ c=25\text{mm}\to \text{m}=25:1000\text{m}=0.025\text{m} \\ p=500{\text{Eur/m}}^3 \\ {V}_1=a\cdot b\cdot c=6\cdot 0.15\cdot 0.025=\frac{9}{400}=0.0225{\text{m}}^3 \\ V=n\cdot V_1=15\cdot 0.0225=\frac{27}{80}=0.3375{\text{m}}^3 \\ x=p\cdot V=500\cdot 0.3375=168.75\text{Eur} \end{gathered}$$

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