Pavilion

The rectangular pavilion with dimensions of 3.5 m and 2.75 m is to be paved with square tiles of side 25 cm, with a price of CZK 22 per 1 piece, or rectangular tiles with sides of 20 cm and 15 cm at the price of CZK 11 per 1 pc. Which solution is cheaper (write its price)?

Correct answer:

x =  3388 Kč

Step-by-step explanation:

$$\begin{gathered} S=3.5\cdot 2.75=9.625{\text{m}}^2 \\ a=25\text{cm}\to \text{m}=25:100\text{m}=0.25\text{m} \\ x=20\text{cm}\to \text{m}=20:100\text{m}=3388\text{m} \\ y=15\text{cm}\to \text{m}=15:100\text{m}=0.15\text{m} \\ {S}_1=a^2=0.25^2=\frac{1}{16}=0.0625{\text{m}}^2 \\ {S}_2=x\cdot y=3388\cdot 0.15=\frac{3}{100}=0.03{\text{m}}^2 \\ {n}_1=[S/S_1]=[9.625/0.0625]=154 \\ {n}_2=[S/S_2]=[9.625/0.03]=321 \\ {c}_1=22\cdot n_1=22\cdot 154=3388\text{Kc} \\ {c}_2=11\cdot n_2=11\cdot 321=3531\text{Kc} \\ {c}_1<c_2 \\ x=c_1=3388=3388\text{Kc} \end{gathered}$$

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