Property

The length of the rectangle-shaped property is 8 meters, less than three times the width. If we increase the width by 5% of the length and the length by 14% of the width, the property perimeter will increase by 13 meters. How much will the property cost per 1 square meter? We will pay € 8.6.

Final Answer:

x =  12235908 eur

Step-by-step explanation:

$$\begin{gathered} r_1=5\%=\frac{5}{100}=\frac{1}{20}=0.05 \\ {r}_2=14\%=\frac{14}{100}=\frac{7}{50}=0.14 \\ a=3b-8 \\ 2[(b+r_1\cdot a)+(a-r_2\cdot b)]=2(a+b)+13 \\ 2[(b+0.05\cdot a)+(a-0.14\cdot b)]=2(a+b)+13 \\ a=3\cdot b-8 \\ 2\cdot ((b+0.05\cdot a)+(a-0.14\cdot b))=2\cdot (a+b)+13 \\ a-3b=-8 \\ 0.1a-0.28b=13 \\ Row2-0.1\cdot Row1\to Row2 \\ 0.02b=13.8 \\ b=\frac{13.8}{0.02}=690 \\ a=-8+3b=-8+3\cdot 690=2062 \\ a=2062 \\ b=690 \\ S=a\cdot b=2062\cdot 690=1422780{\text{m}}^2 \\ x=8.6\cdot S=8.6\cdot 1422780=12235908\text{eur} \end{gathered}$$

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