Flowerbed

We enlarged the circular flower bed, increasing its radius by 3 m. The substrate consumption per enlarged flower bed was nine times greater than before (at the same layer height as before magnification). Determine the original flowerbed radius.

Correct answer:

r₁ =  1.5 m

Step-by-step explanation:

$$\begin{gathered} r_2=r_1+3 \\ {S}_2=9S_1 \\ \pi r_2^2=9\pi r_1^2 \\ {r}_2^2=9r_1^2 \\ {r}_2=3r_1 \\ {r}_2=r_1+3 \\ {r}_2=3\cdot r_1 \\ {r}_1-r_2=-3 \\ 3r_1-r_2=0 \\ Pivot:Row1\leftrightarrow Row2 \\ 3r_1-r_2=0 \\ {r}_1-r_2=-3 \\ Row2-\frac{1}{3}\cdot Row1\to Row2 \\ 3r_1-r_2=0 \\ -0.67r_2=-3 \\ {r}_2=\frac{-3}{-0.66666667}=4.5 \\ {r}_1=\frac{0+r_2}{3}=\frac{0+4.5}{3}=1.5=1.5\text{m} \\ {r}_1=\frac{3}{2}=1.5 \\ {r}_2=\frac{9}{2}=4.5 \end{gathered}$$

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