Flowerbed

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

Correct result:

r₁ =  1.5 m

Solution:

$$\begin{gathered} r_2=r_1+3 \\ {S}_2=9S_1 \\ \pi r_2^2=9\pi r_1^2 \\ {r}_2^2=9r_1^2 \\ {r}_2=3r_1 \\ {r}_2=r_1+3 \\ {r}_2=3\cdot r_1 \\ {r}_1-r_2=-3 \\ 3r_1-r_2=0 \\ {r}_1={\displaystyle \frac{3}{2}}=1.5={\displaystyle \frac{3}{2}}\text{ m}=1.5\text{ m } \\ {r}_2={\displaystyle \frac{9}{2}}=4.5 \end{gathered}$$

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