Lookout tower

How high is the lookout tower? If each step was 3 cm lower, 60 more were on the lookout tower. If it were 3 cm higher again, it would be 40 less than it is now.

Correct answer:

x =  36 m

Step-by-step explanation:

$$\begin{gathered} x=n\cdot s \\ x=(n+60)\cdot (s-3) \\ x=(n-40)\cdot (s+3) \\ n\cdot s=(n+60)\cdot (s-3) \\ n\cdot s=(n-40)\cdot (s+3) \\ 3n-60s=-180 \\ 3n-40s=120 \\ Row2-Row1\to Row2 \\ 3n-60s=-180 \\ 20s=300 \\ s=\frac{300}{20}=15 \\ n=\frac{-180+60s}{3}=\frac{-180+60\cdot 15}{3}=240 \\ n=240 \\ s=15 \\ {s}_1=s\to \text{m}=s:100\text{m}=15:100\text{m}=0.15\text{m} \\ x=n\cdot s_1=240\cdot 0.15=36\text{m} \end{gathered}$$

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