= 2 \cdot \frac{S^2}{5}

February 22, 2026

$= 2 \cdot \frac{S^2}{5}$

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Question:** An anthropologist is studying the relationship between community size and resource allocation. In a hypothetical community, the number of resources \( R \) is directly proportional to the square of the community size \( S \), and inversely proportional to the number of leaders \( L \). If \( R = k \cdot \frac{S^2}{L} \) where \( k \) is a constant, find \( S \) when \( R = 50 \), \( L = 5 \), and \( k = 2 \).
R = k \cdot \frac{S^2}{L}
Substitute the known values into the equation: \( R = 50 \), \( L = 5 \), and \( k = 2 \):
= \frac{2S^2}{5}
Multiply both sides by 5 to eliminate the fraction:
= 2S^2

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