= 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
