\( 92 \frac{3}{4} \div 3 \frac{1}{5} \quad \) of \( 2 \frac{1}{2} \)

To tackle this problem, we first need to convert the mixed numbers into improper fractions. So, \( 92 \frac{3}{4} \) becomes \( \frac{370}{4} \) and \( 3 \frac{1}{5} \) becomes \( \frac{16}{5} \). Now, when we divide \( \frac{370}{4} \) by \( \frac{16}{5} \), we multiply by the reciprocal, resulting in \( \frac{370}{4} \times \frac{5}{16} \). Simplifying gives us \( \frac{1850}{64} \), which reduces to \( \frac{925}{32} \) or \( 28 \frac{29}{32} \). Next, we multiply this result by \( 2 \frac{1}{2} \), which is \( \frac{5}{2} \). Thus we have \( \frac{925}{32} \times \frac{5}{2} = \frac{4625}{64} \). This reduces to \( 72 \frac{17}{64} \). Voilà!