Set up an equation: \(\frac{1}{3}\) of Lay Kim's money = \(\frac{4}{9}\) of Peggy's money.<br><br>
• Let L = Lay Kim's money, P = Peggy's money.<br>
• \(\frac{1}{3}L = \frac{4}{9}P\)<br>
• Multiply both sides by 9: \(3L = 4P\)<br>
• Divide both sides by 4: \(P = \frac{3}{4}L\)<br>
• So Peggy's money is \(\frac{3}{4}\) of Lay Kim's money.<br><br>
Peggy's money expressed as a fraction of Lay Kim's money is \(\frac{3}{4}\).<br>
Check: \(\frac{1}{3} \times 4 = \frac{4}{3}\); \(\frac{4}{9} \times 3 = \frac{12}{9} = \frac{4}{3}\). Equal. ✓<br><br>
Final Answer: C: \(\frac{3}{4}\)