What is the empirical formula for a compound that contains 38.77% Cl and 61.23% O?

W (Cl) = 0.3877

w (O) = 0.6123

M (Cl) = 35.5 g/mol

M (O) = 16.0 g/mol

ClₐOₓ

M (ClₐOₓ) = 35.5a+16.0x

w (Cl) = 35.5a / (35.5a+16.0x)

w (O) = 16.0x / (35.5a+16.0x)

solve a system of two equations with two unknowns

35.5a / (35.5a+16.0x) = 0.3877

16.0x / (35.5a+16.0x) = 0.6123

a=2

x=7

Cl₂O₇ is the empirical formula