Amixture of pure agcl and pure agbr is found to contain 60.94% ag by mass. what are the mass percents of cl and br in the mixture?

First step is to calculate the mass of Ag in each compound separately:
From the periodic table: 
molar mass of Ag is 107.87 gm
molar mass of Cl is 35.45 gm
molar mass of Br is 79.9 gm
For AgCl, mass % of Ag = [107.87/143.32] x 100 = 75.26%
For AgBr, mass % of Ag = [107.87/187.77] x 100 = 57.45 %

Second step is to calculate the mass % of each compound in the mixture:
Assume mass % of AgCl is y and that of AgBr is (1-y) as the total percentage is 100% or 1
0.6094 = 0.7526 y + 0.5745 (1-y)
y = 0.8716
This means that the mixture is almost 87% AgCl and 13% AgBr
The mass % of chlorine and bromine together is (100%-60.94%) which is 39.06%
mass % of chlorine = (1-0.6094)(0.8716) x 100 = 34.044%
mass % of bromine = 39.04 - 34.044 = 5.056%

A.