Chemistry Help!?

Question

It was desired to neutralize a certain solution X that had been prepared by mixing solutions of potassium chloride and hydrobromic acid. Titration of 10.0ml X with 0.100 M silver nitrate required 50.0ml of the latter. The resulting precipitate, containing a mixture of AgCl and AgBr, was dried and found to weigh 0.762g. How much 0.100M sodium hydroxide should be used to nuetralize 10.0ml of solution X?

Answer 1

Use ALGEBRA!
Assume Y L of 0.100M sodium hydroxide should be used to nuetralize 10.0ml of solution X.
Y L of 0.100M NaOH
<==> 0.1*Y mol NaOH
<==> 0.1*Y mol HBr to be neutralized
<==> 0.1*Y mol AgBr can be formed
<==> 18.777*Y g AgBr (since formula mass of AgBr is 187.77 g/mol)
<==> (0.762 - 18.777*Y)g AgCl
<==> (0.762 - 18.777*Y)/143.32 mol AgCl (since formula mass of AgCl is 143.32 g/mol)
<==> (0.1*Y + (0.762 - 18.777*Y)/143.32) mol of precipitated Ag, that can be calculated as 0.100*0.0500 = 0.00500 mol from used AgNO3. Hence:
0.1*Y + (0.762 - 18.777*Y)/143.32 = 0.00500
Solve this equation to get Y, the requested solution!