A certain steel is to be analyzed for Cr and Mn. By suitable treatment, the Cr in the steel is oxidized to Cr₂O₇^2–(aq) and the Mn to MnO₄^–(aq). A 10.000 g sample of steel is used to produce 250.0 mL of a solution containing Cr₂O₇^2–(aq) and MnO₄^–(aq). A 10.00 mL portion of this solution is added to BaCl₂(aq), and by proper adjustment of the pH, the chromium is completely precipitated as BaCrO₄(s); 0.549 g is obtained. A second 10.00 mL portion of the solution requires exactly 15.95 mL of 0.0750 M Fe²⁺(aq) for its titration in acidic solution. Calculate the % Cr and % Mn in the steel sample. In the titration MnO₄^–(aq) is reduced to Mn²⁺(aq) and Cr₂O₇^2–(aq) is reduced to Cr³⁺(aq); the Fe²⁺(aq) is oxidized to Fe³⁺(aq).