A $50-$year$-$old woman who earns $$70,000$ per year moves her $75-$year$-$old widowed mother in to live with her. Her mother receives $$1500$ per month in social security benefits and a $$2000$ per month pre$-$tax pension. Although the woman owns the house, all bills are split equally between the woman and her mother. When reporting their taxes at year's end, what filing status should each person claim?