{"status": "success", "data": {"description_md": "A bag initially contains red marbles and blue marbles only, with more blue than red. Red marbles are added to the bag until only $\\frac{1}{3}$ of the marbles in the bag are blue. Then yellow marbles are added to the bag until only $\\frac{1}{5}$ of the marbles in the bag are blue. Finally, the number of blue marbles in the bag is doubled. What fraction of the marbles now in the bag are blue?\n\n$\\mathrm{(A) \\ } \\frac{1}{5} \\qquad \\mathrm{(B) \\ } \\frac{1}{4} \\qquad \\mathrm{(C) \\ } \\frac{1}{3} \\qquad \\mathrm{(D) \\ } \\frac{2}{5} \\qquad \\mathrm{(E) \\ } \\frac{1}{2}$", "description_html": "<p>A bag initially contains red marbles and blue marbles only, with more blue than red. Red marbles are added to the bag until only  <span class=\"katex--inline\">\\frac{1}{3}</span>  of the marbles in the bag are blue. Then yellow marbles are added to the bag until only  <span class=\"katex--inline\">\\frac{1}{5}</span>  of the marbles in the bag are blue. Finally, the number of blue marbles in the bag is doubled. What fraction of the marbles now in the bag are blue?</p>\n<p> <span class=\"katex--inline\">\\mathrm{(A) \\ } \\frac{1}{5} \\qquad \\mathrm{(B) \\ } \\frac{1}{4} \\qquad \\mathrm{(C) \\ } \\frac{1}{3} \\qquad \\mathrm{(D) \\ } \\frac{2}{5} \\qquad \\mathrm{(E) \\ } \\frac{1}{2}</span> </p>\n<hr><p>Full credit goes to <a href=\"https://maa.org/\">MAA</a> for authoring these problems. These problems were taken on the <a href=\"https://artofproblemsolving.com/\">AOPS</a> website.</p>", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2004 AMC 10B Problem 14", "can_next": true, "can_prev": true, "nxt": "/problem/04_amc10B_p15", "prev": "/problem/04_amc10B_p13"}}