{"status": "success", "data": {"description_md": "Over all solutions to the system of equations,\n\n$144a^2+90b^2+17c^2 = 31217$\n\n$288a-192b-25c=689$\n\n$b(9a+c)= 1272$\n\n\nfind the sum of all possible values of $a+b+c$", "description_html": "<p>Over all solutions to the system of equations,</p>&#10;<p><span class=\"katex--inline\">144a^2+90b^2+17c^2 = 31217</span></p>&#10;<p><span class=\"katex--inline\">288a-192b-25c=689</span></p>&#10;<p><span class=\"katex--inline\">b(9a+c)= 1272</span></p>&#10;<p>find the sum of all possible values of <span class=\"katex--inline\">a+b+c</span></p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 4, "problem_name": "Grinding Aces Math Exam 2025 - Problem 6", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}