{"status": "success", "data": {"description_md": "**POTD July 19, 2024**\n\nLet $(a, b, c, d, e)$ be an integer solution to the system of equations\n$a + d = 12$\n$b + ad + e = 57$\n$c + bd + ae = 134$\n$cd + be = 156$\n$ce = 72$\nFind the sum of all possible values of $b + d$.", "description_html": "<p><strong>POTD July 19, 2024</strong></p>&#10;<p>Let <span class=\"katex--inline\">(a, b, c, d, e)</span> be an integer solution to the system of equations<br/>&#10;<span class=\"katex--inline\">a + d = 12</span><br/>&#10;<span class=\"katex--inline\">b + ad + e = 57</span><br/>&#10;<span class=\"katex--inline\">c + bd + ae = 134</span><br/>&#10;<span class=\"katex--inline\">cd + be = 156</span><br/>&#10;<span class=\"katex--inline\">ce = 72</span><br/>&#10;Find the sum of all possible values of <span class=\"katex--inline\">b + d</span>.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 4, "problem_name": "Problem of the Day #222", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}