{"status": "success", "data": {"description_md": "$x$, $y$, and $z$ are positive numbers satisfying $xyz = 1$, $x + \\dfrac{1}{z} = 10$, and $y + \\dfrac{1}{x} = 17$. If $z + \\dfrac{1}{y} = \\dfrac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m + n$.", "description_html": "<p><span class=\"katex--inline\">x</span>, <span class=\"katex--inline\">y</span>, and <span class=\"katex--inline\">z</span> are positive numbers satisfying <span class=\"katex--inline\">xyz = 1</span>, <span class=\"katex--inline\">x + \\dfrac{1}{z} = 10</span>, and <span class=\"katex--inline\">y + \\dfrac{1}{x} = 17</span>. If <span class=\"katex--inline\">z + \\dfrac{1}{y} = \\dfrac{m}{n}</span>, where <span class=\"katex--inline\">m</span> and <span class=\"katex--inline\">n</span> are relatively prime positive integers. Find <span class=\"katex--inline\">m + n</span>.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 7, "problem_name": "Christmas Contest - Guts Round - Set 7 Problem 3", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}