{"status": "success", "data": {"description_md": "Denote $\\{x\\}$ as the fractional part of $x$. For example, $\\{1.25\\} = 0.25$ and $\\{-6.9\\} = 0.1$. The sum of all values of $x$ that satisfy\n\n$$20x^2 = (x - \\{x\\})(19x+30\\{x\\})$$\n\ncan be written as $\\frac{p}{q}$ for relatively prime positive integers $p$ and $q$. Compute $p+q$.", "description_html": "<p>Denote <span class=\"katex--inline\">\\{x\\}</span> as the fractional part of <span class=\"katex--inline\">x</span>. For example, <span class=\"katex--inline\">\\{1.25\\} = 0.25</span> and <span class=\"katex--inline\">\\{-6.9\\} = 0.1</span>. The sum of all values of <span class=\"katex--inline\">x</span> that satisfy</p>&#10;<p><span class=\"katex--display\">20x^2 = (x - \\{x\\})(19x+30\\{x\\})</span></p>&#10;<p>can be written as <span class=\"katex--inline\">\\frac{p}{q}</span> for relatively prime positive integers <span class=\"katex--inline\">p</span> and <span class=\"katex--inline\">q</span>. Compute <span class=\"katex--inline\">p+q</span>.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "Holiday Contest 2025 - Team Round - Problem 11", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}