{"status": "success", "data": {"description_md": "Anna is performing some scientific experiments. For reasons unknown to mankind, she has $100$ litres of water. She starts by replacing $20$ litres of water with pure vinegar. Next, Anna replaces $25$ litres of the new mixture with pure water. If the ratio of vinegar to water in the final mixture is $\\frac{a}{b}$, where $a$ and $b$ are relatively prime, positive integers, find $a+b$.\n    \n(Assume that the vinegar is uniformly spread across the mixture).", "description_html": "<p>Anna is performing some scientific experiments. For reasons unknown to mankind, she has <span class=\"katex--inline\">100</span> litres of water. She starts by replacing <span class=\"katex--inline\">20</span> litres of water with pure vinegar. Next, Anna replaces <span class=\"katex--inline\">25</span> litres of the new mixture with pure water. If the ratio of vinegar to water in the final mixture is <span class=\"katex--inline\">\\frac{a}{b}</span>, where <span class=\"katex--inline\">a</span> and <span class=\"katex--inline\">b</span> are relatively prime, positive integers, find <span class=\"katex--inline\">a+b</span>.</p>&#10;<p>(Assume that the vinegar is uniformly spread across the mixture).</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 1, "problem_name": "TxO Math Bowl 2024 - Guts Contest - Set 1 Problem 2", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}