{"status": "success", "data": {"description_md": "Gary purchased a large beverage, but drank only $m/n$ of this beverage, where $m$ and $n$ are relatively prime positive integers. If Gary had purchased only half as much and drunk twice as much, he would have wasted only $\\frac{2}{9}$ as much beverage. Find $m+n$.\n___\nLeading zeroes must be inputted, so if your answer is `34`, then input `034`. Full credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "

Gary purchased a large beverage, but drank only m/n of this beverage, where m and n are relatively prime positive integers. If Gary had purchased only half as much and drunk twice as much, he would have wasted only \\frac{2}{9} as much beverage. Find m+n.

Leading zeroes must be inputted, so if your answer is 34, then input 034. Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.

", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2011 AIME II Problem 1", "can_next": true, "can_prev": false, "nxt": "/problem/11_aime_II_p02", "prev": ""}}