{"status": "success", "data": {"description_md": "A bowl contained 320 grams of pure white sugar. Mixture Y was formed by taking $x$ grams of the white sugar out of the bowl, adding $x$ grams of brown sugar to the bowl, and then mixing uniformly. In Mixture Y, the ratio of the mass of the white sugar to the mass of the brown sugar, expressed in lowest terms, was $w : b$. Mixture Z is formed by taking $x$ grams of Mixture Y out of the bowl, adding $x$ grams of brown sugar to the bowl, and then mixing uniformly. In Mixture Z, the ratio of the mass of the white sugar to the mass of the brown sugar is $49 : 15$. The value of $x + w + b$ is\n\n$\\text{(A)}\\ 48\\qquad\\text{(B)}\\ 49\\qquad\\text{(C)}\\ 139\\qquad\\text{(D)}\\ 76\\qquad\\text{(E)}\\ 104$\n\n___\n\n**[Fermat](https://www.cemc.uwaterloo.ca/contests/past_contests.html#pcf), by [CEMC](https://cemc.uwaterloo.ca/), is licensed under the [CC BY-NC 3.0 DEED](https://creativecommons.org/licenses/by-nc/3.0/). They are not affiliated with or endorse TopsOJ in any way.**\n", "description_html": "<p>A bowl contained 320 grams of pure white sugar. Mixture Y was formed by taking <span class=\"katex--inline\">x</span> grams of the white sugar out of the bowl, adding <span class=\"katex--inline\">x</span> grams of brown sugar to the bowl, and then mixing uniformly. In Mixture Y, the ratio of the mass of the white sugar to the mass of the brown sugar, expressed in lowest terms, was <span class=\"katex--inline\">w : b</span>. Mixture Z is formed by taking <span class=\"katex--inline\">x</span> grams of Mixture Y out of the bowl, adding <span class=\"katex--inline\">x</span> grams of brown sugar to the bowl, and then mixing uniformly. In Mixture Z, the ratio of the mass of the white sugar to the mass of the brown sugar is <span class=\"katex--inline\">49 : 15</span>. The value of <span class=\"katex--inline\">x + w + b</span> is</p>\n<p><span class=\"katex--inline\">\\text{(A)}\\ 48\\qquad\\text{(B)}\\ 49\\qquad\\text{(C)}\\ 139\\qquad\\text{(D)}\\ 76\\qquad\\text{(E)}\\ 104</span></p>\n<hr>\n<p><strong><a href=\"https://www.cemc.uwaterloo.ca/contests/past_contests.html#pcf\">Fermat</a>, by <a href=\"https://cemc.uwaterloo.ca/\">CEMC</a>, is licensed under the <a href=\"https://creativecommons.org/licenses/by-nc/3.0/\">CC BY-NC 3.0 DEED</a>. They are not affiliated with or endorse TopsOJ in any way.</strong></p>\n", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2012 Fermat Problem 23", "can_next": true, "can_prev": true, "nxt": "/problem/12_fermat_p24", "prev": "/problem/12_fermat_p22"}}