{"status": "success", "data": {"description_md": "Triangles $ABC$ and $ADE$ have areas $2007$ and $7002,$ respectively, with $B = (0,0),$ $C = (223,0),$ $D = (680,380),$ and $E = (689,389).$ What is the sum of all possible x-coordinates of $A$?<br>\t\n\n$\\mathrm{(A)}\\ 282 \\qquad \\mathrm{(B)}\\ 300 \\qquad \\mathrm{(C)}\\ 600 \\qquad \\mathrm{(D)}\\ 900 \\qquad \\mathrm{(E)}\\ 1200$\n___\nFull credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "<p>Triangles <span class=\"katex--inline\">ABC</span> and <span class=\"katex--inline\">ADE</span> have areas <span class=\"katex--inline\">2007</span> and <span class=\"katex--inline\">7002,</span> respectively, with <span class=\"katex--inline\">B = (0,0),</span> <span class=\"katex--inline\">C = (223,0),</span> <span class=\"katex--inline\">D = (680,380),</span> and <span class=\"katex--inline\">E = (689,389).</span> What is the sum of all possible x-coordinates of <span class=\"katex--inline\">A</span>?<br/></p>&#10;<p><span class=\"katex--inline\">\\mathrm{(A)}\\ 282 \\qquad \\mathrm{(B)}\\ 300 \\qquad \\mathrm{(C)}\\ 600 \\qquad \\mathrm{(D)}\\ 900 \\qquad \\mathrm{(E)}\\ 1200</span></p>&#10;<hr/>&#10;<p>Full credit goes to <a href=\"https://maa.org/\">MAA</a> for authoring these problems. These problems were taken on the <a href=\"https://artofproblemsolving.com/\">AOPS</a> website.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2007 AMC 12A Problem 19", "can_next": true, "can_prev": true, "nxt": "/problem/07_amc12A_p20", "prev": "/problem/07_amc12A_p18"}}