{"status": "success", "data": {"description_md": "The system of equations\n\n$$\\log_{10}(2000xy) - (\\log_{10}x)(\\log_{10}y) = 4$$\n\n$$\\log_{10}(2yz) - (\\log_{10}y)(\\log_{10}z) = 1$$\n\n$$\\log_{10}(zx) - (\\log_{10}z)(\\log_{10}x) = 0$$\n\nhas two solutions $(x_{1},y_{1},z_{1})$ and $(x_{2},y_{2},z_{2})$. Find $y_{1} + y_{2}$.<br>Leading zeroes must be inputted, so if your answer is `34`, then input `034`\n\n___\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>The system of equations</p>&#10;<p><span class=\"katex--display\">\\log_{10}(2000xy) - (\\log_{10}x)(\\log_{10}y) = 4</span></p>&#10;<p><span class=\"katex--display\">\\log_{10}(2yz) - (\\log_{10}y)(\\log_{10}z) = 1</span></p>&#10;<p><span class=\"katex--display\">\\log_{10}(zx) - (\\log_{10}z)(\\log_{10}x) = 0</span></p>&#10;<p>has two solutions <span class=\"katex--inline\">(x_{1},y_{1},z_{1})</span> and <span class=\"katex--inline\">(x_{2},y_{2},z_{2})</span>. Find <span class=\"katex--inline\">y_{1} + y_{2}</span>.<br/>Leading zeroes must be inputted, so if your answer is <code>34</code>, then input <code>034</code></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": 4, "problem_name": "2000 AIME I Problem 9", "can_next": true, "can_prev": true, "nxt": "/problem/00_aime_I_p10", "prev": "/problem/00_aime_I_p08"}}