{"status": "success", "data": {"description_md": "The line $y = -\\frac{3}{4}x + 9$ crosses the $x$-axis at $P$ and the $y$-axis at $Q$. Point $T(r, s)$ is on line segment $PQ$. If the area of $\\triangle POQ$ is three times the area of $\\triangle TOP$, then the value of $r + s$ is\n\n<center><img class=\"problem-image\" src=\"/static/cayley/2006/crops/06_cayley_p20_fig.png\" alt=\"figure\" width=\"286\"></center>\n\n$\\text{(A)}\\ 7\\qquad\\text{(B)}\\ 10\\qquad\\text{(C)}\\ 11\\qquad\\text{(D)}\\ 14\\qquad\\text{(E)}\\ 18$\n\n___\n\n**[Cayley](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>The line <span class=\"katex--inline\">y = -\\frac{3}{4}x + 9</span> crosses the <span class=\"katex--inline\">x</span>-axis at <span class=\"katex--inline\">P</span> and the <span class=\"katex--inline\">y</span>-axis at <span class=\"katex--inline\">Q</span>. Point <span class=\"katex--inline\">T(r, s)</span> is on line segment <span class=\"katex--inline\">PQ</span>. If the area of <span class=\"katex--inline\">\\triangle POQ</span> is three times the area of <span class=\"katex--inline\">\\triangle TOP</span>, then the value of <span class=\"katex--inline\">r + s</span> is</p>\n<center><img class=\"problem-image\" src=\"/static/cayley/2006/crops/06_cayley_p20_fig.png\" alt=\"figure\" width=\"286\"></center>\n<p><span class=\"katex--inline\">\\text{(A)}\\ 7\\qquad\\text{(B)}\\ 10\\qquad\\text{(C)}\\ 11\\qquad\\text{(D)}\\ 14\\qquad\\text{(E)}\\ 18</span></p>\n<hr>\n<p><strong><a href=\"https://www.cemc.uwaterloo.ca/contests/past_contests.html#pcf\">Cayley</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": 2, "problem_name": "2006 Cayley Problem 20", "can_next": true, "can_prev": true, "nxt": "/problem/06_cayley_p21", "prev": "/problem/06_cayley_p19"}}