{"status": "success", "data": {"description_md": "Let $p$, $q$, and $r$ be the distinct roots of the polynomial $x^3 - 22x^2 + 80x - 67$. It is given that there exist real numbers $A$, $B$, and $C$ such that $$\\dfrac{1}{s^3 - 22s^2 + 80s - 67} = \\dfrac{A}{s-p} + \\dfrac{B}{s-q} + \\frac{C}{s-r}$$for all $s$ not in $\\{p,q,r\\}$. What is $\\tfrac1A+\\tfrac1B+\\tfrac1C$?\n\n$\\textbf{(A) }243\\qquad\\textbf{(B) }244\\qquad\\textbf{(C) }245\\qquad\\textbf{(D) }246\\qquad\\textbf{(E) } 247$", "description_html": "<p>Let <span class=\"katex--inline\">p</span>, <span class=\"katex--inline\">q</span>, and <span class=\"katex--inline\">r</span> be the distinct roots of the polynomial <span class=\"katex--inline\">x^3 - 22x^2 + 80x - 67</span>. It is given that there exist real numbers <span class=\"katex--inline\">A</span>, <span class=\"katex--inline\">B</span>, and <span class=\"katex--inline\">C</span> such that <span class=\"katex--display\">\\dfrac{1}{s^3 - 22s^2 + 80s - 67} = \\dfrac{A}{s-p} + \\dfrac{B}{s-q} + \\frac{C}{s-r}</span>for all <span class=\"katex--inline\">s</span> not in <span class=\"katex--inline\">\\{p,q,r\\}</span>. What is <span class=\"katex--inline\">\\tfrac1A+\\tfrac1B+\\tfrac1C</span>?</p>&#10;<p><span class=\"katex--inline\">\\textbf{(A) }243\\qquad\\textbf{(B) }244\\qquad\\textbf{(C) }245\\qquad\\textbf{(D) }246\\qquad\\textbf{(E) } 247</span></p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 4, "problem_name": "2019 AMC 10A Problem 24", "can_next": true, "can_prev": true, "nxt": "/problem/19_amc10A_p25", "prev": "/problem/19_amc10A_p23"}}