{"status": "success", "data": {"description_md": "Let points $A = (0, 0)$, $B = (1, 2)$, $C=(3, 3)$, and $D = (4, 0)$.  Quadrilateral $ABCD$ is cut into equal area pieces by a line passing through $A$.  This line intersects $\\overline{CD}$ at point $\\bigg(\\frac{p}{q}, \\frac{r}{s}\\bigg)$, where these fractions are in lowest terms.  What is $p+q+r+s$?\n\n$\\textbf{(A)}\\ 54\\qquad\\textbf{(B)}\\ 58\\qquad\\textbf{(C)}\\ 62\\qquad\\textbf{(D)}\\ 70\\qquad\\textbf{(E)}\\ 75$", "description_html": "<p>Let points  <span class=\"katex--inline\">A = (0, 0)</span> ,  <span class=\"katex--inline\">B = (1, 2)</span> ,  <span class=\"katex--inline\">C=(3, 3)</span> , and  <span class=\"katex--inline\">D = (4, 0)</span> .  Quadrilateral  <span class=\"katex--inline\">ABCD</span>  is cut into equal area pieces by a line passing through  <span class=\"katex--inline\">A</span> .  This line intersects  <span class=\"katex--inline\">\\overline{CD}</span>  at point  <span class=\"katex--inline\">\\bigg(\\frac{p}{q}, \\frac{r}{s}\\bigg)</span> , where these fractions are in lowest terms.  What is  <span class=\"katex--inline\">p+q+r+s</span> ?</p>\n<p> <span class=\"katex--inline\">\\textbf{(A)}\\ 54\\qquad\\textbf{(B)}\\ 58\\qquad\\textbf{(C)}\\ 62\\qquad\\textbf{(D)}\\ 70\\qquad\\textbf{(E)}\\ 75</span> </p>\n<hr><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>", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2013 AMC 10A Problem 18", "can_next": true, "can_prev": true, "nxt": "/problem/13_amc10A_p19", "prev": "/problem/13_amc10A_p17"}}