{"status": "success", "data": {"description_md": "Let $a$, $b$, and $c$ be three distinct one-digit numbers. What is the maximum value of the sum of the roots of the equation $(x-a)(x-b)+(x-b)(x-c)=0$?\n\n$\\textbf{(A) } 15 \\qquad\\textbf{(B) } 15.5 \\qquad\\textbf{(C) } 16 \\qquad\\textbf{(D) } 16.5 \\qquad\\textbf{(E) } 17$", "description_html": "<p>Let  <span class=\"katex--inline\">a</span> ,  <span class=\"katex--inline\">b</span> , and  <span class=\"katex--inline\">c</span>  be three distinct one-digit numbers. What is the maximum value of the sum of the roots of the equation  <span class=\"katex--inline\">(x-a)(x-b)+(x-b)(x-c)=0</span> ?</p>\n<p> <span class=\"katex--inline\">\\textbf{(A) } 15 \\qquad\\textbf{(B) } 15.5 \\qquad\\textbf{(C) } 16 \\qquad\\textbf{(D) } 16.5 \\qquad\\textbf{(E) } 17</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": "2015 AMC 10B Problem 14", "can_next": true, "can_prev": true, "nxt": "/problem/15_amc10B_p15", "prev": "/problem/15_amc10B_p13"}}