{"status": "success", "data": {"description_md": "There are $3$ numbers $A, B$, and $C$, such that $1001C - 2002A = 4004$, and $1001B + 3003A = 5005$. What is the average of $A, B$, and $C$?\n\n$\\textbf{(A)}\\ 1 \\qquad \\textbf{(B)}\\ 3 \\qquad \\textbf{(C)}\\ 6 \\qquad \\textbf{(D)}\\ 9 \\qquad \\textbf{(E) }\\text{Not uniquely determined}$", "description_html": "<p>There are <span class=\"katex--inline\">3</span> numbers <span class=\"katex--inline\">A, B</span>, and <span class=\"katex--inline\">C</span>, such that <span class=\"katex--inline\">1001C - 2002A = 4004</span>, and <span class=\"katex--inline\">1001B + 3003A = 5005</span>. What is the average of <span class=\"katex--inline\">A, B</span>, and <span class=\"katex--inline\">C</span>?</p>&#10;<p><span class=\"katex--inline\">\\textbf{(A)}\\ 1 \\qquad \\textbf{(B)}\\ 3 \\qquad \\textbf{(C)}\\ 6 \\qquad \\textbf{(D)}\\ 9 \\qquad \\textbf{(E) }\\text{Not uniquely determined}</span></p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 1, "problem_name": "2002 AMC 10A Problem 9", "can_next": true, "can_prev": true, "nxt": "/problem/02_amc10A_p10", "prev": "/problem/02_amc10A_p08"}}