{"status": "success", "data": {"description_md": "$A$, $B$, $C$ are three piles of rocks. The mean weight of the rocks in $A$ is $40$ pounds, the mean weight of the rocks in $B$ is $50$ pounds, the mean weight of the rocks in the combined piles $A$ and $B$ is $43$ pounds, and the mean weight of the rocks in the combined piles $A$ and $C$ is $44$ pounds. What is the greatest possible integer value for the mean in pounds of the rocks in the combined piles $B$ and $C$?\n\n$\\textbf{(A)} \\ 55 \\qquad \\textbf{(B)} \\ 56 \\qquad \\textbf{(C)} \\ 57 \\qquad \\textbf{(D)} \\ 58 \\qquad \\textbf{(E)} \\ 59$\n___\nFull credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "<p> <span class=\"katex--inline\">A</span> ,  <span class=\"katex--inline\">B</span> ,  <span class=\"katex--inline\">C</span>  are three piles of rocks. The mean weight of the rocks in  <span class=\"katex--inline\">A</span>  is  <span class=\"katex--inline\">40</span>  pounds, the mean weight of the rocks in  <span class=\"katex--inline\">B</span>  is  <span class=\"katex--inline\">50</span>  pounds, the mean weight of the rocks in the combined piles  <span class=\"katex--inline\">A</span>  and  <span class=\"katex--inline\">B</span>  is  <span class=\"katex--inline\">43</span>  pounds, and the mean weight of the rocks in the combined piles  <span class=\"katex--inline\">A</span>  and  <span class=\"katex--inline\">C</span>  is  <span class=\"katex--inline\">44</span>  pounds. What is the greatest possible integer value for the mean in pounds of the rocks in the combined piles  <span class=\"katex--inline\">B</span>  and  <span class=\"katex--inline\">C</span> ?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)} \\ 55 \\qquad \\textbf{(B)} \\ 56 \\qquad \\textbf{(C)} \\ 57 \\qquad \\textbf{(D)} \\ 58 \\qquad \\textbf{(E)} \\ 59</span> </p>&#10;<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 12A Problem 16", "can_next": true, "can_prev": true, "nxt": "/problem/13_amc12A_p17", "prev": "/problem/13_amc12A_p15"}}