{"status": "success", "data": {"description_md": "When a bucket is two-thirds full of water, the bucket and water weigh $a$ kilograms. When the bucket is one-half full of water the total weight is $b$ kilograms. In terms of $a$ and $b$, what is the total weight in kilograms when the bucket is full of water?\n\n$\\textbf{(A)}\\ \\frac23a + \\frac13b\\qquad \\textbf{(B)}\\ \\frac32a - \\frac12b\\qquad \\textbf{(C)}\\ \\frac32a + b \\qquad \\textbf{(D)}\\ \\frac32a + 2b\\qquad \\textbf{(E)}\\ 3a - 2b$\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>When a bucket is two-thirds full of water, the bucket and water weigh  <span class=\"katex--inline\">a</span>  kilograms. When the bucket is one-half full of water the total weight is  <span class=\"katex--inline\">b</span>  kilograms. In terms of  <span class=\"katex--inline\">a</span>  and  <span class=\"katex--inline\">b</span> , what is the total weight in kilograms when the bucket is full of water?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)}\\ \\frac23a + \\frac13b\\qquad \\textbf{(B)}\\ \\frac32a - \\frac12b\\qquad \\textbf{(C)}\\ \\frac32a + b \\qquad \\textbf{(D)}\\ \\frac32a + 2b\\qquad \\textbf{(E)}\\ 3a - 2b</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": 2, "problem_name": "2009 AMC 12B Problem 8", "can_next": true, "can_prev": true, "nxt": "/problem/09_amc12B_p09", "prev": "/problem/09_amc12B_p07"}}