{"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$\\text{(A) } \\frac23a + \\frac13b\n\\qquad\n\\text{(B) } \\frac32a - \\frac12b\n\\qquad\n\\text{(C) } \\frac32a + b\n\\qquad\n\\text{(D) } \\frac32a + 2b\n\\qquad\n\\text{(E) } 3a - 2b$", "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>\n<p> <span class=\"katex--inline\">\\text{(A) } \\frac23a + \\frac13b\n\\qquad\n\\text{(B) } \\frac32a - \\frac12b\n\\qquad\n\\text{(C) } \\frac32a + b\n\\qquad\n\\text{(D) } \\frac32a + 2b\n\\qquad\n\\text{(E) } 3a - 2b</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": "2009 AMC 10B Problem 15", "can_next": true, "can_prev": true, "nxt": "/problem/09_amc10B_p16", "prev": "/problem/09_amc10B_p14"}}