{"status": "success", "data": {"description_md": "If $a,b,$ and $c$ are positive real numbers such that $a(b+c) = 152, b(c+a) = 162,$ and $c(a+b) = 170$, then $abc$ is\n\n$\\mathrm{(A)}\\ 672<br>\\qquad\\mathrm{(B)}\\ 688<br>\\qquad\\mathrm{(C)}\\ 704<br>\\qquad\\mathrm{(D)}\\ 720<br>\\qquad\\mathrm{(E)}\\ 750$\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>If  <span class=\"katex--inline\">a,b,</span>  and  <span class=\"katex--inline\">c</span>  are positive real numbers such that  <span class=\"katex--inline\">a(b+c) = 152, b(c+a) = 162,</span>  and  <span class=\"katex--inline\">c(a+b) = 170</span> , then  <span class=\"katex--inline\">abc</span>  is</p>&#10;<p> <span class=\"katex--inline\">\\mathrm{(A)}\\ 672\\qquad\\mathrm{(B)}\\ 688\\qquad\\mathrm{(C)}\\ 704\\qquad\\mathrm{(D)}\\ 720\\qquad\\mathrm{(E)}\\ 750</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": "2002 AMC 12B Problem 19", "can_next": true, "can_prev": true, "nxt": "/problem/02_amc12B_p20", "prev": "/problem/02_amc12B_p18"}}