{"status": "success", "data": {"description_md": "Let $a, b,$ and $c$ be real numbers such that $a-7b+8c=4$ and $8a+4b-c=7.$ Then $a^2-b^2+c^2$ is\n\n$\\mathrm{(A) \\ } 0\\qquad \\mathrm{(B) \\ } 1\\qquad \\mathrm{(C) \\ } 4\\qquad \\mathrm{(D) \\ } 7\\qquad \\mathrm{(E) \\ } 8$", "description_html": "<p>Let  <span class=\"katex--inline\">a, b,</span>  and  <span class=\"katex--inline\">c</span>  be real numbers such that  <span class=\"katex--inline\">a-7b+8c=4</span>  and  <span class=\"katex--inline\">8a+4b-c=7.</span>  Then  <span class=\"katex--inline\">a^2-b^2+c^2</span>  is</p>\n<p> <span class=\"katex--inline\">\\mathrm{(A) \\ } 0\\qquad \\mathrm{(B) \\ } 1\\qquad \\mathrm{(C) \\ } 4\\qquad \\mathrm{(D) \\ } 7\\qquad \\mathrm{(E) \\ } 8</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": "2002 AMC 10B Problem 20", "can_next": true, "can_prev": true, "nxt": "/problem/02_amc10B_p21", "prev": "/problem/02_amc10B_p19"}}