{"status": "success", "data": {"description_md": "On the trip home from the meeting where this AMC10 was constructed, the Contest Chair noted that his airport parking receipt had digits of the form $bbcac,$ where $0 \\le a < b < c \\le 9,$ and $b$ was the average of $a$ and $c.$ How many different five-digit numbers satisfy all these properties?\n\n$\\textbf{(A) } 12 \\qquad\\textbf{(B) } 16 \\qquad\\textbf{(C) } 18 \\qquad\\textbf{(D) } 20 \\qquad\\textbf{(E) } 25$", "description_html": "<p>On the trip home from the meeting where this AMC10 was constructed, the Contest Chair noted that his airport parking receipt had digits of the form  <span class=\"katex--inline\">bbcac,</span>  where  <span class=\"katex--inline\">0 \\le a &lt; b &lt; c \\le 9,</span>  and  <span class=\"katex--inline\">b</span>  was the average of  <span class=\"katex--inline\">a</span>  and  <span class=\"katex--inline\">c.</span>  How many different five-digit numbers satisfy all these properties?</p>\n<p> <span class=\"katex--inline\">\\textbf{(A) } 12 \\qquad\\textbf{(B) } 16 \\qquad\\textbf{(C) } 18 \\qquad\\textbf{(D) } 20 \\qquad\\textbf{(E) } 25</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": 1, "problem_name": "2007 AMC 10B Problem 8", "can_next": true, "can_prev": true, "nxt": "/problem/07_amc10B_p09", "prev": "/problem/07_amc10B_p07"}}