IMC 2008 — Keystage 3 (IWYMIC) — team Question 9

Nine identical-looking coins have weights $a$, seven copies of $b$, and $c$, where $a\lt b\lt c$. Using a beam balance at most four times, decide whether $a+c\lt 2b$, $a+c=2b$, or $a+c\gt 2b$.