I have a packet of biscuits which contains less than $500$ biscuits.  If I put them into piles of $5$, I have one left over.  If I put them into piles of $6$, I have two left over.  If I put them into piles of $11$, I have seven left over.  How many biscuits do I have?  \uline{\textbf{Step 1: Find the common supplement}}  The common supplement is~\uline{~~~~~~~~~~}~.  \uline{\textbf{Step 2: Find the LCM of all the divisors}}  The LCM of $5$, $6$ and $11$ is~\uline{~~~~~~~~~~}~.  \uline{\textbf{Step 3: The unknown = the common multiple of all the divisors} -\textbf{\uline{~~}the common remainder}}  The unknown $=$~\uline{~~~~~~~~~~}~$-$~\uline{~~~~~~~~~~}~$=$~\uline{~~~~~~~~~~}~. 
Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems->Chinese Remainder Theorem->Step-by-step Calculation