Matrices & Systems · Medium problem

For three trading countries, the symmetric matrix $S$ records TOTAL trade between each pair: $S_{ij} = a_{ij}+a_{ji}$, where $a_{ij}$ is country $i$'s exports to country $j$. Suppose $S_{12} = 100$, so $a_{12}+a_{21}=100$. If country $1$ exports exactly $3$ times what it imports from country $2$ (that is, $a_{12} = 3a_{21}$), find $a_{12}$.