If $x \equiv 9[17]$ and $x \equiv 5[11]$, what can be said about $x$ modulo 187?
The inverse of 11 modulo 17 is -3, the inverse of 17 modulo 11 is 2, from which we deduce that $x \equiv$ $9 \cdot 11 \cdot -3 + 5 \cdot 17 \cdot 2 \equiv 60[187]$