[Algebra]
Problem: Given that $a, b, c$, and $d$ are integers such that $a+b c=20$ and $-a+c d=19$, compute the greatest possible value of $c$.

Solution: Adding the two given equations yields $b c+c d=c(b+d)=39$. The greatest possible value of $c$ therefore occurs when $c=\mathbf{3 9}$ and $b+d=1$.

Final answer: 39