jmc

Let $C$, $D$, $E$, and $F$ denote the ages of Chad, Diana, Eduardo, and Faye. We are given three equations. $$\begin{array}{rl}D& =E-3\\ E& =C+4\\ C+3& =F\end{array}$$ Summing these three equations, we find that $E$ and $C$ cancel to leave $D+3=F+1$, which implies $F=D+2$. Since $D=14$, we have $F=\boxed{16}$.