FERMAT 2009 Problem 23

Suppose that a,b,c, and d are positive integers that satisfy the equations<

\begin{array}{l}a b+c d=38 \\ a c+b d=34 \\ a d+b c=43\end{array}

What is the value of a+b+c+d?

Answer Choices
A. 15
B. 16
C. 17
D. 18
E. 19