HMMT 2001 E4

Find $a+b+c+d+e$ if

$$\begin{gathered} 3 a+2 b+4 d=10, \\ 6 a+5 b+4 c+3 d+2 e=8, \\ a+b+2 c+5 e=3, \\ 2 c+3 d+3 e=4, \text { and } \\ a+2 b+3 c+d=7 . \end{gathered}$$