For the following system of equations, what is the value of c?

For the following system of equations, what is the value of c?
$a+b+c+d = 88 \\ a+b+c+e = 84 \\ a+b+d+e = 82 \\ a+c+d+e = 78 \\ b+c+d+e = 72$

$\begin{array}{|lrcll|} \hline (1) & a+b+c+d = 88 \\ (2) & a+b+c+e = 84 \\ (3) & a+b+d+e = 82 \\ (4) & a+c+d+e = 78 \\ (5) & b+c+d+e = 72 \\ \hline (1)+(2)+(3)+(4)+(5): & 4a+4b+4c+4d+4e &=& 88 + 84+82+78+72 \\ & 4(a+b+c+d+e) &=& 404 \quad | \quad : 4 \\ (6) & \mathbf{ a+b+c+d+e } &=& \mathbf{101} \\ \hline (6)-(3): & (a+b+c+d+e)-(a+b+d+e) &=& 101 - 82 \\ & \mathbf{c} &=& \mathbf{19} \\ \hline \end{array}$