The Traffic Through Downtown East Podunk Flows Through the One-Way $a = 400$

The traffic through downtown East Podunk flows through the one-way system shown below:
$a = 400$ , $b = 50$ , $c = 400$
Traffic counters find that 400 vehicles enter town from the west each hour and 400 leave town toward the east each hour. Also, 50 cars drive down Canal Street each hour.

Write down the general solution of the associated system of linear equations. Is it possible to determine the number of vehicles on each street per hour

A) $\begin{array} { l } x = 400 - w \\y = 450 - w \\z = 50 + w \\50 \leq w \leq 400\end{array}$

B) $\begin{array} { l } x = 390 - w \\y = 470 - w \\z = 80 + w \\80 \leq w \leq 390\end{array}$

C) $\begin{array} { l } x = 470 - w \\y = 390 - w \\z = - 80 + w \\80 \leq w \leq 390\end{array}$

D) $\begin{array} { l } x = 400 - w \\y = 470 - w \\z = 50 + w \\400 \leq w \leq 470\end{array}$

E) $\begin{array} { l } x = 450 - w \\y = 400 - w \\z = - 50 + w \\50 \leq w \leq 400\end{array}$