In the analysis of traffic flow, a certain city estimates the following situation for the square of

Question:

In the analysis of traffic flow, a certain city estimates the following situation for the "square" of its downtown district. In the following figure, the arrows indicate the flow of traffic. If x1 represents the number of cars traveling between intersections A and B, x2 represents the number of cars traveling between B and C, x3 the number between C and D, and x4 the number between D and A, we can formulate equations based on the principle that the number of vehicles entering an intersection equals the number leaving it. That is, for intersection A we obtain
200 + x4 = 100 + x1
(a) Formulate equations for the traffic at B, C, and D.
(b) Solve the system of these four equations.
(c) Can the entire traffic flow problem be studied and solved by counting only the x4 cars that travel between A and D? Explain.