We're going to set up the system of equations based on each intersection, where traffic out will equal traffic in: x = April, y = Division, z = Broadway, and w = Embankment
At intersection of April and Broadway: Equation 1) 300 = x + z
Intersection of April and Division: Equation 2) x = 100 + y
Broadway and Embankment Equation 3) z + 100 = w
Embankment and Division: Equation 4) w + y = 300
Then start solving the system of equations by substituting in the variables within each equation:
Plug equation 2 into equation 1: 300 = 100 + y + z 200 = y + z
Plug equation 3 into the above equation: 200 = y + w – 100 300 = y + w
This equation is the same as equation 4, which means effectively we have 4 unknowns (w, x, y, z), and 3 equations. So, we will express answers in terms of w (Embankment). Remember that you can plug in the values for 'w' at the end to see if the values you got were correct.
Solve for x, y, and z in terms of w From using equation 1: x = 300 – z And then, substitute equation 3 into above, where (z = w – 100):
x = 300 – (w – 100)
x = 300 – w + 100
x = 400 – w
Using equation 2 to solve for 'y': y = x – 100 y = 400 – w – 100 y = 300 – w
For z value: z = w – 100
w = w
(x, y, z) = (400 – w, 300 – w, w – 100)
Let me know if you have any other concerns! Thanks again!
Sep 20th, 2015
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