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Solve for T (The force required to keep the pulleys at equilibrium)

See attached image for pulley setup.

2. Homework Equations

W2>W1

N=mg

3. The Attempt at a Solution

Currently I have drawn out all the forces that act on each pulley, and I know there is a way to set up the tensions to solve for T, but since no numerical values are given its a little more complicated.

After applying force diagrams to the hanging weights I got T1=W1g and T3=W2g (with T1 being the tension between Pulley 1 and weight 1, and T3 being the tension between Pulley 2 and weight Which would mean T2=(W2g-W1g)/2, and T2 is the same tension as T, meaning T2 is equivalent to the downward force needed to keep the system at equilibrium. Is this the correct solution?