Double Atwood Machine and tension

[rwx1606]

Homework Statement

Find the tension in the string attached to mass 1 and mass 3. Find the acceleration of masses 1,2, and 3. The problem looks similar to the attached image except m1 and m2 are leveled. Express the answers in the given quantities and constants. I will call the tension in the string attached to mass A, F$$^{1}$$, and the tension attached to mass C, F$$_{T3}$$.

http://session.masteringphysics.com/problemAsset/1038667/6/YF-05-85.jpg

Homework Equations

$$\sum$$F=ma

The Attempt at a Solution

Well aside from setting up the free body diagrams, I've come up with three equations from Newton's 2nd Law.

For mass A, I have the follow:
m$$_{1}$$a$$_{1}$$= F$$_{T1}$$-m$$_{1}$$g
For mass B:
m$$_{2}$$a$$_{2}$$=F$$_{T1}$$-m$$_{2}$$g
For mass C:
m$$_{3}$$a$$_{3}$$=F$$_{T3}$$-m$$_{3}$$g

The first thing that came to mind were the massless pulleys. I assumed both pulleys do not accelerate as a result. So because of this I also assumed mass 3 does not accelerate either or else the bottom pulley would accelerate. In addition I assumed the tension F$$_{T3}$$ is equal to 2F$$_{1}$$. Any help would be appreciated. If my insights are all wrong feel free to direct me towards an alternate way of approaching this problem. Thanks in advance.

 

[rwx1606]

hmm I can't get the subscripts to work for some reason.