Here is the diagram:

h t t p ://img152.imageshack.us/img152/3126/blocksysiv5.png
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What is the mass of block M that will allow it to accelerate from rest to the right with a a = 2 m/s^2? Surfaces are frictionless and pulleys are ideal.

Here is my work:
F = Ma − − > 1kg(8m / s2) = 3kg(a)
a = 2.7m / s2
The tension in the top rope is equal to twice the tension of the bottom rope
T2 − 8N = 1kg(2.7m / s2)
16N − T2 = 2kg(2.7m / s2)
Solve for T2
T2 = 10.7N
T1 = 21.4N
F = Ma − − > 21.4N = M(2m / s2)
M = 10.7kg

Is this the best way to do this type of problem?