Three blocks and a mass system with applied force

[Knight526806]

Homework Statement

problem in attachment

Homework Equations

F= MA

The Attempt at a Solution

for m2: F= ma = T + m3g - m2g
T = -m3g + m2g

for m1: T = m1a
a = T/m1
plug in: a = (-m3g + m2g)/ m1

All 3 blocks: F = (M + m1 + m2 + m3)a

final answer: F = (M + m1 + m2 + m3)[(-m3g + m2g)/ m1]

So yea, I'm thinking this is wrong. Any advice on how to solve this would be appreciated.

 

[collinsmark]

final answer: F = (M + m1 + m2 + m3)[(-m3g + m2g)/ m1]

Looks okay to me.

[Edit: Your answer is generally correct. Realize though that the problem statement gives you the relationship between m₂ and m₃. So you could simplify your final answer by substituting in this relationship, thus getting rid of the m₃ variable.]