Look at each mass in a fed

T1=m1*(g+a3-a1) where a1 is the acceleration of m1 downward and T1 is the tension

note that a3 exists to translate the upward acceleration of the pulley A

now look at m2

T2=m2*(g+a3+a2)

T2=T1

a1=a2

The pulley A

Sum forces

TAB-2*T1=0*a3 (since the pulley has no mass)

Where TAB is the tension on Pulley A

combine

T1=m1*(g+a3-a1)

m2*(g+a3)=(m1-m2)*(g+a3)

a1=(m1-m2)*(g+a3)/(m2+m1)

and

TAB=m1*(g+a3-a1)+m2*(g+a3+a1)

now look at m3

T3=m3*(g-a3)

and TAB=T3

combine with the above

m3*(g-a3)=m1*(g+a3-(m1-m2)*(g+a3)/(m2+...

m3*g-m3*a3=m1*(g+a3)*(1-(m1-m2)/(m2+m1...

plug in some numbers and simplify

a3=g/(4*7.75)