Question 9726
Ok..

We start with B, B = 2*S

A = 2+2*S

F= 2(2+2*S)

S= 2(2+2*S)-40

We now have the formula for all the ages.

Lets solve for S

{{{s=2(2+2*S)-40}}}

Now we distribute

{{{s=4+4S-40}}}

Now we combine Terms

{{{S=4S-36}}}

Add 36 to each side:

{{{S+36=4S-36+36}}} = {{{S+36=4S}}}

Lets subtract s from each side to get {{{S-S+36=4S-S}}} = {{{36=3S}}}

Now lets divide each side by 3:  {{{(36/3)=(3S/3)}}} = {{{12=S}}}

So now we Know the Age of the Sister (s) = 12

so we know A = 2 + 2S, so we substitute in the 12 to get 2 + 2*12 = 2 + 24 = 26

so we know A's age is 26

B = 2*S = 2*12=24 So B's Ages is 24

F = 2(2+2*S) = 2(2+2*12) = 4+48 = 52

Check:

A is elder to B by two years, yes A=26, B=24

A's father F is twice as old as A, yes A=26 F=52

B is twice as old as his sister S, yes B=24 S=12

father and sister differ by forty years, yes S=12 F=52