How old is the mother puzzle

The sum of their (father, mother and son) ages is 70. The father is 6 times as old as the son.
When the sum of their ages is twice 70, the father will be twice as old as the son.
How old is the mother?
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52
Let, in the initial part of the problem,  x be the age of the son and y be the age of the mother  then
                       x+6x+y=70 
                      =>7x+y=70--------I

In the second part of the problem x` and y` be the respective ages afer t years
                      x`+2x`+y`=2*70=140
                       => 3x`+y`=140--------------II
but we know that the second eqn is calculated after t years so we can write from the second eqn
                         7x+y+3t=140
                         70+3t=140
                            t=23.3333
                     
                     II*7-I*3

                and   x-x`=y-y`=t
              we get
                       (21*23)+(3*23)+4y`=770
                       
                                     y`=52.4  ~ 52

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let father's age be 6x and son's age be x.le mother's age be y
so 6x+y+x=70 given
  =>7x+y=70............(2)
   let their sum be 140 after h years.
so age of father at that time is 6x+h
                mother                   is y+h
                son                        is  x+h
given the new sum is 2*70=140
 so 6x+h + y+h + x+h =140
     =>7x+y+3h=140
from (2) we get,
          3h=70 or h=70/3
another condition  father's age after 70/3 years is 6x+70/3
                              son's age after 70/3 years is x+70/3
given 6x+70/3 =2(x+70/3)
  this implies x=70/12
putting this in (2) we get y=350/12=29.1667years

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