Question 862659
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Together, Grandma and Grandpa are 140 years old. How old is Grandma if Grandpa was twice as old 
as Grandma was when Grandpa was as old as Grandma is now.
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Let P be the grandpa age (in years), and 
let M be the grandpa age.


First equation is

    P + M = 140.    (1)



When Grandpa was as old as Grandma ? - It happened (P-M) years ago.
At that time, Grandma was M - (P-M) = 2M - P years old,
while         Grandpa was P - (P-M) = M years old.


So, our second equation is

    M = 2(2M-P),  or  M = 4M - 2P,  which we transform to  2P = 3M.    (2).


So, we transform first equation (1) to

    2P + 2M = 280,

and then replace there 2P by 3M, based on (2).
We get then

    3M + 2M = 280,

       5M   = 280,

        M   = 280/5 = 56.


At this point the solution is complete.


<U>ANSWER</U>.  Currently, grandma is 56 years old.
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Solved.