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 Grandpa's and Grandma's ages, be P, and M, respectively
SInce their ages sum to 140, we get: P + M = 140___M = 140 - P ---- eq (i)

"Grandpa was as old as Grandma is now," clearly signifies that Grandpa is older than Grandma, which means that
the difference in their ages is: P - M
  
When was Grandpa as old as Grandma is now?
This is the SAME as the difference in their ages, or P - M = P - (140 - P) = P - 140 + P = "2P - 140" years ago

So, when Grandpa was as old as Grandma is now, Grandpa was: M, or "140 - P" years-old
And, when Grandpa was as old as Grandma is now, Grandma was: 140 - P - (2P - 140) = 140 - P - 2P + 140 = - 3P + 280

Finally, since "Grandpa was twice as old as Grandma was when Grandpa was as old as Grandma is now,"
we have:        140 - P = 2(- 3P + 280)
                       140 - P = - 6p + 560
                     - P + 6P = 560 - 140
                              5P = 420
Grandpa's age, or {{{P = 420/5 = 84}}}
Therefore, <font color = red><font size = 3>Grandma is</font></font> 140 - P = 140 - 84 = <font color = red><font size = 3>56</font></font></font></font></font></b></pre>