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See how I edited your post to fix it and to make sense.
Gina is 6 years younger than Nancy. In 9 years time their total age will be 34. How old is Nancy now?
Next time PLEASE be more accurate.
The dots separating sentences are NECESSARY.
The CAPITAL letters starting new sentences are NECESSARY, too.
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The way to do it is to write correctly.
Solution
G = N - 6 (1) ("Gina is 6 years younger than Nancy")
In 9 years Gina's age will be (G+9) = ((N-6)+9) = (N+3), while Nancy's age will be (N+9).
From the condition,
(N+3) + (N+9) = 34.
2N + 12 = 34
2= 34 - 12 = 22
N = 22/2 = 11.
ANSWER. Nancy is 11 years old now.
CHECK. The Gina's age is then 11-6 = 5.
In 9 years they will be 11+9 = 20 and 5+9 = 14 years old with the sum of the ages of 20+14 = 34. ! Correct !