Let \( V \) represent Vera's age. Then, Linda's age \( L \) can be expressed as:
\[ L = 2V \]
Tanya's age \( T \) can be expressed as:
\[ T = 4L - 4 \]
Substituting the expression for Linda's age into Tanya's age gives:
\[ T = 4(2V) - 4 = 8V - 4 \]
The total age of Linda, Vera, and Tanya can be expressed as:
\[ L + V + T \]
Substituting the expressions we have for \( L \) and \( T \):
\[ L + V + T = 2V + V + (8V - 4) \] \[ = 2V + V + 8V - 4 = 11V - 4 \]
According to the problem statement, this total age is also equal to two more than nine times Vera's age:
\[ 11V - 4 = 9V + 2 \]
To solve for \( V \), we first isolate \( V \) by moving the terms involving \( V \) to one side:
\[ 11V - 9V = 2 + 4 \] \[ 2V = 6 \] \[ V = 3 \]
Now that we have Vera's age, we can find Linda's age:
\[ L = 2V = 2(3) = 6 \]
Next, we can find Tanya's age using the expression for \( T \):
\[ T = 8V - 4 = 8(3) - 4 = 24 - 4 = 20 \]
Thus, Tanya's age is:
\[ \boxed{20} \]
To verify, we can check the total age calculation:
- Vera's age: \( 3 \)
- Linda's age: \( 6 \)
- Tanya's age: \( 20 \)
Total age = \( 3 + 6 + 20 = 29 \).
Now check the condition \( 9V + 2 \):
\[ 9(3) + 2 = 27 + 2 = 29 \]
Since both totals match, the calculations confirm that Tanya's age is indeed \( \boxed{20} \).