T+25/27-7/9=41/54

To solve the equation \( t + \frac{25}{27} - \frac{7}{9} = \frac{41}{54} \), we first need to simplify the left side of the equation.

1. Find a common denominator for the fractions.
   The denominators are 27 and 9. The least common multiple of 27 and 9 is 27.

2. Convert \(\frac{7}{9}\) to have a denominator of 27.
   \[ \frac{7}{9} = \frac{7 \times 3}{9 \times 3} = \frac{21}{27} \]

3. Substitute back into the equation: \[ t + \frac{25}{27} - \frac{21}{27} = \frac{41}{54} \]

4. Combine the fractions on the left side: \[ t + \frac{25 - 21}{27} = \frac{41}{54} \] \[ t + \frac{4}{27} = \frac{41}{54} \]

5. To isolate \(t\), subtract \(\frac{4}{27}\) from both sides: \[ t = \frac{41}{54} - \frac{4}{27} \]

6. Convert \(\frac{4}{27}\) to have the denominator of 54: \[ \frac{4}{27} = \frac{4 \times 2}{27 \times 2} = \frac{8}{54} \]

7. Now substitute back: \[ t = \frac{41}{54} - \frac{8}{54} \]

8. Combine the fractions: \[ t = \frac{41 - 8}{54} = \frac{33}{54} \]

9. Simplify \(\frac{33}{54}\): \[ \frac{33}{54} = \frac{11}{18} \quad (\text{dividing both numerator and denominator by 3}) \]

Thus, the solution for \(t\) is: \[ \boxed{\frac{11}{18}} \]