To determine the current age of the tortoise, we should start by identifying the appropriate equation.
Joy's grandfather mentioned that the tortoise was 56 years old when Joy was born, and she was born 11 years ago. This information leads us to one equation that accurately describes the situation:
[tex]\[ t - 11 = 56 \][/tex]
Here:
- [tex]\( t \)[/tex] denotes the current age of the tortoise.
- [tex]\( 11 \)[/tex] represents the number of years since Joy was born.
- [tex]\( 56 \)[/tex] is the age of the tortoise when Joy was born.
We need to solve this equation for [tex]\( t \)[/tex] to find the current age of the tortoise.
[tex]\[ t - 11 = 56 \][/tex]
To isolate [tex]\( t \)[/tex], we add 11 to both sides of the equation:
[tex]\[ t - 11 + 11 = 56 + 11 \][/tex]
This simplifies to:
[tex]\[ t = 67 \][/tex]
Therefore, the tortoise is currently [tex]\( \boxed{67} \)[/tex] years old.