Final answer:
The wise man is 95 years old.
Step-by-step explanation:
In order to solve this problem, let's first define the variable x as the wise man's age.
The sentence '500 reduced by twice my age' can be written as:
500 - 2x = 310
Now, let's solve the equation to find the value of x:
Subtract 500 from both sides: -2x = -190
Divide both sides by -2: x = 95
Therefore, the wise man is 95 years old.