Let us say the number was x.
Mike added to it two other numbers.
First number added is 12 less than the original number.
So first number is x-12.
Second number added is 12 more than the original number.
So second number is x+12.
Now we are given that the result of adding all three numbers is 15.
Converting the information given into equation, we have:
original number + first number + second number =15

Adding like terms,

dividing both sides by 3,
x=5
Answer: So the original number that Mike thought was 5.