I am three times the age that you were when I was the age that you are now and when you are the age that I am, then the sum of our ages will be 110 years. Whats my age?
Let's use algebra to solve the problem:
Let x be your current age.
Then, "three times the age that you were when I was the age that you are now" can be expressed as 3(x-(my current age)).
And "when you are the age that I am, then the sum of our ages will be 110 years" can be expressed as (my current age + x) = 110.
Putting it all together:
3(x-(my current age)) = my current age + x - 3x
3x - 3(my current age) = my current age + x - 3x
4x - 4(my current age) = 0
4(my current age) = 4x
(my current age) = x
So, we know that my current age is equal to your current age. And from the second equation we know:
(my current age + x) = 110
2(my current age) = 110
(my current age) = 55
Therefore, I am currently 55 years old.