Mr. Gilliam is 3 years younger than his wife. The sum of their ages is 95. How old is Mr. Gilliam?

Answer:

I'll try to explain in the simplest way possible (hopefully :P)

Explanation:

Let's make Mr Gilliam's age $g$ and his wife's age $w$.
From your question, we can understand that $g$ is 3 less than $w$.

In equation form, this can be written as:
$g + 3 = w$
or
$g = w - 3$

So far so clear?
Next, we know that the sum of $g$ and $w$ is 95.

In equation form, this will be written as:
$g + w = 95$

Now, here's the trick. You need a change in perspective.
We know that $g + 3 = w$ and $g + w = 95$, right?

Therefore, $g + w = 95$ can also be written as $g + \left(g + 3\right) = 95$.
Does that make sense?

If it does, then the equation will become:
$2 g + 3 = 95$ (because you had two $g$s)

After shifting the numbers around a little as below, you will arrive at the answer:
$2 g + 3 - 3 = 95 - 3$
$2 g = 92$
$\frac{2 g}{2} = \frac{92}{2}$
$g = 46$

Therefore, Mr. Gilliam is 46 years old. I hope this helps!