Let the three consecutive even numbers be $x$, $x+2$, and $x+4$.

The sum of these numbers is given as 222:

$x + (x+2) + (x+4) = 222$

Simplifying the left-hand side:

$x + x + 2 + x + 4 = 222$ $3x + 6 = 222$

Now, subtract 6 from both sides:

$3x = 216$

Next, divide both sides by 3:

$x = 72$

So, the three consecutive even numbers are:

$x = 72, \quad x+2 = 74, \quad x+4 = 76$

Thus, the three consecutive even numbers are 72, 74, and 76.

Would you like more details or have any questions?

Here are five related questions:

1. What if the sum of four consecutive even numbers was given instead of three?
2. How would the problem change if the numbers were consecutive odd numbers?
3. Can you find the sum of the squares of the three numbers?
4. How would you solve this if the sum was a decimal number?
5. Can this problem be solved using algebraic inequalities?

Tip: When dealing with consecutive numbers, always represent them in terms of a variable to simplify equations.